TSTP Solution File: SWV875-1 by iProverMo---2.5-0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SWV875-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 19:22:52 EDT 2022
% Result : Unsatisfiable 7.79s 8.12s
% Output : CNFRefutation 7.88s
% 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__HOL_Ominus,axiom,
class_HOL_Ominus(tc_bool),
input ).
fof(clsarity_bool__HOL_Ominus_0,plain,
( class_HOL_Ominus(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__HOL_Ominus]) ).
cnf(clsarity_bool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_bool),
input ).
fof(clsarity_bool__Orderings_Obot_0,plain,
( class_Orderings_Obot(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Orderings_Obot]) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool),
input ).
fof(clsarity_bool__Orderings_Oorder_0,plain,
( class_Orderings_Oorder(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Orderings_Oorder]) ).
cnf(clsarity_bool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_bool),
input ).
fof(clsarity_bool__Lattices_Olattice_0,plain,
( class_Lattices_Olattice(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Lattices_Olattice]) ).
cnf(clsarity_bool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_bool),
input ).
fof(clsarity_bool__Orderings_Opreorder_0,plain,
( class_Orderings_Opreorder(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Orderings_Opreorder]) ).
cnf(clsarity_bool__Finite__Set_Ofinite_Ofinite,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
input ).
fof(clsarity_bool__Finite__Set_Ofinite_Ofinite_0,plain,
( class_Finite__Set_Ofinite_Ofinite(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Finite__Set_Ofinite_Ofinite]) ).
cnf(clsarity_bool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_bool),
input ).
fof(clsarity_bool__Lattices_Obounded__lattice_0,plain,
( class_Lattices_Obounded__lattice(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Lattices_Obounded__lattice]) ).
cnf(clsarity_bool__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
input ).
fof(clsarity_bool__Lattices_Odistrib__lattice_0,plain,
( class_Lattices_Odistrib__lattice(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Lattices_Odistrib__lattice]) ).
cnf(clsarity_bool__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_bool),
input ).
fof(clsarity_bool__Lattices_Olower__semilattice_0,plain,
( class_Lattices_Olower__semilattice(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Lattices_Olower__semilattice]) ).
cnf(clsarity_bool__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
input ).
fof(clsarity_bool__Lattices_Oupper__semilattice_0,plain,
( class_Lattices_Oupper__semilattice(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Lattices_Oupper__semilattice]) ).
cnf(clsarity_bool__Complete__Lattice_Ocomplete__lattice,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
input ).
fof(clsarity_bool__Complete__Lattice_Ocomplete__lattice_0,plain,
( class_Complete__Lattice_Ocomplete__lattice(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__Complete__Lattice_Ocomplete__lattice]) ).
cnf(clsarity_nat__HOL_Oord,axiom,
class_HOL_Oord(tc_nat),
input ).
fof(clsarity_nat__HOL_Oord_0,plain,
( class_HOL_Oord(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__HOL_Oord]) ).
cnf(clsarity_nat__HOL_Ominus,axiom,
class_HOL_Ominus(tc_nat),
input ).
fof(clsarity_nat__HOL_Ominus_0,plain,
( class_HOL_Ominus(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__HOL_Ominus]) ).
cnf(clsarity_nat__Orderings_Obot,axiom,
class_Orderings_Obot(tc_nat),
input ).
fof(clsarity_nat__Orderings_Obot_0,plain,
( class_Orderings_Obot(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Orderings_Obot]) ).
cnf(clsarity_nat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_nat),
input ).
fof(clsarity_nat__Orderings_Oorder_0,plain,
( class_Orderings_Oorder(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Orderings_Oorder]) ).
cnf(clsarity_nat__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_nat),
input ).
fof(clsarity_nat__Lattices_Olattice_0,plain,
( class_Lattices_Olattice(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Lattices_Olattice]) ).
cnf(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat),
input ).
fof(clsarity_nat__Orderings_Olinorder_0,plain,
( class_Orderings_Olinorder(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Orderings_Olinorder]) ).
cnf(clsarity_nat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_nat),
input ).
fof(clsarity_nat__Orderings_Opreorder_0,plain,
( class_Orderings_Opreorder(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Orderings_Opreorder]) ).
cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Omonoid__add_0,plain,
( class_OrderedGroup_Omonoid__add(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Omonoid__add]) ).
cnf(clsarity_nat__Ring__and__Field_Osemiring,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Osemiring_0,plain,
( class_Ring__and__Field_Osemiring(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Osemiring]) ).
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__Ring__and__Field_Omult__mono,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Omult__mono_0,plain,
( class_Ring__and__Field_Omult__mono(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Omult__mono]) ).
cnf(clsarity_nat__Ring__and__Field_Omult__zero,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Omult__zero_0,plain,
( class_Ring__and__Field_Omult__zero(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Omult__zero]) ).
cnf(clsarity_nat__Ring__and__Field_Omult__mono1,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Omult__mono1_0,plain,
( class_Ring__and__Field_Omult__mono1(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Omult__mono1]) ).
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(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Ocomm__monoid__add_0,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Ocomm__monoid__add]) ).
cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Ocomm__semiring_0,plain,
( class_Ring__and__Field_Ocomm__semiring(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Ocomm__semiring]) ).
cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Oab__semigroup__add_0,plain,
( class_OrderedGroup_Oab__semigroup__add(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Oab__semigroup__add]) ).
cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__mult,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Ocomm__monoid__mult_0,plain,
( class_OrderedGroup_Ocomm__monoid__mult(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Ocomm__monoid__mult]) ).
cnf(clsarity_nat__OrderedGroup_Oab__semigroup__mult,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Oab__semigroup__mult_0,plain,
( class_OrderedGroup_Oab__semigroup__mult(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Oab__semigroup__mult]) ).
cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Ocomm__semiring__1_0,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Ocomm__semiring__1]) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Oordered__semidom_0,plain,
( class_Ring__and__Field_Oordered__semidom(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__semidom]) ).
cnf(clsarity_nat__Ring__and__Field_Ono__zero__divisors,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Ono__zero__divisors_0,plain,
( class_Ring__and__Field_Ono__zero__divisors(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Ono__zero__divisors]) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__semiring,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Oordered__semiring_0,plain,
( class_Ring__and__Field_Oordered__semiring(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__semiring]) ).
cnf(clsarity_nat__Ring__and__Field_Opordered__semiring,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Opordered__semiring_0,plain,
( class_Ring__and__Field_Opordered__semiring(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Opordered__semiring]) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Ocancel__semigroup__add_0,plain,
( class_OrderedGroup_Ocancel__semigroup__add(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Ocancel__semigroup__add]) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add_0,plain,
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add]) ).
cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add_0,plain,
( class_OrderedGroup_Opordered__comm__monoid__add(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__comm__monoid__add]) ).
cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add_0,plain,
( class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add]) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__semiring__strict,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Oordered__semiring__strict_0,plain,
( class_Ring__and__Field_Oordered__semiring__strict(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__semiring__strict]) ).
cnf(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring_0,plain,
( class_Ring__and__Field_Opordered__cancel__semiring(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Opordered__cancel__semiring]) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
input ).
fof(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict_0,plain,
( class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict]) ).
cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le_0,plain,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le]) ).
cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
input ).
fof(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add_0,plain,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat)
| $false ),
inference(orientation,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add]) ).
cnf(cls_com_Osimps_I18_J_0,axiom,
c_Com_Ocom_OSKIP != c_Com_Ocom_OBODY(V_pname_H),
input ).
fof(cls_com_Osimps_I18_J_0_0,plain,
! [V_pname_H] :
( c_Com_Ocom_OSKIP != c_Com_Ocom_OBODY(V_pname_H)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I18_J_0]) ).
cnf(cls_doubleton__eq__iff_4,axiom,
hAPP(hAPP(c_Set_Oinsert(T_a),V_xa),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x),hAPP(hAPP(c_Set_Oinsert(T_a),V_xa),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),
input ).
fof(cls_doubleton__eq__iff_4_0,plain,
! [T_a,V_x,V_xa] :
( hAPP(hAPP(c_Set_Oinsert(T_a),V_xa),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x),hAPP(hAPP(c_Set_Oinsert(T_a),V_xa),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))
| $false ),
inference(orientation,[status(thm)],[cls_doubleton__eq__iff_4]) ).
cnf(cls_insert__commute_0,axiom,
hAPP(hAPP(c_Set_Oinsert(T_a),V_x),hAPP(hAPP(c_Set_Oinsert(T_a),V_y),V_A)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_y),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_A)),
input ).
fof(cls_insert__commute_0_0,plain,
! [T_a,V_A,V_x,V_y] :
( hAPP(hAPP(c_Set_Oinsert(T_a),V_x),hAPP(hAPP(c_Set_Oinsert(T_a),V_y),V_A)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_y),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_A))
| $false ),
inference(orientation,[status(thm)],[cls_insert__commute_0]) ).
cnf(cls_insertCI_1,axiom,
hBOOL(hAPP(hAPP(c_in(T_a),V_x),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_B))),
input ).
fof(cls_insertCI_1_0,plain,
! [T_a,V_B,V_x] :
( hBOOL(hAPP(hAPP(c_in(T_a),V_x),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_B)))
| $false ),
inference(orientation,[status(thm)],[cls_insertCI_1]) ).
cnf(cls_insertI1_0,axiom,
hBOOL(hAPP(hAPP(c_in(T_a),V_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B))),
input ).
fof(cls_insertI1_0_0,plain,
! [T_a,V_B,V_a] :
( hBOOL(hAPP(hAPP(c_in(T_a),V_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B)))
| $false ),
inference(orientation,[status(thm)],[cls_insertI1_0]) ).
cnf(cls_insert__iff_1,axiom,
hBOOL(hAPP(hAPP(c_in(T_a),V_x),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_A))),
input ).
fof(cls_insert__iff_1_0,plain,
! [T_a,V_A,V_x] :
( hBOOL(hAPP(hAPP(c_in(T_a),V_x),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_A)))
| $false ),
inference(orientation,[status(thm)],[cls_insert__iff_1]) ).
cnf(cls_insert__not__empty_0,axiom,
hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_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] :
( hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_A) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_insert__not__empty_0]) ).
cnf(cls_insert__absorb2_0,axiom,
hAPP(hAPP(c_Set_Oinsert(T_a),V_x),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_A)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_A),
input ).
fof(cls_insert__absorb2_0_0,plain,
! [T_a,V_A,V_x] :
( hAPP(hAPP(c_Set_Oinsert(T_a),V_x),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_A)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_A)
| $false ),
inference(orientation,[status(thm)],[cls_insert__absorb2_0]) ).
cnf(cls_empty_0,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),T_a),
input ).
fof(cls_empty_0_0,plain,
! [T_a,V_G] :
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_empty_0]) ).
cnf(cls_bot1E_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x)),
input ).
fof(cls_bot1E_0_0,plain,
! [T_a,V_x] :
( ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x))
| $false ),
inference(orientation,[status(thm)],[cls_bot1E_0]) ).
cnf(cls_evalc_OSkip_0,axiom,
hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)),
input ).
fof(cls_evalc_OSkip_0_0,plain,
! [V_s] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s))
| $false ),
inference(orientation,[status(thm)],[cls_evalc_OSkip_0]) ).
cnf(cls_bot__empty__eq_0,axiom,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = hAPP(hAPP(c_in(t_a),v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),
input ).
fof(cls_bot__empty__eq_0_0,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = 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_bot__empty__eq_0]) ).
cnf(cls_empty__not__insert_0,axiom,
c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_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)) != hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_A)
| $false ),
inference(orientation,[status(thm)],[cls_empty__not__insert_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_hoare__derivs_OSkip_0,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OSKIP,V_P,T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))),T_a),
input ).
fof(cls_hoare__derivs_OSkip_0_0,plain,
! [T_a,V_G,V_P] :
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OSKIP,V_P,T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_hoare__derivs_OSkip_0]) ).
cnf(cls_insert__code_1,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_A),V_x)),
input ).
fof(cls_insert__code_1_0,plain,
! [T_a,V_A,V_x] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_A),V_x))
| $false ),
inference(orientation,[status(thm)],[cls_insert__code_1]) ).
cnf(cls_singleton__iff_1,axiom,
hBOOL(hAPP(hAPP(c_in(T_a),V_x),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))),
input ).
fof(cls_singleton__iff_1_0,plain,
! [T_a,V_x] :
( hBOOL(hAPP(hAPP(c_in(T_a),V_x),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))))
| $false ),
inference(orientation,[status(thm)],[cls_singleton__iff_1]) ).
cnf(cls_com_Osimps_I19_J_0,axiom,
c_Com_Ocom_OBODY(V_pname_H) != c_Com_Ocom_OSKIP,
input ).
fof(cls_com_Osimps_I19_J_0_0,plain,
! [V_pname_H] :
( c_Com_Ocom_OBODY(V_pname_H) != c_Com_Ocom_OSKIP
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I19_J_0]) ).
cnf(cls_finite__dom__body_0,axiom,
c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname),
input ).
fof(cls_finite__dom__body_0_0,plain,
( c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)
| $false ),
inference(orientation,[status(thm)],[cls_finite__dom__body_0]) ).
cnf(cls_vimage__singleton__eq_1,axiom,
hBOOL(hAPP(hAPP(c_in(T_aa),V_a),c_Set_Ovimage(V_f,hAPP(hAPP(c_Set_Oinsert(T_a),hAPP(V_f,V_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),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,hAPP(hAPP(c_Set_Oinsert(T_a),hAPP(V_f,V_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),T_aa,T_a)))
| $false ),
inference(orientation,[status(thm)],[cls_vimage__singleton__eq_1]) ).
cnf(cls_MGT__def_0,axiom,
c_Hoare__Mirabelle_OMGT(V_c) = c_Hoare__Mirabelle_Otriple_Otriple(c_fequal(tc_Com_Ostate),V_c,c_Natural_Oevalc(V_c),tc_Com_Ostate),
input ).
fof(cls_MGT__def_0_0,plain,
! [V_c] :
( c_Hoare__Mirabelle_OMGT(V_c) = c_Hoare__Mirabelle_Otriple_Otriple(c_fequal(tc_Com_Ostate),V_c,c_Natural_Oevalc(V_c),tc_Com_Ostate)
| $false ),
inference(orientation,[status(thm)],[cls_MGT__def_0]) ).
cnf(cls_insert__is__Un_0,axiom,
hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_A) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),V_A),
input ).
fof(cls_insert__is__Un_0_0,plain,
! [T_a,V_A,V_a] :
( hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_A) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),V_A)
| $false ),
inference(orientation,[status(thm)],[cls_insert__is__Un_0]) ).
cnf(cls_insert__Diff__single_0,axiom,
hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_HOL_Ominus__class_Ominus(V_A,hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),tc_fun(T_a,tc_bool))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_A),
input ).
fof(cls_insert__Diff__single_0_0,plain,
! [T_a,V_A,V_a] :
( hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_HOL_Ominus__class_Ominus(V_A,hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),tc_fun(T_a,tc_bool))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_A)
| $false ),
inference(orientation,[status(thm)],[cls_insert__Diff__single_0]) ).
cnf(cls_fold1__singleton_0,axiom,
hAPP(c_Finite__Set_Ofold1(V_f,T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) = V_a,
input ).
fof(cls_fold1__singleton_0_0,plain,
! [T_a,V_a,V_f] :
( hAPP(c_Finite__Set_Ofold1(V_f,T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) = V_a
| $false ),
inference(orientation,[status(thm)],[cls_fold1__singleton_0]) ).
cnf(cls_contents__eq_0,axiom,
c_Set_Ocontents(hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),T_a) = V_x,
input ).
fof(cls_contents__eq_0_0,plain,
! [T_a,V_x] :
( c_Set_Ocontents(hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),T_a) = V_x
| $false ),
inference(orientation,[status(thm)],[cls_contents__eq_0]) ).
cnf(cls_Diff__insert_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B),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)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),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,hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B),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)),hAPP(hAPP(c_Set_Oinsert(T_a),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_Diff__insert_0]) ).
cnf(cls_Diff__insert2_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_A,hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),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,hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_A,hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Diff__insert2_0]) ).
cnf(cls_Nitpick_OThe__psimp_0,axiom,
c_The(hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),T_a) = V_x,
input ).
fof(cls_Nitpick_OThe__psimp_0_0,plain,
! [T_a,V_x] :
( c_The(hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),T_a) = V_x
| $false ),
inference(orientation,[status(thm)],[cls_Nitpick_OThe__psimp_0]) ).
cnf(cls_fold1Set__sing_1,axiom,
hBOOL(hAPP(c_Finite__Set_Ofold1Set(V_f,hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),T_a),V_x)),
input ).
fof(cls_fold1Set__sing_1_0,plain,
! [T_a,V_f,V_x] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(V_f,hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),T_a),V_x))
| $false ),
inference(orientation,[status(thm)],[cls_fold1Set__sing_1]) ).
cnf(cls_the_Osimps_0,axiom,
c_Option_Othe(hAPP(c_Option_Ooption_OSome(T_a),V_x),T_a) = V_x,
input ).
fof(cls_the_Osimps_0_0,plain,
! [T_a,V_x] :
( c_Option_Othe(hAPP(c_Option_Ooption_OSome(T_a),V_x),T_a) = V_x
| $false ),
inference(orientation,[status(thm)],[cls_the_Osimps_0]) ).
cnf(cls_the__sym__eq__trivial_0,axiom,
c_The(hAPP(c_fequal(T_a),V_x),T_a) = V_x,
input ).
fof(cls_the__sym__eq__trivial_0_0,plain,
! [T_a,V_x] :
( c_The(hAPP(c_fequal(T_a),V_x),T_a) = V_x
| $false ),
inference(orientation,[status(thm)],[cls_the__sym__eq__trivial_0]) ).
cnf(cls_map__add__assoc_0,axiom,
c_Map_Omap__add(V_m1,c_Map_Omap__add(V_m2,V_m3,T_a,T_b),T_a,T_b) = c_Map_Omap__add(c_Map_Omap__add(V_m1,V_m2,T_a,T_b),V_m3,T_a,T_b),
input ).
fof(cls_map__add__assoc_0_0,plain,
! [T_a,T_b,V_m1,V_m2,V_m3] :
( c_Map_Omap__add(V_m1,c_Map_Omap__add(V_m2,V_m3,T_a,T_b),T_a,T_b) = c_Map_Omap__add(c_Map_Omap__add(V_m1,V_m2,T_a,T_b),V_m3,T_a,T_b)
| $false ),
inference(orientation,[status(thm)],[cls_map__add__assoc_0]) ).
cnf(cls_not__None__eq_1,axiom,
hAPP(c_Option_Ooption_OSome(T_a),V_xa) != c_Option_Ooption_ONone(T_a),
input ).
fof(cls_not__None__eq_1_0,plain,
! [T_a,V_xa] :
( hAPP(c_Option_Ooption_OSome(T_a),V_xa) != c_Option_Ooption_ONone(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_not__None__eq_1]) ).
cnf(cls_option_Osimps_I3_J_0,axiom,
hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a),
input ).
fof(cls_option_Osimps_I3_J_0_0,plain,
! [T_a,V_a_H] :
( hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_option_Osimps_I3_J_0]) ).
cnf(cls_dom__map__add_0,axiom,
c_Map_Odom(c_Map_Omap__add(V_m,V_n,T_a,T_b),T_a,T_b) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Map_Odom(V_n,T_a,T_b)),c_Map_Odom(V_m,T_a,T_b)),
input ).
fof(cls_dom__map__add_0_0,plain,
! [T_a,T_b,V_m,V_n] :
( c_Map_Odom(c_Map_Omap__add(V_m,V_n,T_a,T_b),T_a,T_b) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Map_Odom(V_n,T_a,T_b)),c_Map_Odom(V_m,T_a,T_b))
| $false ),
inference(orientation,[status(thm)],[cls_dom__map__add_0]) ).
cnf(cls_map__le__refl_0,axiom,
c_Map_Omap__le(V_f,V_f,T_a,T_b),
input ).
fof(cls_map__le__refl_0_0,plain,
! [T_a,T_b,V_f] :
( c_Map_Omap__le(V_f,V_f,T_a,T_b)
| $false ),
inference(orientation,[status(thm)],[cls_map__le__refl_0]) ).
cnf(cls_vimage__Diff_0,axiom,
c_Set_Ovimage(V_f,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_b,tc_bool)),T_a,T_b) = c_HOL_Ominus__class_Ominus(c_Set_Ovimage(V_f,V_A,T_a,T_b),c_Set_Ovimage(V_f,V_B,T_a,T_b),tc_fun(T_a,tc_bool)),
input ).
fof(cls_vimage__Diff_0_0,plain,
! [T_a,T_b,V_A,V_B,V_f] :
( c_Set_Ovimage(V_f,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_b,tc_bool)),T_a,T_b) = c_HOL_Ominus__class_Ominus(c_Set_Ovimage(V_f,V_A,T_a,T_b),c_Set_Ovimage(V_f,V_B,T_a,T_b),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_vimage__Diff_0]) ).
cnf(cls_fold1__def_0,axiom,
hAPP(c_Finite__Set_Ofold1(V_f,T_a),V_A) = c_The(c_Finite__Set_Ofold1Set(V_f,V_A,T_a),T_a),
input ).
fof(cls_fold1__def_0_0,plain,
! [T_a,V_A,V_f] :
( hAPP(c_Finite__Set_Ofold1(V_f,T_a),V_A) = c_The(c_Finite__Set_Ofold1Set(V_f,V_A,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_fold1__def_0]) ).
cnf(cls_Un__absorb_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_A) = V_A,
input ).
fof(cls_Un__absorb_0_0,plain,
! [T_a,V_A] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_A) = V_A
| $false ),
inference(orientation,[status(thm)],[cls_Un__absorb_0]) ).
cnf(cls_Diff__idemp_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),
input ).
fof(cls_Diff__idemp_0_0,plain,
! [T_a,V_A,V_B] :
( c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Diff__idemp_0]) ).
cnf(cls_not__Some__eq_1,axiom,
c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_y),
input ).
fof(cls_not__Some__eq_1_0,plain,
! [T_a,V_y] :
( c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_y)
| $false ),
inference(orientation,[status(thm)],[cls_not__Some__eq_1]) ).
cnf(cls_option_Osimps_I2_J_0,axiom,
c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H),
input ).
fof(cls_option_Osimps_I2_J_0_0,plain,
! [T_a,V_a_H] :
( c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H)
| $false ),
inference(orientation,[status(thm)],[cls_option_Osimps_I2_J_0]) ).
cnf(cls_Un__left__commute_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_C)),
input ).
fof(cls_Un__left__commute_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_C))
| $false ),
inference(orientation,[status(thm)],[cls_Un__left__commute_0]) ).
cnf(cls_Un__assoc_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)),
input ).
fof(cls_Un__assoc_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C))
| $false ),
inference(orientation,[status(thm)],[cls_Un__assoc_0]) ).
cnf(cls_Un__Diff__cancel2_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool))),V_A) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_A),
input ).
fof(cls_Un__Diff__cancel2_0_0,plain,
! [T_a,V_A,V_B] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool))),V_A) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_A)
| $false ),
inference(orientation,[status(thm)],[cls_Un__Diff__cancel2_0]) ).
cnf(cls_Un__Diff__cancel_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool))) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),
input ).
fof(cls_Un__Diff__cancel_0_0,plain,
! [T_a,V_A,V_B] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool))) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)
| $false ),
inference(orientation,[status(thm)],[cls_Un__Diff__cancel_0]) ).
cnf(cls_Un__Diff_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),V_C,tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),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))),
input ).
fof(cls_Un__Diff_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),V_C,tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),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)))
| $false ),
inference(orientation,[status(thm)],[cls_Un__Diff_0]) ).
cnf(cls_Un__commute_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_A),
input ).
fof(cls_Un__commute_0_0,plain,
! [T_a,V_A,V_B] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_A)
| $false ),
inference(orientation,[status(thm)],[cls_Un__commute_0]) ).
cnf(cls_Un__left__absorb_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),
input ).
fof(cls_Un__left__absorb_0_0,plain,
! [T_a,V_A,V_B] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)
| $false ),
inference(orientation,[status(thm)],[cls_Un__left__absorb_0]) ).
cnf(cls_vimage__Un_0,axiom,
c_Set_Ovimage(V_f,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_b,tc_bool)),V_A),V_B),T_a,T_b) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Set_Ovimage(V_f,V_A,T_a,T_b)),c_Set_Ovimage(V_f,V_B,T_a,T_b)),
input ).
fof(cls_vimage__Un_0_0,plain,
! [T_a,T_b,V_A,V_B,V_f] :
( c_Set_Ovimage(V_f,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_b,tc_bool)),V_A),V_B),T_a,T_b) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Set_Ovimage(V_f,V_A,T_a,T_b)),c_Set_Ovimage(V_f,V_B,T_a,T_b))
| $false ),
inference(orientation,[status(thm)],[cls_vimage__Un_0]) ).
cnf(cls_map__le__map__add_0,axiom,
c_Map_Omap__le(V_f,c_Map_Omap__add(V_g,V_f,T_a,T_b),T_a,T_b),
input ).
fof(cls_map__le__map__add_0_0,plain,
! [T_a,T_b,V_f,V_g] :
( c_Map_Omap__le(V_f,c_Map_Omap__add(V_g,V_f,T_a,T_b),T_a,T_b)
| $false ),
inference(orientation,[status(thm)],[cls_map__le__map__add_0]) ).
cnf(cls_vimage__empty_0,axiom,
c_Set_Ovimage(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_a,T_b) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
input ).
fof(cls_vimage__empty_0_0,plain,
! [T_a,T_b,V_f] :
( c_Set_Ovimage(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_a,T_b) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_vimage__empty_0]) ).
cnf(cls_Un__empty_2,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
input ).
fof(cls_Un__empty_2_0,plain,
! [T_a] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__empty_2]) ).
cnf(cls_empty__fold1SetE_0,axiom,
~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_x)),
input ).
fof(cls_empty__fold1SetE_0_0,plain,
! [T_a,V_f,V_x] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_x))
| $false ),
inference(orientation,[status(thm)],[cls_empty__fold1SetE_0]) ).
cnf(cls_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_Un__empty__right_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = V_A,
input ).
fof(cls_Un__empty__right_0_0,plain,
! [T_a,V_A] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = V_A
| $false ),
inference(orientation,[status(thm)],[cls_Un__empty__right_0]) ).
cnf(cls_Un__empty__left_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),V_B) = V_B,
input ).
fof(cls_Un__empty__left_0_0,plain,
! [T_a,V_B] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),V_B) = V_B
| $false ),
inference(orientation,[status(thm)],[cls_Un__empty__left_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_dom__eq__singleton__conv_1,axiom,
c_Map_Odom(c_Fun_Ofun__upd(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),V_x,hAPP(c_Option_Ooption_OSome(T_b),V_xa),T_a,tc_Option_Ooption(T_b)),T_a,T_b) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),
input ).
fof(cls_dom__eq__singleton__conv_1_0,plain,
! [T_a,T_b,V_x,V_xa] :
( c_Map_Odom(c_Fun_Ofun__upd(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),V_x,hAPP(c_Option_Ooption_OSome(T_b),V_xa),T_a,tc_Option_Ooption(T_b)),T_a,T_b) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))
| $false ),
inference(orientation,[status(thm)],[cls_dom__eq__singleton__conv_1]) ).
cnf(cls_sup__Un__eq_0,axiom,
hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),V_R)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),V_S)),v_x) = hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),V_R),V_S)),
input ).
fof(cls_sup__Un__eq_0_0,plain,
! [V_R,V_S] :
( hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),V_R)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),V_S)),v_x) = hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),V_R),V_S))
| $false ),
inference(orientation,[status(thm)],[cls_sup__Un__eq_0]) ).
cnf(cls_Option_Oset_Osimps_I2_J_0,axiom,
c_Option_Oset(hAPP(c_Option_Ooption_OSome(T_a),V_x),T_a) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),
input ).
fof(cls_Option_Oset_Osimps_I2_J_0_0,plain,
! [T_a,V_x] :
( c_Option_Oset(hAPP(c_Option_Ooption_OSome(T_a),V_x),T_a) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))
| $false ),
inference(orientation,[status(thm)],[cls_Option_Oset_Osimps_I2_J_0]) ).
cnf(cls_restrict__map__to__empty_0,axiom,
hAPP(c_Map_Orestrict__map(V_m,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a,T_b),v_x) = c_Option_Ooption_ONone(T_b),
input ).
fof(cls_restrict__map__to__empty_0_0,plain,
! [T_b,V_m] :
( hAPP(c_Map_Orestrict__map(V_m,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a,T_b),v_x) = c_Option_Ooption_ONone(T_b)
| $false ),
inference(orientation,[status(thm)],[cls_restrict__map__to__empty_0]) ).
cnf(cls_dom__empty_0,axiom,
c_Map_Odom(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),T_a,T_b) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
input ).
fof(cls_dom__empty_0_0,plain,
! [T_a,T_b] :
( c_Map_Odom(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),T_a,T_b) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_dom__empty_0]) ).
cnf(cls_map__add__def_0,axiom,
hAPP(c_Map_Omap__add(V_m1,V_m2,t_a,T_b),v_x) = c_Option_Ooption_Ooption__case(hAPP(V_m1,v_x),c_Option_Ooption_OSome(T_b),hAPP(V_m2,v_x),tc_Option_Ooption(T_b),T_b),
input ).
fof(cls_map__add__def_0_0,plain,
! [T_b,V_m1,V_m2] :
( hAPP(c_Map_Omap__add(V_m1,V_m2,t_a,T_b),v_x) = c_Option_Ooption_Ooption__case(hAPP(V_m1,v_x),c_Option_Ooption_OSome(T_b),hAPP(V_m2,v_x),tc_Option_Ooption(T_b),T_b)
| $false ),
inference(orientation,[status(thm)],[cls_map__add__def_0]) ).
cnf(cls_MGT__def__raw_0,axiom,
c_Hoare__Mirabelle_OMGT(v_c) = c_Hoare__Mirabelle_Otriple_Otriple(c_fequal(tc_Com_Ostate),v_c,c_Natural_Oevalc(v_c),tc_Com_Ostate),
input ).
fof(cls_MGT__def__raw_0_0,plain,
( c_Hoare__Mirabelle_OMGT(v_c) = c_Hoare__Mirabelle_Otriple_Otriple(c_fequal(tc_Com_Ostate),v_c,c_Natural_Oevalc(v_c),tc_Com_Ostate)
| $false ),
inference(orientation,[status(thm)],[cls_MGT__def__raw_0]) ).
cnf(cls_dom__fun__upd_0,axiom,
c_Map_Odom(c_Fun_Ofun__upd(V_f,V_x,c_Option_Ooption_ONone(T_b),T_a,tc_Option_Ooption(T_b)),T_a,T_b) = c_HOL_Ominus__class_Ominus(c_Map_Odom(V_f,T_a,T_b),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),tc_fun(T_a,tc_bool)),
input ).
fof(cls_dom__fun__upd_0_0,plain,
! [T_a,T_b,V_f,V_x] :
( c_Map_Odom(c_Fun_Ofun__upd(V_f,V_x,c_Option_Ooption_ONone(T_b),T_a,tc_Option_Ooption(T_b)),T_a,T_b) = c_HOL_Ominus__class_Ominus(c_Map_Odom(V_f,T_a,T_b),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_dom__fun__upd_0]) ).
cnf(cls_Nitpick_OEx1__def_2,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),T_a))),
input ).
fof(cls_Nitpick_OEx1__def_2_0,plain,
! [T_a,V_x] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),T_a)))
| $false ),
inference(orientation,[status(thm)],[cls_Nitpick_OEx1__def_2]) ).
cnf(cls_com_Osimps_I13_J_0,axiom,
c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP,
input ).
fof(cls_com_Osimps_I13_J_0_0,plain,
! [V_com1_H,V_com2_H] :
( c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I13_J_0]) ).
cnf(cls_com_Osimps_I12_J_0,axiom,
c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H),
input ).
fof(cls_com_Osimps_I12_J_0_0,plain,
! [V_com1_H,V_com2_H] :
( c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I12_J_0]) ).
cnf(cls_com_Osimps_I48_J_0,axiom,
c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OBODY(V_pname_H),
input ).
fof(cls_com_Osimps_I48_J_0_0,plain,
! [V_com1,V_com2,V_pname_H] :
( c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OBODY(V_pname_H)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I48_J_0]) ).
cnf(cls_com_Osimps_I49_J_0,axiom,
c_Com_Ocom_OBODY(V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2),
input ).
fof(cls_com_Osimps_I49_J_0_0,plain,
! [V_com1,V_com2,V_pname_H] :
( c_Com_Ocom_OBODY(V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2)
| $false ),
inference(orientation,[status(thm)],[cls_com_Osimps_I49_J_0]) ).
cnf(cls_Un__insert__left_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B)),V_C) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)),
input ).
fof(cls_Un__insert__left_0_0,plain,
! [T_a,V_B,V_C,V_a] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B)),V_C) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C))
| $false ),
inference(orientation,[status(thm)],[cls_Un__insert__left_0]) ).
cnf(cls_Un__insert__right_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),
input ).
fof(cls_Un__insert__right_0_0,plain,
! [T_a,V_A,V_B,V_a] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B))
| $false ),
inference(orientation,[status(thm)],[cls_Un__insert__right_0]) ).
cnf(cls_vimage__insert_0,axiom,
c_Set_Ovimage(V_f,hAPP(hAPP(c_Set_Oinsert(T_b),V_a),V_B),T_a,T_b) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Set_Ovimage(V_f,hAPP(hAPP(c_Set_Oinsert(T_b),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))),T_a,T_b)),c_Set_Ovimage(V_f,V_B,T_a,T_b)),
input ).
fof(cls_vimage__insert_0_0,plain,
! [T_a,T_b,V_B,V_a,V_f] :
( c_Set_Ovimage(V_f,hAPP(hAPP(c_Set_Oinsert(T_b),V_a),V_B),T_a,T_b) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Set_Ovimage(V_f,hAPP(hAPP(c_Set_Oinsert(T_b),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))),T_a,T_b)),c_Set_Ovimage(V_f,V_B,T_a,T_b))
| $false ),
inference(orientation,[status(thm)],[cls_vimage__insert_0]) ).
cnf(cls_finite_OemptyI_0,axiom,
c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),
input ).
fof(cls_finite_OemptyI_0_0,plain,
! [T_a] :
( c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_finite_OemptyI_0]) ).
cnf(cls_Diff__empty_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A,
input ).
fof(cls_Diff__empty_0_0,plain,
! [T_a,V_A] :
( c_HOL_Ominus__class_Ominus(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A
| $false ),
inference(orientation,[status(thm)],[cls_Diff__empty_0]) ).
cnf(cls_map__le__empty_0,axiom,
c_Map_Omap__le(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),V_g,T_a,T_b),
input ).
fof(cls_map__le__empty_0_0,plain,
! [T_a,T_b,V_g] :
( c_Map_Omap__le(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),V_g,T_a,T_b)
| $false ),
inference(orientation,[status(thm)],[cls_map__le__empty_0]) ).
cnf(cls_upd__None__map__le_0,axiom,
c_Map_Omap__le(c_Fun_Ofun__upd(V_f,V_x,c_Option_Ooption_ONone(T_b),T_a,tc_Option_Ooption(T_b)),V_f,T_a,T_b),
input ).
fof(cls_upd__None__map__le_0_0,plain,
! [T_a,T_b,V_f,V_x] :
( c_Map_Omap__le(c_Fun_Ofun__upd(V_f,V_x,c_Option_Ooption_ONone(T_b),T_a,tc_Option_Ooption(T_b)),V_f,T_a,T_b)
| $false ),
inference(orientation,[status(thm)],[cls_upd__None__map__le_0]) ).
cnf(cls_map__add__empty_0,axiom,
c_Map_Omap__add(V_m,c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),T_a,T_b) = V_m,
input ).
fof(cls_map__add__empty_0_0,plain,
! [T_a,T_b,V_m] :
( c_Map_Omap__add(V_m,c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),T_a,T_b) = V_m
| $false ),
inference(orientation,[status(thm)],[cls_map__add__empty_0]) ).
cnf(cls_empty__map__add_0,axiom,
c_Map_Omap__add(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),V_m,T_a,T_b) = V_m,
input ).
fof(cls_empty__map__add_0_0,plain,
! [T_a,T_b,V_m] :
( c_Map_Omap__add(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),V_m,T_a,T_b) = V_m
| $false ),
inference(orientation,[status(thm)],[cls_empty__map__add_0]) ).
cnf(cls_map__add__upd_0,axiom,
c_Map_Omap__add(V_f,c_Fun_Ofun__upd(V_g,V_x,hAPP(c_Option_Ooption_OSome(T_b),V_y),T_a,tc_Option_Ooption(T_b)),T_a,T_b) = c_Fun_Ofun__upd(c_Map_Omap__add(V_f,V_g,T_a,T_b),V_x,hAPP(c_Option_Ooption_OSome(T_b),V_y),T_a,tc_Option_Ooption(T_b)),
input ).
fof(cls_map__add__upd_0_0,plain,
! [T_a,T_b,V_f,V_g,V_x,V_y] :
( c_Map_Omap__add(V_f,c_Fun_Ofun__upd(V_g,V_x,hAPP(c_Option_Ooption_OSome(T_b),V_y),T_a,tc_Option_Ooption(T_b)),T_a,T_b) = c_Fun_Ofun__upd(c_Map_Omap__add(V_f,V_g,T_a,T_b),V_x,hAPP(c_Option_Ooption_OSome(T_b),V_y),T_a,tc_Option_Ooption(T_b))
| $false ),
inference(orientation,[status(thm)],[cls_map__add__upd_0]) ).
cnf(cls_set__empty__eq_1,axiom,
c_Option_Oset(c_Option_Ooption_ONone(T_a),T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
input ).
fof(cls_set__empty__eq_1_0,plain,
! [T_a] :
( c_Option_Oset(c_Option_Ooption_ONone(T_a),T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_set__empty__eq_1]) ).
cnf(cls_Diff__Int_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))),c_HOL_Ominus__class_Ominus(V_A,V_C,tc_fun(T_a,tc_bool))),
input ).
fof(cls_Diff__Int_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( c_HOL_Ominus__class_Ominus(V_A,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))),c_HOL_Ominus__class_Ominus(V_A,V_C,tc_fun(T_a,tc_bool)))
| $false ),
inference(orientation,[status(thm)],[cls_Diff__Int_0]) ).
cnf(cls_Diff__Un_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C),tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))),c_HOL_Ominus__class_Ominus(V_A,V_C,tc_fun(T_a,tc_bool))),
input ).
fof(cls_Diff__Un_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( c_HOL_Ominus__class_Ominus(V_A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C),tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))),c_HOL_Ominus__class_Ominus(V_A,V_C,tc_fun(T_a,tc_bool)))
| $false ),
inference(orientation,[status(thm)],[cls_Diff__Un_0]) ).
cnf(cls_Un__Diff__Int_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)) = V_A,
input ).
fof(cls_Un__Diff__Int_0_0,plain,
! [T_a,V_A,V_B] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)) = V_A
| $false ),
inference(orientation,[status(thm)],[cls_Un__Diff__Int_0]) ).
cnf(cls_Diff__disjoint_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
input ).
fof(cls_Diff__disjoint_0_0,plain,
! [T_a,V_A,V_B] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Diff__disjoint_0]) ).
cnf(cls_elem__set_1,axiom,
hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Option_Oset(hAPP(c_Option_Ooption_OSome(T_a),V_x),T_a))),
input ).
fof(cls_elem__set_1_0,plain,
! [T_a,V_x] :
( hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Option_Oset(hAPP(c_Option_Ooption_OSome(T_a),V_x),T_a)))
| $false ),
inference(orientation,[status(thm)],[cls_elem__set_1]) ).
cnf(cls_fun__upd__restrict_0,axiom,
c_Fun_Ofun__upd(c_Map_Orestrict__map(V_m,V_D,T_a,T_b),V_x,V_y,T_a,tc_Option_Ooption(T_b)) = c_Fun_Ofun__upd(c_Map_Orestrict__map(V_m,c_HOL_Ominus__class_Ominus(V_D,hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),tc_fun(T_a,tc_bool)),T_a,T_b),V_x,V_y,T_a,tc_Option_Ooption(T_b)),
input ).
fof(cls_fun__upd__restrict_0_0,plain,
! [T_a,T_b,V_D,V_m,V_x,V_y] :
( c_Fun_Ofun__upd(c_Map_Orestrict__map(V_m,V_D,T_a,T_b),V_x,V_y,T_a,tc_Option_Ooption(T_b)) = c_Fun_Ofun__upd(c_Map_Orestrict__map(V_m,c_HOL_Ominus__class_Ominus(V_D,hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),tc_fun(T_a,tc_bool)),T_a,T_b),V_x,V_y,T_a,tc_Option_Ooption(T_b))
| $false ),
inference(orientation,[status(thm)],[cls_fun__upd__restrict_0]) ).
cnf(cls_insert__inter__insert_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_A)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),
input ).
fof(cls_insert__inter__insert_0_0,plain,
! [T_a,V_A,V_B,V_a] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_A)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B))
| $false ),
inference(orientation,[status(thm)],[cls_insert__inter__insert_0]) ).
cnf(cls_subset__insertI_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B))),
input ).
fof(cls_subset__insertI_0_0,plain,
! [T_a,V_B,V_a] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B)))
| $false ),
inference(orientation,[status(thm)],[cls_subset__insertI_0]) ).
cnf(cls_inf__Int__eq_0,axiom,
hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),V_R)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),V_S)),v_x) = hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),V_R),V_S)),
input ).
fof(cls_inf__Int__eq_0_0,plain,
! [V_R,V_S] :
( hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),V_R)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),V_S)),v_x) = hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),V_R),V_S))
| $false ),
inference(orientation,[status(thm)],[cls_inf__Int__eq_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,
hBOOL(hAPP(c_Finite__Set_Ofold__graph(V_f,V_z,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a,T_b),V_z)),
input ).
fof(cls_fold__graph_OemptyI_0_0,plain,
! [T_a,T_b,V_f,V_z] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(V_f,V_z,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a,T_b),V_z))
| $false ),
inference(orientation,[status(thm)],[cls_fold__graph_OemptyI_0]) ).
cnf(cls_empty__subsetI_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),V_A)),
input ).
fof(cls_empty__subsetI_0_0,plain,
! [T_a,V_A] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),V_A))
| $false ),
inference(orientation,[status(thm)],[cls_empty__subsetI_0]) ).
cnf(cls_Int__empty__left_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),V_B) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
input ).
fof(cls_Int__empty__left_0_0,plain,
! [T_a,V_B] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),V_B) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Int__empty__left_0]) ).
cnf(cls_Int__empty__right_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
input ).
fof(cls_Int__empty__right_0_0,plain,
! [T_a,V_A] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Int__empty__right_0]) ).
cnf(cls_not__psubset__empty_0,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),
input ).
fof(cls_not__psubset__empty_0_0,plain,
! [T_a,V_A] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))
| $false ),
inference(orientation,[status(thm)],[cls_not__psubset__empty_0]) ).
cnf(cls_subset__empty_1,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),
input ).
fof(cls_subset__empty_1_0,plain,
! [T_a] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))
| $false ),
inference(orientation,[status(thm)],[cls_subset__empty_1]) ).
cnf(cls_fold__empty_0,axiom,
c_Finite__Set_Ofold(V_f,V_z,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a) = V_z,
input ).
fof(cls_fold__empty_0_0,plain,
! [T_a,T_b,V_f,V_z] :
( c_Finite__Set_Ofold(V_f,V_z,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a) = V_z
| $false ),
inference(orientation,[status(thm)],[cls_fold__empty_0]) ).
cnf(cls_fold__image__empty_0,axiom,
c_Finite__Set_Ofold__image(V_f,V_g,V_z,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_a,T_b) = V_z,
input ).
fof(cls_fold__image__empty_0_0,plain,
! [T_a,T_b,V_f,V_g,V_z] :
( c_Finite__Set_Ofold__image(V_f,V_g,V_z,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_a,T_b) = V_z
| $false ),
inference(orientation,[status(thm)],[cls_fold__image__empty_0]) ).
cnf(cls_vimage__Int_0,axiom,
c_Set_Ovimage(V_f,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_b,tc_bool)),V_A),V_B),T_a,T_b) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Ovimage(V_f,V_A,T_a,T_b)),c_Set_Ovimage(V_f,V_B,T_a,T_b)),
input ).
fof(cls_vimage__Int_0_0,plain,
! [T_a,T_b,V_A,V_B,V_f] :
( c_Set_Ovimage(V_f,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_b,tc_bool)),V_A),V_B),T_a,T_b) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Ovimage(V_f,V_A,T_a,T_b)),c_Set_Ovimage(V_f,V_B,T_a,T_b))
| $false ),
inference(orientation,[status(thm)],[cls_vimage__Int_0]) ).
cnf(cls_map__upd__Some__unfold_3,axiom,
hAPP(c_Fun_Ofun__upd(V_m,V_xa,hAPP(c_Option_Ooption_OSome(T_a),V_x),T_aa,tc_Option_Ooption(T_a)),V_xa) = hAPP(c_Option_Ooption_OSome(T_a),V_x),
input ).
fof(cls_map__upd__Some__unfold_3_0,plain,
! [T_a,T_aa,V_m,V_x,V_xa] :
( hAPP(c_Fun_Ofun__upd(V_m,V_xa,hAPP(c_Option_Ooption_OSome(T_a),V_x),T_aa,tc_Option_Ooption(T_a)),V_xa) = hAPP(c_Option_Ooption_OSome(T_a),V_x)
| $false ),
inference(orientation,[status(thm)],[cls_map__upd__Some__unfold_3]) ).
cnf(cls_Int__Diff_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),V_C,tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ominus__class_Ominus(V_B,V_C,tc_fun(T_a,tc_bool))),
input ).
fof(cls_Int__Diff_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),V_C,tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ominus__class_Ominus(V_B,V_C,tc_fun(T_a,tc_bool)))
| $false ),
inference(orientation,[status(thm)],[cls_Int__Diff_0]) ).
cnf(cls_subset__refl_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_A)),
input ).
fof(cls_subset__refl_0_0,plain,
! [T_a,V_A] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_A))
| $false ),
inference(orientation,[status(thm)],[cls_subset__refl_0]) ).
cnf(cls_equalityE_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_x),V_x)),
input ).
fof(cls_equalityE_0_0,plain,
! [T_a,V_x] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_x),V_x))
| $false ),
inference(orientation,[status(thm)],[cls_equalityE_0]) ).
cnf(cls_Int__absorb_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_A) = V_A,
input ).
fof(cls_Int__absorb_0_0,plain,
! [T_a,V_A] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_A) = V_A
| $false ),
inference(orientation,[status(thm)],[cls_Int__absorb_0]) ).
cnf(cls_n__not__Suc__n_0,axiom,
V_n != c_Suc(V_n),
input ).
fof(cls_n__not__Suc__n_0_0,plain,
! [V_n] :
( V_n != c_Suc(V_n)
| $false ),
inference(orientation,[status(thm)],[cls_n__not__Suc__n_0]) ).
cnf(cls_Suc__n__not__n_0,axiom,
c_Suc(V_n) != V_n,
input ).
fof(cls_Suc__n__not__n_0_0,plain,
! [V_n] :
( c_Suc(V_n) != V_n
| $false ),
inference(orientation,[status(thm)],[cls_Suc__n__not__n_0]) ).
cnf(cls_Un__Int__crazy_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_C),V_A)),
input ).
fof(cls_Un__Int__crazy_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_C),V_A))
| $false ),
inference(orientation,[status(thm)],[cls_Un__Int__crazy_0]) ).
cnf(cls_Diff__subset_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))),V_A)),
input ).
fof(cls_Diff__subset_0_0,plain,
! [T_a,V_A,V_B] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))),V_A))
| $false ),
inference(orientation,[status(thm)],[cls_Diff__subset_0]) ).
cnf(cls_Int__commute_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_A),
input ).
fof(cls_Int__commute_0_0,plain,
! [T_a,V_A,V_B] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_A)
| $false ),
inference(orientation,[status(thm)],[cls_Int__commute_0]) ).
cnf(cls_Un__upper1_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B))),
input ).
fof(cls_Un__upper1_0_0,plain,
! [T_a,V_A,V_B] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)))
| $false ),
inference(orientation,[status(thm)],[cls_Un__upper1_0]) ).
cnf(cls_Un__upper2_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B))),
input ).
fof(cls_Un__upper2_0_0,plain,
! [T_a,V_A,V_B] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)))
| $false ),
inference(orientation,[status(thm)],[cls_Un__upper2_0]) ).
cnf(cls_Int__left__absorb_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),
input ).
fof(cls_Int__left__absorb_0_0,plain,
! [T_a,V_A,V_B] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)
| $false ),
inference(orientation,[status(thm)],[cls_Int__left__absorb_0]) ).
cnf(cls_Un__Int__distrib2_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)),V_A) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_A)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_C),V_A)),
input ).
fof(cls_Un__Int__distrib2_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)),V_A) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_A)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_C),V_A))
| $false ),
inference(orientation,[status(thm)],[cls_Un__Int__distrib2_0]) ).
cnf(cls_Un__Int__distrib_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_C)),
input ).
fof(cls_Un__Int__distrib_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_C))
| $false ),
inference(orientation,[status(thm)],[cls_Un__Int__distrib_0]) ).
cnf(cls_Int__lower2_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),V_B)),
input ).
fof(cls_Int__lower2_0_0,plain,
! [T_a,V_A,V_B] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),V_B))
| $false ),
inference(orientation,[status(thm)],[cls_Int__lower2_0]) ).
cnf(cls_Int__lower1_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),V_A)),
input ).
fof(cls_Int__lower1_0_0,plain,
! [T_a,V_A,V_B] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),V_A))
| $false ),
inference(orientation,[status(thm)],[cls_Int__lower1_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_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__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__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__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_less__Suc__eq_2,axiom,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),c_Suc(V_x))),
input ).
fof(cls_less__Suc__eq_2_0,plain,
! [V_x] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),c_Suc(V_x)))
| $false ),
inference(orientation,[status(thm)],[cls_less__Suc__eq_2]) ).
cnf(cls_lessI_0,axiom,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),c_Suc(V_n))),
input ).
fof(cls_lessI_0_0,plain,
! [V_n] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),c_Suc(V_n)))
| $false ),
inference(orientation,[status(thm)],[cls_lessI_0]) ).
cnf(cls_option_Osimps_I4_J_0,axiom,
c_Option_Ooption_Ooption__case(V_f1,V_f2,c_Option_Ooption_ONone(T_b),T_a,T_b) = V_f1,
input ).
fof(cls_option_Osimps_I4_J_0_0,plain,
! [T_a,T_b,V_f1,V_f2] :
( c_Option_Ooption_Ooption__case(V_f1,V_f2,c_Option_Ooption_ONone(T_b),T_a,T_b) = V_f1
| $false ),
inference(orientation,[status(thm)],[cls_option_Osimps_I4_J_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_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_Int__Un__distrib_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C)),
input ).
fof(cls_Int__Un__distrib_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C))
| $false ),
inference(orientation,[status(thm)],[cls_Int__Un__distrib_0]) ).
cnf(cls_Int__Un__distrib2_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)),V_A) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A)),
input ).
fof(cls_Int__Un__distrib2_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)),V_A) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A))
| $false ),
inference(orientation,[status(thm)],[cls_Int__Un__distrib2_0]) ).
cnf(cls_option_Osimps_I5_J_0,axiom,
c_Option_Ooption_Ooption__case(V_f1,V_f2,hAPP(c_Option_Ooption_OSome(T_b),V_a),T_a,T_b) = hAPP(V_f2,V_a),
input ).
fof(cls_option_Osimps_I5_J_0_0,plain,
! [T_a,T_b,V_a,V_f1,V_f2] :
( c_Option_Ooption_Ooption__case(V_f1,V_f2,hAPP(c_Option_Ooption_OSome(T_b),V_a),T_a,T_b) = hAPP(V_f2,V_a)
| $false ),
inference(orientation,[status(thm)],[cls_option_Osimps_I5_J_0]) ).
cnf(cls_dom__restrict_0,axiom,
c_Map_Odom(c_Map_Orestrict__map(V_m,V_A,T_a,T_b),T_a,T_b) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Map_Odom(V_m,T_a,T_b)),V_A),
input ).
fof(cls_dom__restrict_0_0,plain,
! [T_a,T_b,V_A,V_m] :
( c_Map_Odom(c_Map_Orestrict__map(V_m,V_A,T_a,T_b),T_a,T_b) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Map_Odom(V_m,T_a,T_b)),V_A)
| $false ),
inference(orientation,[status(thm)],[cls_dom__restrict_0]) ).
cnf(cls_less__not__refl_0,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),V_n)),
input ).
fof(cls_less__not__refl_0_0,plain,
! [V_n] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),V_n))
| $false ),
inference(orientation,[status(thm)],[cls_less__not__refl_0]) ).
cnf(cls_nat__less__le_1,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),V_x)),
input ).
fof(cls_nat__less__le_1_0,plain,
! [V_x] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),V_x))
| $false ),
inference(orientation,[status(thm)],[cls_nat__less__le_1]) ).
cnf(cls_psubset__eq_1,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_x),V_x)),
input ).
fof(cls_psubset__eq_1_0,plain,
! [T_a,V_x] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_x),V_x))
| $false ),
inference(orientation,[status(thm)],[cls_psubset__eq_1]) ).
cnf(cls_Diff__Int2_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C),V_B,tc_fun(T_a,tc_bool)),
input ).
fof(cls_Diff__Int2_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C),V_B,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Diff__Int2_0]) ).
cnf(cls_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_Diff__Int__distrib2_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))),V_C) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Diff__Int__distrib2_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))),V_C) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Diff__Int__distrib2_0]) ).
cnf(cls_Diff__Int__distrib_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_B),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Diff__Int__distrib_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_B),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Diff__Int__distrib_0]) ).
cnf(cls_restrict__map__insert_0,axiom,
c_Map_Orestrict__map(V_f,hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_A),T_a,T_b) = c_Fun_Ofun__upd(c_Map_Orestrict__map(V_f,V_A,T_a,T_b),V_a,hAPP(V_f,V_a),T_a,tc_Option_Ooption(T_b)),
input ).
fof(cls_restrict__map__insert_0_0,plain,
! [T_a,T_b,V_A,V_a,V_f] :
( c_Map_Orestrict__map(V_f,hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_A),T_a,T_b) = c_Fun_Ofun__upd(c_Map_Orestrict__map(V_f,V_A,T_a,T_b),V_a,hAPP(V_f,V_a),T_a,tc_Option_Ooption(T_b))
| $false ),
inference(orientation,[status(thm)],[cls_restrict__map__insert_0]) ).
cnf(cls_restrict__map__empty_0,axiom,
hAPP(c_Map_Orestrict__map(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),t_a),V_D,t_a,T_b),v_x) = c_Option_Ooption_ONone(T_b),
input ).
fof(cls_restrict__map__empty_0_0,plain,
! [T_b,V_D] :
( hAPP(c_Map_Orestrict__map(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),t_a),V_D,t_a,T_b),v_x) = c_Option_Ooption_ONone(T_b)
| $false ),
inference(orientation,[status(thm)],[cls_restrict__map__empty_0]) ).
cnf(cls_restrict__restrict_0,axiom,
c_Map_Orestrict__map(c_Map_Orestrict__map(V_m,V_A,T_a,T_b),V_B,T_a,T_b) = c_Map_Orestrict__map(V_m,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b),
input ).
fof(cls_restrict__restrict_0_0,plain,
! [T_a,T_b,V_A,V_B,V_m] :
( c_Map_Orestrict__map(c_Map_Orestrict__map(V_m,V_A,T_a,T_b),V_B,T_a,T_b) = c_Map_Orestrict__map(V_m,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b)
| $false ),
inference(orientation,[status(thm)],[cls_restrict__restrict_0]) ).
cnf(cls_Int__left__commute_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C)),
input ).
fof(cls_Int__left__commute_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C))
| $false ),
inference(orientation,[status(thm)],[cls_Int__left__commute_0]) ).
cnf(cls_Int__assoc_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)),
input ).
fof(cls_Int__assoc_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C))
| $false ),
inference(orientation,[status(thm)],[cls_Int__assoc_0]) ).
cnf(cls_map__upd__nonempty_0,axiom,
c_Fun_Ofun__upd(V_t,V_k,hAPP(c_Option_Ooption_OSome(T_b),V_x),T_a,tc_Option_Ooption(T_b)) != c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),
input ).
fof(cls_map__upd__nonempty_0_0,plain,
! [T_a,T_b,V_k,V_t,V_x] :
( c_Fun_Ofun__upd(V_t,V_k,hAPP(c_Option_Ooption_OSome(T_b),V_x),T_a,tc_Option_Ooption(T_b)) != c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_map__upd__nonempty_0]) ).
cnf(cls_fold__def_0,axiom,
c_Finite__Set_Ofold(V_f,V_z,V_A,T_b,T_a) = c_The(c_Finite__Set_Ofold__graph(V_f,V_z,V_A,T_b,T_a),T_a),
input ).
fof(cls_fold__def_0_0,plain,
! [T_a,T_b,V_A,V_f,V_z] :
( c_Finite__Set_Ofold(V_f,V_z,V_A,T_b,T_a) = c_The(c_Finite__Set_Ofold__graph(V_f,V_z,V_A,T_b,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_fold__def_0]) ).
cnf(cls_the__eq__trivial_0,axiom,
c_The(hAPP(c_COMBC(c_fequal(T_a),T_a,T_a,tc_bool),V_a),T_a) = V_a,
input ).
fof(cls_the__eq__trivial_0_0,plain,
! [T_a,V_a] :
( c_The(hAPP(c_COMBC(c_fequal(T_a),T_a,T_a,tc_bool),V_a),T_a) = V_a
| $false ),
inference(orientation,[status(thm)],[cls_the__eq__trivial_0]) ).
fof(def_lhs_atom1,axiom,
! [V_a,T_a] :
( lhs_atom1(V_a,T_a)
<=> c_The(hAPP(c_COMBC(c_fequal(T_a),T_a,T_a,tc_bool),V_a),T_a) = V_a ),
inference(definition,[],]) ).
fof(to_be_clausified_0,plain,
! [T_a,V_a] :
( lhs_atom1(V_a,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_the__eq__trivial_0_0,def_lhs_atom1]) ).
fof(def_lhs_atom2,axiom,
! [V_z,V_f,V_A,T_b,T_a] :
( lhs_atom2(V_z,V_f,V_A,T_b,T_a)
<=> c_Finite__Set_Ofold(V_f,V_z,V_A,T_b,T_a) = c_The(c_Finite__Set_Ofold__graph(V_f,V_z,V_A,T_b,T_a),T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_1,plain,
! [T_a,T_b,V_A,V_f,V_z] :
( lhs_atom2(V_z,V_f,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_fold__def_0_0,def_lhs_atom2]) ).
fof(def_lhs_atom3,axiom,
! [V_x,V_t,V_k,T_b,T_a] :
( lhs_atom3(V_x,V_t,V_k,T_b,T_a)
<=> c_Fun_Ofun__upd(V_t,V_k,hAPP(c_Option_Ooption_OSome(T_b),V_x),T_a,tc_Option_Ooption(T_b)) != c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_2,plain,
! [T_a,T_b,V_k,V_t,V_x] :
( lhs_atom3(V_x,V_t,V_k,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_map__upd__nonempty_0_0,def_lhs_atom3]) ).
fof(def_lhs_atom4,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom4(V_C,V_B,V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)) ),
inference(definition,[],]) ).
fof(to_be_clausified_3,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom4(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__assoc_0_0,def_lhs_atom4]) ).
fof(def_lhs_atom5,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom5(V_C,V_B,V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C)) ),
inference(definition,[],]) ).
fof(to_be_clausified_4,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom5(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__left__commute_0_0,def_lhs_atom5]) ).
fof(def_lhs_atom6,axiom,
! [V_m,V_B,V_A,T_b,T_a] :
( lhs_atom6(V_m,V_B,V_A,T_b,T_a)
<=> c_Map_Orestrict__map(c_Map_Orestrict__map(V_m,V_A,T_a,T_b),V_B,T_a,T_b) = c_Map_Orestrict__map(V_m,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b) ),
inference(definition,[],]) ).
fof(to_be_clausified_5,plain,
! [T_a,T_b,V_A,V_B,V_m] :
( lhs_atom6(V_m,V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_restrict__restrict_0_0,def_lhs_atom6]) ).
fof(def_lhs_atom7,axiom,
! [V_D,T_b] :
( lhs_atom7(V_D,T_b)
<=> hAPP(c_Map_Orestrict__map(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),t_a),V_D,t_a,T_b),v_x) = c_Option_Ooption_ONone(T_b) ),
inference(definition,[],]) ).
fof(to_be_clausified_6,plain,
! [T_b,V_D] :
( lhs_atom7(V_D,T_b)
| $false ),
inference(fold_definition,[status(thm)],[cls_restrict__map__empty_0_0,def_lhs_atom7]) ).
fof(def_lhs_atom8,axiom,
! [V_f,V_a,V_A,T_b,T_a] :
( lhs_atom8(V_f,V_a,V_A,T_b,T_a)
<=> c_Map_Orestrict__map(V_f,hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_A),T_a,T_b) = c_Fun_Ofun__upd(c_Map_Orestrict__map(V_f,V_A,T_a,T_b),V_a,hAPP(V_f,V_a),T_a,tc_Option_Ooption(T_b)) ),
inference(definition,[],]) ).
fof(to_be_clausified_7,plain,
! [T_a,T_b,V_A,V_a,V_f] :
( lhs_atom8(V_f,V_a,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_restrict__map__insert_0_0,def_lhs_atom8]) ).
fof(def_lhs_atom9,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom9(V_C,V_B,V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_B),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_8,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom9(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__Int__distrib_0_0,def_lhs_atom9]) ).
fof(def_lhs_atom10,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom10(V_C,V_B,V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))),V_C) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_9,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom10(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__Int__distrib2_0_0,def_lhs_atom10]) ).
fof(def_lhs_atom11,axiom,
! [V_z,V_y,V_x,V_f,T_b,T_a] :
( lhs_atom11(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_10,plain,
! [T_a,T_b,V_f,V_x,V_y,V_z] :
( lhs_atom11(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_atom11]) ).
fof(def_lhs_atom12,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom12(V_C,V_B,V_A,T_a)
<=> c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C),V_B,tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_11,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom12(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__Int2_0_0,def_lhs_atom12]) ).
fof(def_lhs_atom13,axiom,
! [V_x,T_a] :
( lhs_atom13(V_x,T_a)
<=> ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_x),V_x)) ),
inference(definition,[],]) ).
fof(to_be_clausified_12,plain,
! [T_a,V_x] :
( lhs_atom13(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_psubset__eq_1_0,def_lhs_atom13]) ).
fof(def_lhs_atom14,axiom,
! [V_x] :
( lhs_atom14(V_x)
<=> ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),V_x)) ),
inference(definition,[],]) ).
fof(to_be_clausified_13,plain,
! [V_x] :
( lhs_atom14(V_x)
| $false ),
inference(fold_definition,[status(thm)],[cls_nat__less__le_1_0,def_lhs_atom14]) ).
fof(def_lhs_atom15,axiom,
! [V_n] :
( lhs_atom15(V_n)
<=> ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),V_n)) ),
inference(definition,[],]) ).
fof(to_be_clausified_14,plain,
! [V_n] :
( lhs_atom15(V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_less__not__refl_0_0,def_lhs_atom15]) ).
fof(def_lhs_atom16,axiom,
! [V_m,V_A,T_b,T_a] :
( lhs_atom16(V_m,V_A,T_b,T_a)
<=> c_Map_Odom(c_Map_Orestrict__map(V_m,V_A,T_a,T_b),T_a,T_b) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Map_Odom(V_m,T_a,T_b)),V_A) ),
inference(definition,[],]) ).
fof(to_be_clausified_15,plain,
! [T_a,T_b,V_A,V_m] :
( lhs_atom16(V_m,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_dom__restrict_0_0,def_lhs_atom16]) ).
fof(def_lhs_atom17,axiom,
! [V_f2,V_f1,V_a,T_b,T_a] :
( lhs_atom17(V_f2,V_f1,V_a,T_b,T_a)
<=> c_Option_Ooption_Ooption__case(V_f1,V_f2,hAPP(c_Option_Ooption_OSome(T_b),V_a),T_a,T_b) = hAPP(V_f2,V_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_16,plain,
! [T_a,T_b,V_a,V_f1,V_f2] :
( lhs_atom17(V_f2,V_f1,V_a,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_option_Osimps_I5_J_0_0,def_lhs_atom17]) ).
fof(def_lhs_atom18,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom18(V_C,V_B,V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)),V_A) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_17,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom18(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__Un__distrib2_0_0,def_lhs_atom18]) ).
fof(def_lhs_atom19,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom19(V_C,V_B,V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C)) ),
inference(definition,[],]) ).
fof(to_be_clausified_18,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom19(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__Un__distrib_0_0,def_lhs_atom19]) ).
fof(def_lhs_atom20,axiom,
! [V_R,V_Q,V_P,T_c,T_b,T_a] :
( lhs_atom20(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_19,plain,
! [T_a,T_b,T_c,V_P,V_Q,V_R] :
( lhs_atom20(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_atom20]) ).
fof(def_lhs_atom21,axiom,
! [V_Q,V_P,T_b,T_a] :
( lhs_atom21(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_20,plain,
! [T_a,T_b,V_P,V_Q] :
( lhs_atom21(V_Q,V_P,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_COMBK__def_0_0,def_lhs_atom21]) ).
fof(def_lhs_atom22,axiom,
! [V_f2,V_f1,T_b,T_a] :
( lhs_atom22(V_f2,V_f1,T_b,T_a)
<=> c_Option_Ooption_Ooption__case(V_f1,V_f2,c_Option_Ooption_ONone(T_b),T_a,T_b) = V_f1 ),
inference(definition,[],]) ).
fof(to_be_clausified_21,plain,
! [T_a,T_b,V_f1,V_f2] :
( lhs_atom22(V_f2,V_f1,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_option_Osimps_I4_J_0_0,def_lhs_atom22]) ).
fof(def_lhs_atom23,axiom,
! [V_n] :
( lhs_atom23(V_n)
<=> hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),c_Suc(V_n))) ),
inference(definition,[],]) ).
fof(to_be_clausified_22,plain,
! [V_n] :
( lhs_atom23(V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_lessI_0_0,def_lhs_atom23]) ).
fof(def_lhs_atom24,axiom,
! [V_x] :
( lhs_atom24(V_x)
<=> hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),c_Suc(V_x))) ),
inference(definition,[],]) ).
fof(to_be_clausified_23,plain,
! [V_x] :
( lhs_atom24(V_x)
| $false ),
inference(fold_definition,[status(thm)],[cls_less__Suc__eq_2_0,def_lhs_atom24]) ).
fof(def_lhs_atom25,axiom,
! [V_x,V_f,T_b,T_a] :
( lhs_atom25(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_24,plain,
! [T_a,T_b,V_f,V_x] :
( lhs_atom25(V_x,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_fun__upd__idem_0_0,def_lhs_atom25]) ).
fof(def_lhs_atom26,axiom,
! [V_y,V_x,V_f,T_b,T_a] :
( lhs_atom26(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_25,plain,
! [T_a,T_b,V_f,V_x,V_y] :
( lhs_atom26(V_y,V_x,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_fun__upd__same_0_0,def_lhs_atom26]) ).
fof(def_lhs_atom27,axiom,
! [V_x,V_f,T_b,T_a] :
( lhs_atom27(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_26,plain,
! [T_a,T_b,V_f,V_x] :
( lhs_atom27(V_x,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_fun__upd__triv_0_0,def_lhs_atom27]) ).
fof(def_lhs_atom28,axiom,
! [V_y,V_x,V_f,T_aa,T_a] :
( lhs_atom28(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_27,plain,
! [T_a,T_aa,V_f,V_x,V_y] :
( lhs_atom28(V_y,V_x,V_f,T_aa,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_fun__upd__apply_0_0,def_lhs_atom28]) ).
fof(def_lhs_atom29,axiom,
! [V_x,V_f,T_aa,T_a] :
( lhs_atom29(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_28,plain,
! [T_a,T_aa,V_f,V_x] :
( lhs_atom29(V_x,V_f,T_aa,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_fun__upd__idem__iff_1_0,def_lhs_atom29]) ).
fof(def_lhs_atom30,axiom,
! [V_B,V_A,T_a] :
( lhs_atom30(V_B,V_A,T_a)
<=> hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),V_A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_29,plain,
! [T_a,V_A,V_B] :
( lhs_atom30(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__lower1_0_0,def_lhs_atom30]) ).
fof(def_lhs_atom31,axiom,
! [V_B,V_A,T_a] :
( lhs_atom31(V_B,V_A,T_a)
<=> hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),V_B)) ),
inference(definition,[],]) ).
fof(to_be_clausified_30,plain,
! [T_a,V_A,V_B] :
( lhs_atom31(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__lower2_0_0,def_lhs_atom31]) ).
fof(def_lhs_atom32,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom32(V_C,V_B,V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_C)) ),
inference(definition,[],]) ).
fof(to_be_clausified_31,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom32(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__Int__distrib_0_0,def_lhs_atom32]) ).
fof(def_lhs_atom33,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom33(V_C,V_B,V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)),V_A) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_A)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_C),V_A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_32,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom33(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__Int__distrib2_0_0,def_lhs_atom33]) ).
fof(def_lhs_atom34,axiom,
! [V_B,V_A,T_a] :
( lhs_atom34(V_B,V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) ),
inference(definition,[],]) ).
fof(to_be_clausified_33,plain,
! [T_a,V_A,V_B] :
( lhs_atom34(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__left__absorb_0_0,def_lhs_atom34]) ).
fof(def_lhs_atom35,axiom,
! [V_B,V_A,T_a] :
( lhs_atom35(V_B,V_A,T_a)
<=> hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B))) ),
inference(definition,[],]) ).
fof(to_be_clausified_34,plain,
! [T_a,V_A,V_B] :
( lhs_atom35(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__upper2_0_0,def_lhs_atom35]) ).
fof(def_lhs_atom36,axiom,
! [V_B,V_A,T_a] :
( lhs_atom36(V_B,V_A,T_a)
<=> hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B))) ),
inference(definition,[],]) ).
fof(to_be_clausified_35,plain,
! [T_a,V_A,V_B] :
( lhs_atom36(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__upper1_0_0,def_lhs_atom36]) ).
fof(def_lhs_atom37,axiom,
! [V_B,V_A,T_a] :
( lhs_atom37(V_B,V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_A) ),
inference(definition,[],]) ).
fof(to_be_clausified_36,plain,
! [T_a,V_A,V_B] :
( lhs_atom37(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__commute_0_0,def_lhs_atom37]) ).
fof(def_lhs_atom38,axiom,
! [V_B,V_A,T_a] :
( lhs_atom38(V_B,V_A,T_a)
<=> hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))),V_A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_37,plain,
! [T_a,V_A,V_B] :
( lhs_atom38(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__subset_0_0,def_lhs_atom38]) ).
fof(def_lhs_atom39,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom39(V_C,V_B,V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_C),V_A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_38,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom39(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__Int__crazy_0_0,def_lhs_atom39]) ).
fof(def_lhs_atom40,axiom,
! [V_n] :
( lhs_atom40(V_n)
<=> c_Suc(V_n) != V_n ),
inference(definition,[],]) ).
fof(to_be_clausified_39,plain,
! [V_n] :
( lhs_atom40(V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_Suc__n__not__n_0_0,def_lhs_atom40]) ).
fof(def_lhs_atom41,axiom,
! [V_n] :
( lhs_atom41(V_n)
<=> V_n != c_Suc(V_n) ),
inference(definition,[],]) ).
fof(to_be_clausified_40,plain,
! [V_n] :
( lhs_atom41(V_n)
| $false ),
inference(fold_definition,[status(thm)],[cls_n__not__Suc__n_0_0,def_lhs_atom41]) ).
fof(def_lhs_atom42,axiom,
! [V_A,T_a] :
( lhs_atom42(V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_A) = V_A ),
inference(definition,[],]) ).
fof(to_be_clausified_41,plain,
! [T_a,V_A] :
( lhs_atom42(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__absorb_0_0,def_lhs_atom42]) ).
fof(def_lhs_atom43,axiom,
! [V_x,T_a] :
( lhs_atom43(V_x,T_a)
<=> hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_x),V_x)) ),
inference(definition,[],]) ).
fof(to_be_clausified_42,plain,
! [T_a,V_x] :
( lhs_atom43(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_equalityE_0_0,def_lhs_atom43]) ).
fof(def_lhs_atom44,axiom,
! [V_A,T_a] :
( lhs_atom44(V_A,T_a)
<=> hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_43,plain,
! [T_a,V_A] :
( lhs_atom44(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_subset__refl_0_0,def_lhs_atom44]) ).
fof(def_lhs_atom45,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom45(V_C,V_B,V_A,T_a)
<=> c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),V_C,tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ominus__class_Ominus(V_B,V_C,tc_fun(T_a,tc_bool))) ),
inference(definition,[],]) ).
fof(to_be_clausified_44,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom45(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__Diff_0_0,def_lhs_atom45]) ).
fof(def_lhs_atom46,axiom,
! [V_xa,V_x,V_m,T_aa,T_a] :
( lhs_atom46(V_xa,V_x,V_m,T_aa,T_a)
<=> hAPP(c_Fun_Ofun__upd(V_m,V_xa,hAPP(c_Option_Ooption_OSome(T_a),V_x),T_aa,tc_Option_Ooption(T_a)),V_xa) = hAPP(c_Option_Ooption_OSome(T_a),V_x) ),
inference(definition,[],]) ).
fof(to_be_clausified_45,plain,
! [T_a,T_aa,V_m,V_x,V_xa] :
( lhs_atom46(V_xa,V_x,V_m,T_aa,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_map__upd__Some__unfold_3_0,def_lhs_atom46]) ).
fof(def_lhs_atom47,axiom,
! [V_f,V_B,V_A,T_b,T_a] :
( lhs_atom47(V_f,V_B,V_A,T_b,T_a)
<=> c_Set_Ovimage(V_f,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_b,tc_bool)),V_A),V_B),T_a,T_b) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Ovimage(V_f,V_A,T_a,T_b)),c_Set_Ovimage(V_f,V_B,T_a,T_b)) ),
inference(definition,[],]) ).
fof(to_be_clausified_46,plain,
! [T_a,T_b,V_A,V_B,V_f] :
( lhs_atom47(V_f,V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_vimage__Int_0_0,def_lhs_atom47]) ).
fof(def_lhs_atom48,axiom,
! [V_z,V_g,V_f,T_b,T_a] :
( lhs_atom48(V_z,V_g,V_f,T_b,T_a)
<=> c_Finite__Set_Ofold__image(V_f,V_g,V_z,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_a,T_b) = V_z ),
inference(definition,[],]) ).
fof(to_be_clausified_47,plain,
! [T_a,T_b,V_f,V_g,V_z] :
( lhs_atom48(V_z,V_g,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_fold__image__empty_0_0,def_lhs_atom48]) ).
fof(def_lhs_atom49,axiom,
! [V_z,V_f,T_b,T_a] :
( lhs_atom49(V_z,V_f,T_b,T_a)
<=> c_Finite__Set_Ofold(V_f,V_z,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a) = V_z ),
inference(definition,[],]) ).
fof(to_be_clausified_48,plain,
! [T_a,T_b,V_f,V_z] :
( lhs_atom49(V_z,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_fold__empty_0_0,def_lhs_atom49]) ).
fof(def_lhs_atom50,axiom,
! [T_a] :
( lhs_atom50(T_a)
<=> hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) ),
inference(definition,[],]) ).
fof(to_be_clausified_49,plain,
! [T_a] :
( lhs_atom50(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_subset__empty_1_0,def_lhs_atom50]) ).
fof(def_lhs_atom51,axiom,
! [V_A,T_a] :
( lhs_atom51(V_A,T_a)
<=> ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) ),
inference(definition,[],]) ).
fof(to_be_clausified_50,plain,
! [T_a,V_A] :
( lhs_atom51(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_not__psubset__empty_0_0,def_lhs_atom51]) ).
fof(def_lhs_atom52,axiom,
! [V_A,T_a] :
( lhs_atom52(V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_51,plain,
! [T_a,V_A] :
( lhs_atom52(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__empty__right_0_0,def_lhs_atom52]) ).
fof(def_lhs_atom53,axiom,
! [V_B,T_a] :
( lhs_atom53(V_B,T_a)
<=> hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),V_B) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_52,plain,
! [T_a,V_B] :
( lhs_atom53(V_B,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__empty__left_0_0,def_lhs_atom53]) ).
fof(def_lhs_atom54,axiom,
! [V_A,T_a] :
( lhs_atom54(V_A,T_a)
<=> hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),V_A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_53,plain,
! [T_a,V_A] :
( lhs_atom54(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_empty__subsetI_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)
<=> hBOOL(hAPP(c_Finite__Set_Ofold__graph(V_f,V_z,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a,T_b),V_z)) ),
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_S,V_R] :
( lhs_atom57(V_S,V_R)
<=> hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),V_R)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),V_S)),v_x) = hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),V_R),V_S)) ),
inference(definition,[],]) ).
fof(to_be_clausified_56,plain,
! [V_R,V_S] :
( lhs_atom57(V_S,V_R)
| $false ),
inference(fold_definition,[status(thm)],[cls_inf__Int__eq_0_0,def_lhs_atom57]) ).
fof(def_lhs_atom58,axiom,
! [V_a,V_B,T_a] :
( lhs_atom58(V_a,V_B,T_a)
<=> hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B))) ),
inference(definition,[],]) ).
fof(to_be_clausified_57,plain,
! [T_a,V_B,V_a] :
( lhs_atom58(V_a,V_B,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_subset__insertI_0_0,def_lhs_atom58]) ).
fof(def_lhs_atom59,axiom,
! [V_a,V_B,V_A,T_a] :
( lhs_atom59(V_a,V_B,V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_A)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)) ),
inference(definition,[],]) ).
fof(to_be_clausified_58,plain,
! [T_a,V_A,V_B,V_a] :
( lhs_atom59(V_a,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__inter__insert_0_0,def_lhs_atom59]) ).
fof(def_lhs_atom60,axiom,
! [V_y,V_x,V_m,V_D,T_b,T_a] :
( lhs_atom60(V_y,V_x,V_m,V_D,T_b,T_a)
<=> c_Fun_Ofun__upd(c_Map_Orestrict__map(V_m,V_D,T_a,T_b),V_x,V_y,T_a,tc_Option_Ooption(T_b)) = c_Fun_Ofun__upd(c_Map_Orestrict__map(V_m,c_HOL_Ominus__class_Ominus(V_D,hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),tc_fun(T_a,tc_bool)),T_a,T_b),V_x,V_y,T_a,tc_Option_Ooption(T_b)) ),
inference(definition,[],]) ).
fof(to_be_clausified_59,plain,
! [T_a,T_b,V_D,V_m,V_x,V_y] :
( lhs_atom60(V_y,V_x,V_m,V_D,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_fun__upd__restrict_0_0,def_lhs_atom60]) ).
fof(def_lhs_atom61,axiom,
! [V_x,T_a] :
( lhs_atom61(V_x,T_a)
<=> hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Option_Oset(hAPP(c_Option_Ooption_OSome(T_a),V_x),T_a))) ),
inference(definition,[],]) ).
fof(to_be_clausified_60,plain,
! [T_a,V_x] :
( lhs_atom61(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_elem__set_1_0,def_lhs_atom61]) ).
fof(def_lhs_atom62,axiom,
! [V_B,V_A,T_a] :
( lhs_atom62(V_B,V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_61,plain,
! [T_a,V_A,V_B] :
( lhs_atom62(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__disjoint_0_0,def_lhs_atom62]) ).
fof(def_lhs_atom63,axiom,
! [V_B,V_A,T_a] :
( lhs_atom63(V_B,V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)) = V_A ),
inference(definition,[],]) ).
fof(to_be_clausified_62,plain,
! [T_a,V_A,V_B] :
( lhs_atom63(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__Diff__Int_0_0,def_lhs_atom63]) ).
fof(def_lhs_atom64,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom64(V_C,V_B,V_A,T_a)
<=> c_HOL_Ominus__class_Ominus(V_A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C),tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))),c_HOL_Ominus__class_Ominus(V_A,V_C,tc_fun(T_a,tc_bool))) ),
inference(definition,[],]) ).
fof(to_be_clausified_63,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom64(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__Un_0_0,def_lhs_atom64]) ).
fof(def_lhs_atom65,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom65(V_C,V_B,V_A,T_a)
<=> c_HOL_Ominus__class_Ominus(V_A,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))),c_HOL_Ominus__class_Ominus(V_A,V_C,tc_fun(T_a,tc_bool))) ),
inference(definition,[],]) ).
fof(to_be_clausified_64,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom65(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__Int_0_0,def_lhs_atom65]) ).
fof(def_lhs_atom66,axiom,
! [T_a] :
( lhs_atom66(T_a)
<=> c_Option_Oset(c_Option_Ooption_ONone(T_a),T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_65,plain,
! [T_a] :
( lhs_atom66(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_set__empty__eq_1_0,def_lhs_atom66]) ).
fof(def_lhs_atom67,axiom,
! [V_y,V_x,V_g,V_f,T_b,T_a] :
( lhs_atom67(V_y,V_x,V_g,V_f,T_b,T_a)
<=> c_Map_Omap__add(V_f,c_Fun_Ofun__upd(V_g,V_x,hAPP(c_Option_Ooption_OSome(T_b),V_y),T_a,tc_Option_Ooption(T_b)),T_a,T_b) = c_Fun_Ofun__upd(c_Map_Omap__add(V_f,V_g,T_a,T_b),V_x,hAPP(c_Option_Ooption_OSome(T_b),V_y),T_a,tc_Option_Ooption(T_b)) ),
inference(definition,[],]) ).
fof(to_be_clausified_66,plain,
! [T_a,T_b,V_f,V_g,V_x,V_y] :
( lhs_atom67(V_y,V_x,V_g,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_map__add__upd_0_0,def_lhs_atom67]) ).
fof(def_lhs_atom68,axiom,
! [V_m,T_b,T_a] :
( lhs_atom68(V_m,T_b,T_a)
<=> c_Map_Omap__add(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),V_m,T_a,T_b) = V_m ),
inference(definition,[],]) ).
fof(to_be_clausified_67,plain,
! [T_a,T_b,V_m] :
( lhs_atom68(V_m,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_empty__map__add_0_0,def_lhs_atom68]) ).
fof(def_lhs_atom69,axiom,
! [V_m,T_b,T_a] :
( lhs_atom69(V_m,T_b,T_a)
<=> c_Map_Omap__add(V_m,c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),T_a,T_b) = V_m ),
inference(definition,[],]) ).
fof(to_be_clausified_68,plain,
! [T_a,T_b,V_m] :
( lhs_atom69(V_m,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_map__add__empty_0_0,def_lhs_atom69]) ).
fof(def_lhs_atom70,axiom,
! [V_x,V_f,T_b,T_a] :
( lhs_atom70(V_x,V_f,T_b,T_a)
<=> c_Map_Omap__le(c_Fun_Ofun__upd(V_f,V_x,c_Option_Ooption_ONone(T_b),T_a,tc_Option_Ooption(T_b)),V_f,T_a,T_b) ),
inference(definition,[],]) ).
fof(to_be_clausified_69,plain,
! [T_a,T_b,V_f,V_x] :
( lhs_atom70(V_x,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_upd__None__map__le_0_0,def_lhs_atom70]) ).
fof(def_lhs_atom71,axiom,
! [V_g,T_b,T_a] :
( lhs_atom71(V_g,T_b,T_a)
<=> c_Map_Omap__le(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),V_g,T_a,T_b) ),
inference(definition,[],]) ).
fof(to_be_clausified_70,plain,
! [T_a,T_b,V_g] :
( lhs_atom71(V_g,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_map__le__empty_0_0,def_lhs_atom71]) ).
fof(def_lhs_atom72,axiom,
! [V_A,T_a] :
( lhs_atom72(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_71,plain,
! [T_a,V_A] :
( lhs_atom72(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__empty_0_0,def_lhs_atom72]) ).
fof(def_lhs_atom73,axiom,
! [T_a] :
( lhs_atom73(T_a)
<=> c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_72,plain,
! [T_a] :
( lhs_atom73(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_finite_OemptyI_0_0,def_lhs_atom73]) ).
fof(def_lhs_atom74,axiom,
! [V_f,V_a,V_B,T_b,T_a] :
( lhs_atom74(V_f,V_a,V_B,T_b,T_a)
<=> c_Set_Ovimage(V_f,hAPP(hAPP(c_Set_Oinsert(T_b),V_a),V_B),T_a,T_b) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Set_Ovimage(V_f,hAPP(hAPP(c_Set_Oinsert(T_b),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))),T_a,T_b)),c_Set_Ovimage(V_f,V_B,T_a,T_b)) ),
inference(definition,[],]) ).
fof(to_be_clausified_73,plain,
! [T_a,T_b,V_B,V_a,V_f] :
( lhs_atom74(V_f,V_a,V_B,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_vimage__insert_0_0,def_lhs_atom74]) ).
fof(def_lhs_atom75,axiom,
! [V_a,V_B,V_A,T_a] :
( lhs_atom75(V_a,V_B,V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)) ),
inference(definition,[],]) ).
fof(to_be_clausified_74,plain,
! [T_a,V_A,V_B,V_a] :
( lhs_atom75(V_a,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__insert__right_0_0,def_lhs_atom75]) ).
fof(def_lhs_atom76,axiom,
! [V_a,V_C,V_B,T_a] :
( lhs_atom76(V_a,V_C,V_B,T_a)
<=> hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B)),V_C) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)) ),
inference(definition,[],]) ).
fof(to_be_clausified_75,plain,
! [T_a,V_B,V_C,V_a] :
( lhs_atom76(V_a,V_C,V_B,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__insert__left_0_0,def_lhs_atom76]) ).
fof(def_lhs_atom77,axiom,
! [V_pname_H,V_com2,V_com1] :
( lhs_atom77(V_pname_H,V_com2,V_com1)
<=> c_Com_Ocom_OBODY(V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ),
inference(definition,[],]) ).
fof(to_be_clausified_76,plain,
! [V_com1,V_com2,V_pname_H] :
( lhs_atom77(V_pname_H,V_com2,V_com1)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I49_J_0_0,def_lhs_atom77]) ).
fof(def_lhs_atom78,axiom,
! [V_pname_H,V_com2,V_com1] :
( lhs_atom78(V_pname_H,V_com2,V_com1)
<=> c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OBODY(V_pname_H) ),
inference(definition,[],]) ).
fof(to_be_clausified_77,plain,
! [V_com1,V_com2,V_pname_H] :
( lhs_atom78(V_pname_H,V_com2,V_com1)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I48_J_0_0,def_lhs_atom78]) ).
fof(def_lhs_atom79,axiom,
! [V_com2_H,V_com1_H] :
( lhs_atom79(V_com2_H,V_com1_H)
<=> c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ),
inference(definition,[],]) ).
fof(to_be_clausified_78,plain,
! [V_com1_H,V_com2_H] :
( lhs_atom79(V_com2_H,V_com1_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I12_J_0_0,def_lhs_atom79]) ).
fof(def_lhs_atom80,axiom,
! [V_com2_H,V_com1_H] :
( lhs_atom80(V_com2_H,V_com1_H)
<=> c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ),
inference(definition,[],]) ).
fof(to_be_clausified_79,plain,
! [V_com1_H,V_com2_H] :
( lhs_atom80(V_com2_H,V_com1_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I13_J_0_0,def_lhs_atom80]) ).
fof(def_lhs_atom81,axiom,
! [V_x,T_a] :
( lhs_atom81(V_x,T_a)
<=> hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),T_a))) ),
inference(definition,[],]) ).
fof(to_be_clausified_80,plain,
! [T_a,V_x] :
( lhs_atom81(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Nitpick_OEx1__def_2_0,def_lhs_atom81]) ).
fof(def_lhs_atom82,axiom,
! [V_x,V_f,T_b,T_a] :
( lhs_atom82(V_x,V_f,T_b,T_a)
<=> c_Map_Odom(c_Fun_Ofun__upd(V_f,V_x,c_Option_Ooption_ONone(T_b),T_a,tc_Option_Ooption(T_b)),T_a,T_b) = c_HOL_Ominus__class_Ominus(c_Map_Odom(V_f,T_a,T_b),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_81,plain,
! [T_a,T_b,V_f,V_x] :
( lhs_atom82(V_x,V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_dom__fun__upd_0_0,def_lhs_atom82]) ).
fof(def_lhs_atom83,axiom,
( lhs_atom83
<=> c_Hoare__Mirabelle_OMGT(v_c) = c_Hoare__Mirabelle_Otriple_Otriple(c_fequal(tc_Com_Ostate),v_c,c_Natural_Oevalc(v_c),tc_Com_Ostate) ),
inference(definition,[],]) ).
fof(to_be_clausified_82,plain,
( lhs_atom83
| $false ),
inference(fold_definition,[status(thm)],[cls_MGT__def__raw_0_0,def_lhs_atom83]) ).
fof(def_lhs_atom84,axiom,
! [V_m2,V_m1,T_b] :
( lhs_atom84(V_m2,V_m1,T_b)
<=> hAPP(c_Map_Omap__add(V_m1,V_m2,t_a,T_b),v_x) = c_Option_Ooption_Ooption__case(hAPP(V_m1,v_x),c_Option_Ooption_OSome(T_b),hAPP(V_m2,v_x),tc_Option_Ooption(T_b),T_b) ),
inference(definition,[],]) ).
fof(to_be_clausified_83,plain,
! [T_b,V_m1,V_m2] :
( lhs_atom84(V_m2,V_m1,T_b)
| $false ),
inference(fold_definition,[status(thm)],[cls_map__add__def_0_0,def_lhs_atom84]) ).
fof(def_lhs_atom85,axiom,
! [T_b,T_a] :
( lhs_atom85(T_b,T_a)
<=> c_Map_Odom(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),T_a,T_b) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_84,plain,
! [T_a,T_b] :
( lhs_atom85(T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_dom__empty_0_0,def_lhs_atom85]) ).
fof(def_lhs_atom86,axiom,
! [V_m,T_b] :
( lhs_atom86(V_m,T_b)
<=> hAPP(c_Map_Orestrict__map(V_m,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a,T_b),v_x) = c_Option_Ooption_ONone(T_b) ),
inference(definition,[],]) ).
fof(to_be_clausified_85,plain,
! [T_b,V_m] :
( lhs_atom86(V_m,T_b)
| $false ),
inference(fold_definition,[status(thm)],[cls_restrict__map__to__empty_0_0,def_lhs_atom86]) ).
fof(def_lhs_atom87,axiom,
! [V_x,T_a] :
( lhs_atom87(V_x,T_a)
<=> c_Option_Oset(hAPP(c_Option_Ooption_OSome(T_a),V_x),T_a) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) ),
inference(definition,[],]) ).
fof(to_be_clausified_86,plain,
! [T_a,V_x] :
( lhs_atom87(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Option_Oset_Osimps_I2_J_0_0,def_lhs_atom87]) ).
fof(def_lhs_atom88,axiom,
! [V_S,V_R] :
( lhs_atom88(V_S,V_R)
<=> hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),V_R)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),V_S)),v_x) = hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),V_R),V_S)) ),
inference(definition,[],]) ).
fof(to_be_clausified_87,plain,
! [V_R,V_S] :
( lhs_atom88(V_S,V_R)
| $false ),
inference(fold_definition,[status(thm)],[cls_sup__Un__eq_0_0,def_lhs_atom88]) ).
fof(def_lhs_atom89,axiom,
! [V_xa,V_x,T_b,T_a] :
( lhs_atom89(V_xa,V_x,T_b,T_a)
<=> c_Map_Odom(c_Fun_Ofun__upd(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),V_x,hAPP(c_Option_Ooption_OSome(T_b),V_xa),T_a,tc_Option_Ooption(T_b)),T_a,T_b) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) ),
inference(definition,[],]) ).
fof(to_be_clausified_88,plain,
! [T_a,T_b,V_x,V_xa] :
( lhs_atom89(V_xa,V_x,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_dom__eq__singleton__conv_1_0,def_lhs_atom89]) ).
fof(def_lhs_atom90,axiom,
! [V_A,T_a] :
( lhs_atom90(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_89,plain,
! [T_a,V_A] :
( lhs_atom90(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__cancel_0_0,def_lhs_atom90]) ).
fof(def_lhs_atom91,axiom,
! [V_B,T_a] :
( lhs_atom91(V_B,T_a)
<=> hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),V_B) = V_B ),
inference(definition,[],]) ).
fof(to_be_clausified_90,plain,
! [T_a,V_B] :
( lhs_atom91(V_B,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__empty__left_0_0,def_lhs_atom91]) ).
fof(def_lhs_atom92,axiom,
! [V_A,T_a] :
( lhs_atom92(V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = V_A ),
inference(definition,[],]) ).
fof(to_be_clausified_91,plain,
! [T_a,V_A] :
( lhs_atom92(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__empty__right_0_0,def_lhs_atom92]) ).
fof(def_lhs_atom93,axiom,
! [V_A,T_a] :
( lhs_atom93(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_92,plain,
! [T_a,V_A] :
( lhs_atom93(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_empty__Diff_0_0,def_lhs_atom93]) ).
fof(def_lhs_atom94,axiom,
! [V_x,V_f,T_a] :
( lhs_atom94(V_x,V_f,T_a)
<=> ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_x)) ),
inference(definition,[],]) ).
fof(to_be_clausified_93,plain,
! [T_a,V_f,V_x] :
( lhs_atom94(V_x,V_f,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_empty__fold1SetE_0_0,def_lhs_atom94]) ).
fof(def_lhs_atom95,axiom,
! [T_a] :
( lhs_atom95(T_a)
<=> hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_94,plain,
! [T_a] :
( lhs_atom95(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__empty_2_0,def_lhs_atom95]) ).
fof(def_lhs_atom96,axiom,
! [V_f,T_b,T_a] :
( lhs_atom96(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_95,plain,
! [T_a,T_b,V_f] :
( lhs_atom96(V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_vimage__empty_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_Map_Omap__le(V_f,c_Map_Omap__add(V_g,V_f,T_a,T_b),T_a,T_b) ),
inference(definition,[],]) ).
fof(to_be_clausified_96,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_map__le__map__add_0_0,def_lhs_atom97]) ).
fof(def_lhs_atom98,axiom,
! [V_f,V_B,V_A,T_b,T_a] :
( lhs_atom98(V_f,V_B,V_A,T_b,T_a)
<=> c_Set_Ovimage(V_f,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_b,tc_bool)),V_A),V_B),T_a,T_b) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Set_Ovimage(V_f,V_A,T_a,T_b)),c_Set_Ovimage(V_f,V_B,T_a,T_b)) ),
inference(definition,[],]) ).
fof(to_be_clausified_97,plain,
! [T_a,T_b,V_A,V_B,V_f] :
( lhs_atom98(V_f,V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_vimage__Un_0_0,def_lhs_atom98]) ).
fof(def_lhs_atom99,axiom,
! [V_B,V_A,T_a] :
( lhs_atom99(V_B,V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B) ),
inference(definition,[],]) ).
fof(to_be_clausified_98,plain,
! [T_a,V_A,V_B] :
( lhs_atom99(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__left__absorb_0_0,def_lhs_atom99]) ).
fof(def_lhs_atom100,axiom,
! [V_B,V_A,T_a] :
( lhs_atom100(V_B,V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_A) ),
inference(definition,[],]) ).
fof(to_be_clausified_99,plain,
! [T_a,V_A,V_B] :
( lhs_atom100(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__commute_0_0,def_lhs_atom100]) ).
fof(def_lhs_atom101,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom101(V_C,V_B,V_A,T_a)
<=> c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),V_C,tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),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))) ),
inference(definition,[],]) ).
fof(to_be_clausified_100,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom101(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__Diff_0_0,def_lhs_atom101]) ).
fof(def_lhs_atom102,axiom,
! [V_B,V_A,T_a] :
( lhs_atom102(V_B,V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool))) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B) ),
inference(definition,[],]) ).
fof(to_be_clausified_101,plain,
! [T_a,V_A,V_B] :
( lhs_atom102(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__Diff__cancel_0_0,def_lhs_atom102]) ).
fof(def_lhs_atom103,axiom,
! [V_B,V_A,T_a] :
( lhs_atom103(V_B,V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool))),V_A) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_A) ),
inference(definition,[],]) ).
fof(to_be_clausified_102,plain,
! [T_a,V_A,V_B] :
( lhs_atom103(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__Diff__cancel2_0_0,def_lhs_atom103]) ).
fof(def_lhs_atom104,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom104(V_C,V_B,V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)) ),
inference(definition,[],]) ).
fof(to_be_clausified_103,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom104(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__assoc_0_0,def_lhs_atom104]) ).
fof(def_lhs_atom105,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom105(V_C,V_B,V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_C)) ),
inference(definition,[],]) ).
fof(to_be_clausified_104,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom105(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__left__commute_0_0,def_lhs_atom105]) ).
fof(def_lhs_atom106,axiom,
! [V_a_H,T_a] :
( lhs_atom106(V_a_H,T_a)
<=> c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H) ),
inference(definition,[],]) ).
fof(to_be_clausified_105,plain,
! [T_a,V_a_H] :
( lhs_atom106(V_a_H,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_option_Osimps_I2_J_0_0,def_lhs_atom106]) ).
fof(def_lhs_atom107,axiom,
! [V_y,T_a] :
( lhs_atom107(V_y,T_a)
<=> c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_y) ),
inference(definition,[],]) ).
fof(to_be_clausified_106,plain,
! [T_a,V_y] :
( lhs_atom107(V_y,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_not__Some__eq_1_0,def_lhs_atom107]) ).
fof(def_lhs_atom108,axiom,
! [V_B,V_A,T_a] :
( lhs_atom108(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_107,plain,
! [T_a,V_A,V_B] :
( lhs_atom108(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__idemp_0_0,def_lhs_atom108]) ).
fof(def_lhs_atom109,axiom,
! [V_A,T_a] :
( lhs_atom109(V_A,T_a)
<=> hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_A) = V_A ),
inference(definition,[],]) ).
fof(to_be_clausified_108,plain,
! [T_a,V_A] :
( lhs_atom109(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__absorb_0_0,def_lhs_atom109]) ).
fof(def_lhs_atom110,axiom,
! [V_f,V_A,T_a] :
( lhs_atom110(V_f,V_A,T_a)
<=> hAPP(c_Finite__Set_Ofold1(V_f,T_a),V_A) = c_The(c_Finite__Set_Ofold1Set(V_f,V_A,T_a),T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_109,plain,
! [T_a,V_A,V_f] :
( lhs_atom110(V_f,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_fold1__def_0_0,def_lhs_atom110]) ).
fof(def_lhs_atom111,axiom,
! [V_f,V_B,V_A,T_b,T_a] :
( lhs_atom111(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_110,plain,
! [T_a,T_b,V_A,V_B,V_f] :
( lhs_atom111(V_f,V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_vimage__Diff_0_0,def_lhs_atom111]) ).
fof(def_lhs_atom112,axiom,
! [V_f,T_b,T_a] :
( lhs_atom112(V_f,T_b,T_a)
<=> c_Map_Omap__le(V_f,V_f,T_a,T_b) ),
inference(definition,[],]) ).
fof(to_be_clausified_111,plain,
! [T_a,T_b,V_f] :
( lhs_atom112(V_f,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_map__le__refl_0_0,def_lhs_atom112]) ).
fof(def_lhs_atom113,axiom,
! [V_n,V_m,T_b,T_a] :
( lhs_atom113(V_n,V_m,T_b,T_a)
<=> c_Map_Odom(c_Map_Omap__add(V_m,V_n,T_a,T_b),T_a,T_b) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Map_Odom(V_n,T_a,T_b)),c_Map_Odom(V_m,T_a,T_b)) ),
inference(definition,[],]) ).
fof(to_be_clausified_112,plain,
! [T_a,T_b,V_m,V_n] :
( lhs_atom113(V_n,V_m,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_dom__map__add_0_0,def_lhs_atom113]) ).
fof(def_lhs_atom114,axiom,
! [V_a_H,T_a] :
( lhs_atom114(V_a_H,T_a)
<=> hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_113,plain,
! [T_a,V_a_H] :
( lhs_atom114(V_a_H,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_option_Osimps_I3_J_0_0,def_lhs_atom114]) ).
fof(def_lhs_atom115,axiom,
! [V_xa,T_a] :
( lhs_atom115(V_xa,T_a)
<=> hAPP(c_Option_Ooption_OSome(T_a),V_xa) != c_Option_Ooption_ONone(T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_114,plain,
! [T_a,V_xa] :
( lhs_atom115(V_xa,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_not__None__eq_1_0,def_lhs_atom115]) ).
fof(def_lhs_atom116,axiom,
! [V_m3,V_m2,V_m1,T_b,T_a] :
( lhs_atom116(V_m3,V_m2,V_m1,T_b,T_a)
<=> c_Map_Omap__add(V_m1,c_Map_Omap__add(V_m2,V_m3,T_a,T_b),T_a,T_b) = c_Map_Omap__add(c_Map_Omap__add(V_m1,V_m2,T_a,T_b),V_m3,T_a,T_b) ),
inference(definition,[],]) ).
fof(to_be_clausified_115,plain,
! [T_a,T_b,V_m1,V_m2,V_m3] :
( lhs_atom116(V_m3,V_m2,V_m1,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_map__add__assoc_0_0,def_lhs_atom116]) ).
fof(def_lhs_atom117,axiom,
! [V_x,T_a] :
( lhs_atom117(V_x,T_a)
<=> c_The(hAPP(c_fequal(T_a),V_x),T_a) = V_x ),
inference(definition,[],]) ).
fof(to_be_clausified_116,plain,
! [T_a,V_x] :
( lhs_atom117(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_the__sym__eq__trivial_0_0,def_lhs_atom117]) ).
fof(def_lhs_atom118,axiom,
! [V_x,T_a] :
( lhs_atom118(V_x,T_a)
<=> c_Option_Othe(hAPP(c_Option_Ooption_OSome(T_a),V_x),T_a) = V_x ),
inference(definition,[],]) ).
fof(to_be_clausified_117,plain,
! [T_a,V_x] :
( lhs_atom118(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_the_Osimps_0_0,def_lhs_atom118]) ).
fof(def_lhs_atom119,axiom,
! [V_x,V_f,T_a] :
( lhs_atom119(V_x,V_f,T_a)
<=> hBOOL(hAPP(c_Finite__Set_Ofold1Set(V_f,hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),T_a),V_x)) ),
inference(definition,[],]) ).
fof(to_be_clausified_118,plain,
! [T_a,V_f,V_x] :
( lhs_atom119(V_x,V_f,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_fold1Set__sing_1_0,def_lhs_atom119]) ).
fof(def_lhs_atom120,axiom,
! [V_x,T_a] :
( lhs_atom120(V_x,T_a)
<=> c_The(hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),T_a) = V_x ),
inference(definition,[],]) ).
fof(to_be_clausified_119,plain,
! [T_a,V_x] :
( lhs_atom120(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Nitpick_OThe__psimp_0_0,def_lhs_atom120]) ).
fof(def_lhs_atom121,axiom,
! [V_a,V_B,V_A,T_a] :
( lhs_atom121(V_a,V_B,V_A,T_a)
<=> c_HOL_Ominus__class_Ominus(V_A,hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_A,hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_120,plain,
! [T_a,V_A,V_B,V_a] :
( lhs_atom121(V_a,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__insert2_0_0,def_lhs_atom121]) ).
fof(def_lhs_atom122,axiom,
! [V_a,V_B,V_A,T_a] :
( lhs_atom122(V_a,V_B,V_A,T_a)
<=> c_HOL_Ominus__class_Ominus(V_A,hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B),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)),hAPP(hAPP(c_Set_Oinsert(T_a),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_121,plain,
! [T_a,V_A,V_B,V_a] :
( lhs_atom122(V_a,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Diff__insert_0_0,def_lhs_atom122]) ).
fof(def_lhs_atom123,axiom,
! [V_x,T_a] :
( lhs_atom123(V_x,T_a)
<=> c_Set_Ocontents(hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),T_a) = V_x ),
inference(definition,[],]) ).
fof(to_be_clausified_122,plain,
! [T_a,V_x] :
( lhs_atom123(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_contents__eq_0_0,def_lhs_atom123]) ).
fof(def_lhs_atom124,axiom,
! [V_f,V_a,T_a] :
( lhs_atom124(V_f,V_a,T_a)
<=> hAPP(c_Finite__Set_Ofold1(V_f,T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) = V_a ),
inference(definition,[],]) ).
fof(to_be_clausified_123,plain,
! [T_a,V_a,V_f] :
( lhs_atom124(V_f,V_a,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_fold1__singleton_0_0,def_lhs_atom124]) ).
fof(def_lhs_atom125,axiom,
! [V_a,V_A,T_a] :
( lhs_atom125(V_a,V_A,T_a)
<=> hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_HOL_Ominus__class_Ominus(V_A,hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),tc_fun(T_a,tc_bool))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_A) ),
inference(definition,[],]) ).
fof(to_be_clausified_124,plain,
! [T_a,V_A,V_a] :
( lhs_atom125(V_a,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__Diff__single_0_0,def_lhs_atom125]) ).
fof(def_lhs_atom126,axiom,
! [V_a,V_A,T_a] :
( lhs_atom126(V_a,V_A,T_a)
<=> hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_A) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),V_A) ),
inference(definition,[],]) ).
fof(to_be_clausified_125,plain,
! [T_a,V_A,V_a] :
( lhs_atom126(V_a,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__is__Un_0_0,def_lhs_atom126]) ).
fof(def_lhs_atom127,axiom,
! [V_c] :
( lhs_atom127(V_c)
<=> c_Hoare__Mirabelle_OMGT(V_c) = c_Hoare__Mirabelle_Otriple_Otriple(c_fequal(tc_Com_Ostate),V_c,c_Natural_Oevalc(V_c),tc_Com_Ostate) ),
inference(definition,[],]) ).
fof(to_be_clausified_126,plain,
! [V_c] :
( lhs_atom127(V_c)
| $false ),
inference(fold_definition,[status(thm)],[cls_MGT__def_0_0,def_lhs_atom127]) ).
fof(def_lhs_atom128,axiom,
! [V_f,V_a,T_aa,T_a] :
( lhs_atom128(V_f,V_a,T_aa,T_a)
<=> hBOOL(hAPP(hAPP(c_in(T_aa),V_a),c_Set_Ovimage(V_f,hAPP(hAPP(c_Set_Oinsert(T_a),hAPP(V_f,V_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),T_aa,T_a))) ),
inference(definition,[],]) ).
fof(to_be_clausified_127,plain,
! [T_a,T_aa,V_a,V_f] :
( lhs_atom128(V_f,V_a,T_aa,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_vimage__singleton__eq_1_0,def_lhs_atom128]) ).
fof(def_lhs_atom129,axiom,
( lhs_atom129
<=> c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname) ),
inference(definition,[],]) ).
fof(to_be_clausified_128,plain,
( lhs_atom129
| $false ),
inference(fold_definition,[status(thm)],[cls_finite__dom__body_0_0,def_lhs_atom129]) ).
fof(def_lhs_atom130,axiom,
! [V_pname_H] :
( lhs_atom130(V_pname_H)
<=> c_Com_Ocom_OBODY(V_pname_H) != c_Com_Ocom_OSKIP ),
inference(definition,[],]) ).
fof(to_be_clausified_129,plain,
! [V_pname_H] :
( lhs_atom130(V_pname_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I19_J_0_0,def_lhs_atom130]) ).
fof(def_lhs_atom131,axiom,
! [V_x,T_a] :
( lhs_atom131(V_x,T_a)
<=> hBOOL(hAPP(hAPP(c_in(T_a),V_x),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))) ),
inference(definition,[],]) ).
fof(to_be_clausified_130,plain,
! [T_a,V_x] :
( lhs_atom131(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_singleton__iff_1_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(hAPP(c_Set_Oinsert(T_a),V_x),V_A),V_x)) ),
inference(definition,[],]) ).
fof(to_be_clausified_131,plain,
! [T_a,V_A,V_x] :
( lhs_atom132(V_x,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__code_1_0,def_lhs_atom132]) ).
fof(def_lhs_atom133,axiom,
! [V_P,V_G,T_a] :
( lhs_atom133(V_P,V_G,T_a)
<=> c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OSKIP,V_P,T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))),T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_132,plain,
! [T_a,V_G,V_P] :
( lhs_atom133(V_P,V_G,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_hoare__derivs_OSkip_0_0,def_lhs_atom133]) ).
fof(def_lhs_atom134,axiom,
! [V_x,T_a] :
( lhs_atom134(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_133,plain,
! [T_a,V_x] :
( lhs_atom134(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_ex__in__conv_0_0,def_lhs_atom134]) ).
fof(def_lhs_atom135,axiom,
! [V_c,T_a] :
( lhs_atom135(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_134,plain,
! [T_a,V_c] :
( lhs_atom135(V_c,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_empty__iff_0_0,def_lhs_atom135]) ).
fof(def_lhs_atom136,axiom,
! [V_a,T_a] :
( lhs_atom136(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_135,plain,
! [T_a,V_a] :
( lhs_atom136(V_a,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_emptyE_0_0,def_lhs_atom136]) ).
fof(def_lhs_atom137,axiom,
! [V_a,V_A,T_a] :
( lhs_atom137(V_a,V_A,T_a)
<=> c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_A) ),
inference(definition,[],]) ).
fof(to_be_clausified_136,plain,
! [T_a,V_A,V_a] :
( lhs_atom137(V_a,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_empty__not__insert_0_0,def_lhs_atom137]) ).
fof(def_lhs_atom138,axiom,
( lhs_atom138
<=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = 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_137,plain,
( lhs_atom138
| $false ),
inference(fold_definition,[status(thm)],[cls_bot__empty__eq_0_0,def_lhs_atom138]) ).
fof(def_lhs_atom139,axiom,
! [V_s] :
( lhs_atom139(V_s)
<=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)) ),
inference(definition,[],]) ).
fof(to_be_clausified_138,plain,
! [V_s] :
( lhs_atom139(V_s)
| $false ),
inference(fold_definition,[status(thm)],[cls_evalc_OSkip_0_0,def_lhs_atom139]) ).
fof(def_lhs_atom140,axiom,
! [V_x,T_a] :
( lhs_atom140(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_139,plain,
! [T_a,V_x] :
( lhs_atom140(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_bot1E_0_0,def_lhs_atom140]) ).
fof(def_lhs_atom141,axiom,
! [V_G,T_a] :
( lhs_atom141(V_G,T_a)
<=> c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_140,plain,
! [T_a,V_G] :
( lhs_atom141(V_G,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_empty_0_0,def_lhs_atom141]) ).
fof(def_lhs_atom142,axiom,
! [V_x,V_A,T_a] :
( lhs_atom142(V_x,V_A,T_a)
<=> hAPP(hAPP(c_Set_Oinsert(T_a),V_x),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_A)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_A) ),
inference(definition,[],]) ).
fof(to_be_clausified_141,plain,
! [T_a,V_A,V_x] :
( lhs_atom142(V_x,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__absorb2_0_0,def_lhs_atom142]) ).
fof(def_lhs_atom143,axiom,
! [V_a,V_A,T_a] :
( lhs_atom143(V_a,V_A,T_a)
<=> hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_A) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_142,plain,
! [T_a,V_A,V_a] :
( lhs_atom143(V_a,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__not__empty_0_0,def_lhs_atom143]) ).
fof(def_lhs_atom144,axiom,
! [V_x,V_A,T_a] :
( lhs_atom144(V_x,V_A,T_a)
<=> hBOOL(hAPP(hAPP(c_in(T_a),V_x),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_A))) ),
inference(definition,[],]) ).
fof(to_be_clausified_143,plain,
! [T_a,V_A,V_x] :
( lhs_atom144(V_x,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__iff_1_0,def_lhs_atom144]) ).
fof(def_lhs_atom145,axiom,
! [V_a,V_B,T_a] :
( lhs_atom145(V_a,V_B,T_a)
<=> hBOOL(hAPP(hAPP(c_in(T_a),V_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B))) ),
inference(definition,[],]) ).
fof(to_be_clausified_144,plain,
! [T_a,V_B,V_a] :
( lhs_atom145(V_a,V_B,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insertI1_0_0,def_lhs_atom145]) ).
fof(def_lhs_atom146,axiom,
! [V_x,V_B,T_a] :
( lhs_atom146(V_x,V_B,T_a)
<=> hBOOL(hAPP(hAPP(c_in(T_a),V_x),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_B))) ),
inference(definition,[],]) ).
fof(to_be_clausified_145,plain,
! [T_a,V_B,V_x] :
( lhs_atom146(V_x,V_B,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insertCI_1_0,def_lhs_atom146]) ).
fof(def_lhs_atom147,axiom,
! [V_y,V_x,V_A,T_a] :
( lhs_atom147(V_y,V_x,V_A,T_a)
<=> hAPP(hAPP(c_Set_Oinsert(T_a),V_x),hAPP(hAPP(c_Set_Oinsert(T_a),V_y),V_A)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_y),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_A)) ),
inference(definition,[],]) ).
fof(to_be_clausified_146,plain,
! [T_a,V_A,V_x,V_y] :
( lhs_atom147(V_y,V_x,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__commute_0_0,def_lhs_atom147]) ).
fof(def_lhs_atom148,axiom,
! [V_xa,V_x,T_a] :
( lhs_atom148(V_xa,V_x,T_a)
<=> hAPP(hAPP(c_Set_Oinsert(T_a),V_xa),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x),hAPP(hAPP(c_Set_Oinsert(T_a),V_xa),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) ),
inference(definition,[],]) ).
fof(to_be_clausified_147,plain,
! [T_a,V_x,V_xa] :
( lhs_atom148(V_xa,V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_doubleton__eq__iff_4_0,def_lhs_atom148]) ).
fof(def_lhs_atom149,axiom,
! [V_pname_H] :
( lhs_atom149(V_pname_H)
<=> c_Com_Ocom_OSKIP != c_Com_Ocom_OBODY(V_pname_H) ),
inference(definition,[],]) ).
fof(to_be_clausified_148,plain,
! [V_pname_H] :
( lhs_atom149(V_pname_H)
| $false ),
inference(fold_definition,[status(thm)],[cls_com_Osimps_I18_J_0_0,def_lhs_atom149]) ).
fof(def_lhs_atom150,axiom,
( lhs_atom150
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_149,plain,
( lhs_atom150
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add_0,def_lhs_atom150]) ).
fof(def_lhs_atom151,axiom,
( lhs_atom151
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_150,plain,
( lhs_atom151
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le_0,def_lhs_atom151]) ).
fof(def_lhs_atom152,axiom,
( lhs_atom152
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_151,plain,
( lhs_atom152
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict_0,def_lhs_atom152]) ).
fof(def_lhs_atom153,axiom,
( lhs_atom153
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_152,plain,
( lhs_atom153
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Opordered__cancel__semiring_0,def_lhs_atom153]) ).
fof(def_lhs_atom154,axiom,
( lhs_atom154
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_153,plain,
( lhs_atom154
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__semiring__strict_0,def_lhs_atom154]) ).
fof(def_lhs_atom155,axiom,
( lhs_atom155
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_154,plain,
( lhs_atom155
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add_0,def_lhs_atom155]) ).
fof(def_lhs_atom156,axiom,
( lhs_atom156
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_155,plain,
( lhs_atom156
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Opordered__comm__monoid__add_0,def_lhs_atom156]) ).
fof(def_lhs_atom157,axiom,
( lhs_atom157
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_156,plain,
( lhs_atom157
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add_0,def_lhs_atom157]) ).
fof(def_lhs_atom158,axiom,
( lhs_atom158
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_157,plain,
( lhs_atom158
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Ocancel__semigroup__add_0,def_lhs_atom158]) ).
fof(def_lhs_atom159,axiom,
( lhs_atom159
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_158,plain,
( lhs_atom159
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Opordered__semiring_0,def_lhs_atom159]) ).
fof(def_lhs_atom160,axiom,
( lhs_atom160
<=> class_Ring__and__Field_Oordered__semiring(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_159,plain,
( lhs_atom160
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__semiring_0,def_lhs_atom160]) ).
fof(def_lhs_atom161,axiom,
( lhs_atom161
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_160,plain,
( lhs_atom161
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Ono__zero__divisors_0,def_lhs_atom161]) ).
fof(def_lhs_atom162,axiom,
( lhs_atom162
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_161,plain,
( lhs_atom162
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Oordered__semidom_0,def_lhs_atom162]) ).
fof(def_lhs_atom163,axiom,
( lhs_atom163
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_162,plain,
( lhs_atom163
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Ocomm__semiring__1_0,def_lhs_atom163]) ).
fof(def_lhs_atom164,axiom,
( lhs_atom164
<=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_163,plain,
( lhs_atom164
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Oab__semigroup__mult_0,def_lhs_atom164]) ).
fof(def_lhs_atom165,axiom,
( lhs_atom165
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_164,plain,
( lhs_atom165
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Ocomm__monoid__mult_0,def_lhs_atom165]) ).
fof(def_lhs_atom166,axiom,
( lhs_atom166
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_165,plain,
( lhs_atom166
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Oab__semigroup__add_0,def_lhs_atom166]) ).
fof(def_lhs_atom167,axiom,
( lhs_atom167
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_166,plain,
( lhs_atom167
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Ocomm__semiring_0,def_lhs_atom167]) ).
fof(def_lhs_atom168,axiom,
( lhs_atom168
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_167,plain,
( lhs_atom168
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Ocomm__monoid__add_0,def_lhs_atom168]) ).
fof(def_lhs_atom169,axiom,
( lhs_atom169
<=> class_Lattices_Oupper__semilattice(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_168,plain,
( lhs_atom169
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Lattices_Oupper__semilattice_0,def_lhs_atom169]) ).
fof(def_lhs_atom170,axiom,
( lhs_atom170
<=> class_Lattices_Olower__semilattice(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_169,plain,
( lhs_atom170
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Lattices_Olower__semilattice_0,def_lhs_atom170]) ).
fof(def_lhs_atom171,axiom,
( lhs_atom171
<=> class_Ring__and__Field_Omult__mono1(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_170,plain,
( lhs_atom171
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Omult__mono1_0,def_lhs_atom171]) ).
fof(def_lhs_atom172,axiom,
( lhs_atom172
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_171,plain,
( lhs_atom172
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Omult__zero_0,def_lhs_atom172]) ).
fof(def_lhs_atom173,axiom,
( lhs_atom173
<=> class_Ring__and__Field_Omult__mono(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_172,plain,
( lhs_atom173
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Omult__mono_0,def_lhs_atom173]) ).
fof(def_lhs_atom174,axiom,
( lhs_atom174
<=> class_Lattices_Odistrib__lattice(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_173,plain,
( lhs_atom174
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Lattices_Odistrib__lattice_0,def_lhs_atom174]) ).
fof(def_lhs_atom175,axiom,
( lhs_atom175
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_174,plain,
( lhs_atom175
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Ring__and__Field_Osemiring_0,def_lhs_atom175]) ).
fof(def_lhs_atom176,axiom,
( lhs_atom176
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_175,plain,
( lhs_atom176
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__OrderedGroup_Omonoid__add_0,def_lhs_atom176]) ).
fof(def_lhs_atom177,axiom,
( lhs_atom177
<=> class_Orderings_Opreorder(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_176,plain,
( lhs_atom177
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Opreorder_0,def_lhs_atom177]) ).
fof(def_lhs_atom178,axiom,
( lhs_atom178
<=> class_Orderings_Olinorder(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_177,plain,
( lhs_atom178
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Olinorder_0,def_lhs_atom178]) ).
fof(def_lhs_atom179,axiom,
( lhs_atom179
<=> class_Lattices_Olattice(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_178,plain,
( lhs_atom179
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Lattices_Olattice_0,def_lhs_atom179]) ).
fof(def_lhs_atom180,axiom,
( lhs_atom180
<=> class_Orderings_Oorder(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_179,plain,
( lhs_atom180
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Oorder_0,def_lhs_atom180]) ).
fof(def_lhs_atom181,axiom,
( lhs_atom181
<=> class_Orderings_Obot(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_180,plain,
( lhs_atom181
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__Orderings_Obot_0,def_lhs_atom181]) ).
fof(def_lhs_atom182,axiom,
( lhs_atom182
<=> class_HOL_Ominus(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_181,plain,
( lhs_atom182
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__HOL_Ominus_0,def_lhs_atom182]) ).
fof(def_lhs_atom183,axiom,
( lhs_atom183
<=> class_HOL_Oord(tc_nat) ),
inference(definition,[],]) ).
fof(to_be_clausified_182,plain,
( lhs_atom183
| $false ),
inference(fold_definition,[status(thm)],[clsarity_nat__HOL_Oord_0,def_lhs_atom183]) ).
fof(def_lhs_atom184,axiom,
( lhs_atom184
<=> class_Complete__Lattice_Ocomplete__lattice(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_183,plain,
( lhs_atom184
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Complete__Lattice_Ocomplete__lattice_0,def_lhs_atom184]) ).
fof(def_lhs_atom185,axiom,
( lhs_atom185
<=> class_Lattices_Oupper__semilattice(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_184,plain,
( lhs_atom185
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Lattices_Oupper__semilattice_0,def_lhs_atom185]) ).
fof(def_lhs_atom186,axiom,
( lhs_atom186
<=> class_Lattices_Olower__semilattice(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_185,plain,
( lhs_atom186
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Lattices_Olower__semilattice_0,def_lhs_atom186]) ).
fof(def_lhs_atom187,axiom,
( lhs_atom187
<=> class_Lattices_Odistrib__lattice(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_186,plain,
( lhs_atom187
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Lattices_Odistrib__lattice_0,def_lhs_atom187]) ).
fof(def_lhs_atom188,axiom,
( lhs_atom188
<=> class_Lattices_Obounded__lattice(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_187,plain,
( lhs_atom188
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Lattices_Obounded__lattice_0,def_lhs_atom188]) ).
fof(def_lhs_atom189,axiom,
( lhs_atom189
<=> class_Finite__Set_Ofinite_Ofinite(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_188,plain,
( lhs_atom189
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Finite__Set_Ofinite_Ofinite_0,def_lhs_atom189]) ).
fof(def_lhs_atom190,axiom,
( lhs_atom190
<=> class_Orderings_Opreorder(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_189,plain,
( lhs_atom190
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Orderings_Opreorder_0,def_lhs_atom190]) ).
fof(def_lhs_atom191,axiom,
( lhs_atom191
<=> class_Lattices_Olattice(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_190,plain,
( lhs_atom191
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Lattices_Olattice_0,def_lhs_atom191]) ).
fof(def_lhs_atom192,axiom,
( lhs_atom192
<=> class_Orderings_Oorder(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_191,plain,
( lhs_atom192
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Orderings_Oorder_0,def_lhs_atom192]) ).
fof(def_lhs_atom193,axiom,
( lhs_atom193
<=> class_Orderings_Obot(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_192,plain,
( lhs_atom193
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Orderings_Obot_0,def_lhs_atom193]) ).
fof(def_lhs_atom194,axiom,
( lhs_atom194
<=> class_HOL_Ominus(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_193,plain,
( lhs_atom194
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__HOL_Ominus_0,def_lhs_atom194]) ).
fof(def_lhs_atom195,axiom,
( lhs_atom195
<=> class_HOL_Oord(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_194,plain,
( lhs_atom195
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__HOL_Oord_0,def_lhs_atom195]) ).
fof(def_lhs_atom196,axiom,
! [V_x,T_a] :
( lhs_atom196(V_x,T_a)
<=> hBOOL(hAPP(hAPP(c_fequal(T_a),V_x),V_x)) ),
inference(definition,[],]) ).
fof(to_be_clausified_195,plain,
! [T_a,V_x] :
( lhs_atom196(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_ATP__Linkup_Oequal__imp__fequal_0_0,def_lhs_atom196]) ).
% Start CNF derivation
fof(c_0_0,axiom,
! [X14,X7,X24,X4,X6,X2] :
( lhs_atom67(X14,X7,X24,X4,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_66) ).
fof(c_0_1,axiom,
! [X14,X7,X12,X13,X6,X2] :
( lhs_atom60(X14,X7,X12,X13,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_59) ).
fof(c_0_2,axiom,
! [X18,X19,X20,X21,X6,X2] :
( lhs_atom20(X18,X19,X20,X21,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_19) ).
fof(c_0_3,axiom,
! [X3,X14,X7,X4,X6,X2] :
( lhs_atom11(X3,X14,X7,X4,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_10) ).
fof(c_0_4,axiom,
! [X34,X31,X32,X6,X2] :
( lhs_atom116(X34,X31,X32,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_115) ).
fof(c_0_5,axiom,
! [X4,X11,X5,X6,X2] :
( lhs_atom111(X4,X11,X5,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_110) ).
fof(c_0_6,axiom,
! [X4,X11,X5,X6,X2] :
( lhs_atom98(X4,X11,X5,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_97) ).
fof(c_0_7,axiom,
! [X4,X1,X11,X6,X2] :
( lhs_atom74(X4,X1,X11,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_73) ).
fof(c_0_8,axiom,
! [X3,X24,X4,X6,X2] :
( lhs_atom48(X3,X24,X4,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_47) ).
fof(c_0_9,axiom,
! [X4,X11,X5,X6,X2] :
( lhs_atom47(X4,X11,X5,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_46) ).
fof(c_0_10,axiom,
! [X23,X7,X12,X22,X2] :
( lhs_atom46(X23,X7,X12,X22,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_45) ).
fof(c_0_11,axiom,
! [X14,X7,X4,X22,X2] :
( lhs_atom28(X14,X7,X4,X22,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_27) ).
fof(c_0_12,axiom,
! [X14,X7,X4,X6,X2] :
( lhs_atom26(X14,X7,X4,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_25) ).
fof(c_0_13,axiom,
! [X16,X17,X1,X6,X2] :
( lhs_atom17(X16,X17,X1,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_16) ).
fof(c_0_14,axiom,
! [X4,X1,X5,X6,X2] :
( lhs_atom8(X4,X1,X5,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_7) ).
fof(c_0_15,axiom,
! [X12,X11,X5,X6,X2] :
( lhs_atom6(X12,X11,X5,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_5) ).
fof(c_0_16,axiom,
! [X7,X8,X9,X6,X2] :
( lhs_atom3(X7,X8,X9,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_2) ).
fof(c_0_17,axiom,
! [X3,X4,X5,X6,X2] :
( lhs_atom2(X3,X4,X5,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_1) ).
fof(c_0_18,axiom,
! [X14,X7,X5,X2] :
( lhs_atom147(X14,X7,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_146) ).
fof(c_0_19,axiom,
! [X4,X1,X22,X2] :
( lhs_atom128(X4,X1,X22,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_127) ).
fof(c_0_20,axiom,
! [X1,X11,X5,X2] :
( lhs_atom122(X1,X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_121) ).
fof(c_0_21,axiom,
! [X1,X11,X5,X2] :
( lhs_atom121(X1,X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_120) ).
fof(c_0_22,axiom,
! [X15,X12,X6,X2] :
( lhs_atom113(X15,X12,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_112) ).
fof(c_0_23,axiom,
! [X10,X11,X5,X2] :
( lhs_atom105(X10,X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_104) ).
fof(c_0_24,axiom,
! [X10,X11,X5,X2] :
( lhs_atom104(X10,X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_103) ).
fof(c_0_25,axiom,
! [X10,X11,X5,X2] :
( lhs_atom101(X10,X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_100) ).
fof(c_0_26,axiom,
! [X24,X4,X6,X2] :
( lhs_atom97(X24,X4,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_96) ).
fof(c_0_27,axiom,
! [X23,X7,X6,X2] :
( lhs_atom89(X23,X7,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_88) ).
fof(c_0_28,axiom,
! [X7,X4,X6,X2] :
( lhs_atom82(X7,X4,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_81) ).
fof(c_0_29,axiom,
! [X1,X10,X11,X2] :
( lhs_atom76(X1,X10,X11,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_75) ).
fof(c_0_30,axiom,
! [X1,X11,X5,X2] :
( lhs_atom75(X1,X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_74) ).
fof(c_0_31,axiom,
! [X7,X4,X6,X2] :
( lhs_atom70(X7,X4,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_69) ).
fof(c_0_32,axiom,
! [X10,X11,X5,X2] :
( lhs_atom65(X10,X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_64) ).
fof(c_0_33,axiom,
! [X10,X11,X5,X2] :
( lhs_atom64(X10,X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_63) ).
fof(c_0_34,axiom,
! [X1,X11,X5,X2] :
( lhs_atom59(X1,X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_58) ).
fof(c_0_35,axiom,
! [X3,X4,X6,X2] :
( lhs_atom56(X3,X4,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_55) ).
fof(c_0_36,axiom,
! [X3,X4,X6,X2] :
( lhs_atom55(X3,X4,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_54) ).
fof(c_0_37,axiom,
! [X3,X4,X6,X2] :
( lhs_atom49(X3,X4,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_48) ).
fof(c_0_38,axiom,
! [X10,X11,X5,X2] :
( lhs_atom45(X10,X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_44) ).
fof(c_0_39,axiom,
! [X10,X11,X5,X2] :
( lhs_atom39(X10,X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_38) ).
fof(c_0_40,axiom,
! [X10,X11,X5,X2] :
( lhs_atom33(X10,X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_32) ).
fof(c_0_41,axiom,
! [X10,X11,X5,X2] :
( lhs_atom32(X10,X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_31) ).
fof(c_0_42,axiom,
! [X7,X4,X22,X2] :
( lhs_atom29(X7,X4,X22,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_28) ).
fof(c_0_43,axiom,
! [X7,X4,X6,X2] :
( lhs_atom27(X7,X4,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_26) ).
fof(c_0_44,axiom,
! [X7,X4,X6,X2] :
( lhs_atom25(X7,X4,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_24) ).
fof(c_0_45,axiom,
! [X16,X17,X6,X2] :
( lhs_atom22(X16,X17,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_21) ).
fof(c_0_46,axiom,
! [X19,X20,X6,X2] :
( lhs_atom21(X19,X20,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_20) ).
fof(c_0_47,axiom,
! [X10,X11,X5,X2] :
( lhs_atom19(X10,X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_18) ).
fof(c_0_48,axiom,
! [X10,X11,X5,X2] :
( lhs_atom18(X10,X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_17) ).
fof(c_0_49,axiom,
! [X12,X5,X6,X2] :
( lhs_atom16(X12,X5,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_15) ).
fof(c_0_50,axiom,
! [X10,X11,X5,X2] :
( lhs_atom12(X10,X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_11) ).
fof(c_0_51,axiom,
! [X10,X11,X5,X2] :
( lhs_atom10(X10,X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_9) ).
fof(c_0_52,axiom,
! [X10,X11,X5,X2] :
( lhs_atom9(X10,X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_8) ).
fof(c_0_53,axiom,
! [X10,X11,X5,X2] :
( lhs_atom5(X10,X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_4) ).
fof(c_0_54,axiom,
! [X10,X11,X5,X2] :
( lhs_atom4(X10,X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_3) ).
fof(c_0_55,axiom,
! [X23,X7,X2] :
( lhs_atom148(X23,X7,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_147) ).
fof(c_0_56,axiom,
! [X7,X11,X2] :
( lhs_atom146(X7,X11,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_145) ).
fof(c_0_57,axiom,
! [X1,X11,X2] :
( lhs_atom145(X1,X11,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_144) ).
fof(c_0_58,axiom,
! [X7,X5,X2] :
( lhs_atom144(X7,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_143) ).
fof(c_0_59,axiom,
! [X1,X5,X2] :
( lhs_atom143(X1,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_142) ).
fof(c_0_60,axiom,
! [X7,X5,X2] :
( lhs_atom142(X7,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_141) ).
fof(c_0_61,axiom,
! [X1,X5,X2] :
( lhs_atom137(X1,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_136) ).
fof(c_0_62,axiom,
! [X20,X36,X2] :
( lhs_atom133(X20,X36,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_132) ).
fof(c_0_63,axiom,
! [X7,X5,X2] :
( lhs_atom132(X7,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_131) ).
fof(c_0_64,axiom,
! [X1,X5,X2] :
( lhs_atom126(X1,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_125) ).
fof(c_0_65,axiom,
! [X1,X5,X2] :
( lhs_atom125(X1,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_124) ).
fof(c_0_66,axiom,
! [X4,X1,X2] :
( lhs_atom124(X4,X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_123) ).
fof(c_0_67,axiom,
! [X7,X4,X2] :
( lhs_atom119(X7,X4,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_118) ).
fof(c_0_68,axiom,
! [X4,X6,X2] :
( lhs_atom112(X4,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_111) ).
fof(c_0_69,axiom,
! [X4,X5,X2] :
( lhs_atom110(X4,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_109) ).
fof(c_0_70,axiom,
! [X11,X5,X2] :
( lhs_atom108(X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_107) ).
fof(c_0_71,axiom,
! [X11,X5,X2] :
( lhs_atom103(X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_102) ).
fof(c_0_72,axiom,
! [X11,X5,X2] :
( lhs_atom102(X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_101) ).
fof(c_0_73,axiom,
! [X11,X5,X2] :
( lhs_atom100(X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_99) ).
fof(c_0_74,axiom,
! [X11,X5,X2] :
( lhs_atom99(X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_98) ).
fof(c_0_75,axiom,
! [X4,X6,X2] :
( lhs_atom96(X4,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_95) ).
fof(c_0_76,axiom,
! [X7,X4,X2] :
( lhs_atom94(X7,X4,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_93) ).
fof(c_0_77,axiom,
! [X31,X32,X6] :
( lhs_atom84(X31,X32,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_83) ).
fof(c_0_78,axiom,
! [X26,X27,X28] :
( lhs_atom78(X26,X27,X28)
| ~ $true ),
file('<stdin>',to_be_clausified_77) ).
fof(c_0_79,axiom,
! [X26,X27,X28] :
( lhs_atom77(X26,X27,X28)
| ~ $true ),
file('<stdin>',to_be_clausified_76) ).
fof(c_0_80,axiom,
! [X24,X6,X2] :
( lhs_atom71(X24,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_70) ).
fof(c_0_81,axiom,
! [X12,X6,X2] :
( lhs_atom69(X12,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_68) ).
fof(c_0_82,axiom,
! [X12,X6,X2] :
( lhs_atom68(X12,X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_67) ).
fof(c_0_83,axiom,
! [X11,X5,X2] :
( lhs_atom63(X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_62) ).
fof(c_0_84,axiom,
! [X11,X5,X2] :
( lhs_atom62(X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_61) ).
fof(c_0_85,axiom,
! [X1,X11,X2] :
( lhs_atom58(X1,X11,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_57) ).
fof(c_0_86,axiom,
! [X11,X5,X2] :
( lhs_atom38(X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_37) ).
fof(c_0_87,axiom,
! [X11,X5,X2] :
( lhs_atom37(X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_36) ).
fof(c_0_88,axiom,
! [X11,X5,X2] :
( lhs_atom36(X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_35) ).
fof(c_0_89,axiom,
! [X11,X5,X2] :
( lhs_atom35(X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_34) ).
fof(c_0_90,axiom,
! [X11,X5,X2] :
( lhs_atom34(X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_33) ).
fof(c_0_91,axiom,
! [X11,X5,X2] :
( lhs_atom31(X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_30) ).
fof(c_0_92,axiom,
! [X11,X5,X2] :
( lhs_atom30(X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_29) ).
fof(c_0_93,axiom,
! [X7,X2] :
( lhs_atom196(X7,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_195) ).
fof(c_0_94,axiom,
! [X36,X2] :
( lhs_atom141(X36,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_140) ).
fof(c_0_95,axiom,
! [X7,X2] :
( lhs_atom140(X7,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_139) ).
fof(c_0_96,axiom,
! [X1,X2] :
( lhs_atom136(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_135) ).
fof(c_0_97,axiom,
! [X35,X2] :
( lhs_atom135(X35,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_134) ).
fof(c_0_98,axiom,
! [X7,X2] :
( lhs_atom134(X7,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_133) ).
fof(c_0_99,axiom,
! [X7,X2] :
( lhs_atom131(X7,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_130) ).
fof(c_0_100,axiom,
! [X7,X2] :
( lhs_atom123(X7,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_122) ).
fof(c_0_101,axiom,
! [X7,X2] :
( lhs_atom120(X7,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_119) ).
fof(c_0_102,axiom,
! [X7,X2] :
( lhs_atom118(X7,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_117) ).
fof(c_0_103,axiom,
! [X7,X2] :
( lhs_atom117(X7,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_116) ).
fof(c_0_104,axiom,
! [X23,X2] :
( lhs_atom115(X23,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_114) ).
fof(c_0_105,axiom,
! [X33,X2] :
( lhs_atom114(X33,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_113) ).
fof(c_0_106,axiom,
! [X5,X2] :
( lhs_atom109(X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_108) ).
fof(c_0_107,axiom,
! [X14,X2] :
( lhs_atom107(X14,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_106) ).
fof(c_0_108,axiom,
! [X33,X2] :
( lhs_atom106(X33,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_105) ).
fof(c_0_109,axiom,
! [X5,X2] :
( lhs_atom93(X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_92) ).
fof(c_0_110,axiom,
! [X5,X2] :
( lhs_atom92(X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_91) ).
fof(c_0_111,axiom,
! [X11,X2] :
( lhs_atom91(X11,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_90) ).
fof(c_0_112,axiom,
! [X5,X2] :
( lhs_atom90(X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_89) ).
fof(c_0_113,axiom,
! [X25,X18] :
( lhs_atom88(X25,X18)
| ~ $true ),
file('<stdin>',to_be_clausified_87) ).
fof(c_0_114,axiom,
! [X7,X2] :
( lhs_atom87(X7,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_86) ).
fof(c_0_115,axiom,
! [X12,X6] :
( lhs_atom86(X12,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_85) ).
fof(c_0_116,axiom,
! [X6,X2] :
( lhs_atom85(X6,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_84) ).
fof(c_0_117,axiom,
! [X7,X2] :
( lhs_atom81(X7,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_80) ).
fof(c_0_118,axiom,
! [X29,X30] :
( lhs_atom80(X29,X30)
| ~ $true ),
file('<stdin>',to_be_clausified_79) ).
fof(c_0_119,axiom,
! [X29,X30] :
( lhs_atom79(X29,X30)
| ~ $true ),
file('<stdin>',to_be_clausified_78) ).
fof(c_0_120,axiom,
! [X5,X2] :
( lhs_atom72(X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_71) ).
fof(c_0_121,axiom,
! [X7,X2] :
( lhs_atom61(X7,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_60) ).
fof(c_0_122,axiom,
! [X25,X18] :
( lhs_atom57(X25,X18)
| ~ $true ),
file('<stdin>',to_be_clausified_56) ).
fof(c_0_123,axiom,
! [X5,X2] :
( lhs_atom54(X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_53) ).
fof(c_0_124,axiom,
! [X11,X2] :
( lhs_atom53(X11,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_52) ).
fof(c_0_125,axiom,
! [X5,X2] :
( lhs_atom52(X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_51) ).
fof(c_0_126,axiom,
! [X5,X2] :
( lhs_atom51(X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_50) ).
fof(c_0_127,axiom,
! [X5,X2] :
( lhs_atom44(X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_43) ).
fof(c_0_128,axiom,
! [X7,X2] :
( lhs_atom43(X7,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_42) ).
fof(c_0_129,axiom,
! [X5,X2] :
( lhs_atom42(X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_41) ).
fof(c_0_130,axiom,
! [X7,X2] :
( lhs_atom13(X7,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_12) ).
fof(c_0_131,axiom,
! [X13,X6] :
( lhs_atom7(X13,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_6) ).
fof(c_0_132,axiom,
! [X1,X2] :
( lhs_atom1(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_0) ).
fof(c_0_133,axiom,
! [X26] :
( lhs_atom149(X26)
| ~ $true ),
file('<stdin>',to_be_clausified_148) ).
fof(c_0_134,axiom,
! [X37] :
( lhs_atom139(X37)
| ~ $true ),
file('<stdin>',to_be_clausified_138) ).
fof(c_0_135,axiom,
! [X26] :
( lhs_atom130(X26)
| ~ $true ),
file('<stdin>',to_be_clausified_129) ).
fof(c_0_136,axiom,
! [X35] :
( lhs_atom127(X35)
| ~ $true ),
file('<stdin>',to_be_clausified_126) ).
fof(c_0_137,axiom,
! [X2] :
( lhs_atom95(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_94) ).
fof(c_0_138,axiom,
! [X2] :
( lhs_atom73(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_72) ).
fof(c_0_139,axiom,
! [X2] :
( lhs_atom66(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_65) ).
fof(c_0_140,axiom,
! [X2] :
( lhs_atom50(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_49) ).
fof(c_0_141,axiom,
! [X15] :
( lhs_atom41(X15)
| ~ $true ),
file('<stdin>',to_be_clausified_40) ).
fof(c_0_142,axiom,
! [X15] :
( lhs_atom40(X15)
| ~ $true ),
file('<stdin>',to_be_clausified_39) ).
fof(c_0_143,axiom,
! [X7] :
( lhs_atom24(X7)
| ~ $true ),
file('<stdin>',to_be_clausified_23) ).
fof(c_0_144,axiom,
! [X15] :
( lhs_atom23(X15)
| ~ $true ),
file('<stdin>',to_be_clausified_22) ).
fof(c_0_145,axiom,
! [X15] :
( lhs_atom15(X15)
| ~ $true ),
file('<stdin>',to_be_clausified_14) ).
fof(c_0_146,axiom,
! [X7] :
( lhs_atom14(X7)
| ~ $true ),
file('<stdin>',to_be_clausified_13) ).
fof(c_0_147,axiom,
( lhs_atom195
| ~ $true ),
file('<stdin>',to_be_clausified_194) ).
fof(c_0_148,axiom,
( lhs_atom194
| ~ $true ),
file('<stdin>',to_be_clausified_193) ).
fof(c_0_149,axiom,
( lhs_atom193
| ~ $true ),
file('<stdin>',to_be_clausified_192) ).
fof(c_0_150,axiom,
( lhs_atom192
| ~ $true ),
file('<stdin>',to_be_clausified_191) ).
fof(c_0_151,axiom,
( lhs_atom191
| ~ $true ),
file('<stdin>',to_be_clausified_190) ).
fof(c_0_152,axiom,
( lhs_atom190
| ~ $true ),
file('<stdin>',to_be_clausified_189) ).
fof(c_0_153,axiom,
( lhs_atom189
| ~ $true ),
file('<stdin>',to_be_clausified_188) ).
fof(c_0_154,axiom,
( lhs_atom188
| ~ $true ),
file('<stdin>',to_be_clausified_187) ).
fof(c_0_155,axiom,
( lhs_atom187
| ~ $true ),
file('<stdin>',to_be_clausified_186) ).
fof(c_0_156,axiom,
( lhs_atom186
| ~ $true ),
file('<stdin>',to_be_clausified_185) ).
fof(c_0_157,axiom,
( lhs_atom185
| ~ $true ),
file('<stdin>',to_be_clausified_184) ).
fof(c_0_158,axiom,
( lhs_atom184
| ~ $true ),
file('<stdin>',to_be_clausified_183) ).
fof(c_0_159,axiom,
( lhs_atom183
| ~ $true ),
file('<stdin>',to_be_clausified_182) ).
fof(c_0_160,axiom,
( lhs_atom182
| ~ $true ),
file('<stdin>',to_be_clausified_181) ).
fof(c_0_161,axiom,
( lhs_atom181
| ~ $true ),
file('<stdin>',to_be_clausified_180) ).
fof(c_0_162,axiom,
( lhs_atom180
| ~ $true ),
file('<stdin>',to_be_clausified_179) ).
fof(c_0_163,axiom,
( lhs_atom179
| ~ $true ),
file('<stdin>',to_be_clausified_178) ).
fof(c_0_164,axiom,
( lhs_atom178
| ~ $true ),
file('<stdin>',to_be_clausified_177) ).
fof(c_0_165,axiom,
( lhs_atom177
| ~ $true ),
file('<stdin>',to_be_clausified_176) ).
fof(c_0_166,axiom,
( lhs_atom176
| ~ $true ),
file('<stdin>',to_be_clausified_175) ).
fof(c_0_167,axiom,
( lhs_atom175
| ~ $true ),
file('<stdin>',to_be_clausified_174) ).
fof(c_0_168,axiom,
( lhs_atom174
| ~ $true ),
file('<stdin>',to_be_clausified_173) ).
fof(c_0_169,axiom,
( lhs_atom173
| ~ $true ),
file('<stdin>',to_be_clausified_172) ).
fof(c_0_170,axiom,
( lhs_atom172
| ~ $true ),
file('<stdin>',to_be_clausified_171) ).
fof(c_0_171,axiom,
( lhs_atom171
| ~ $true ),
file('<stdin>',to_be_clausified_170) ).
fof(c_0_172,axiom,
( lhs_atom170
| ~ $true ),
file('<stdin>',to_be_clausified_169) ).
fof(c_0_173,axiom,
( lhs_atom169
| ~ $true ),
file('<stdin>',to_be_clausified_168) ).
fof(c_0_174,axiom,
( lhs_atom168
| ~ $true ),
file('<stdin>',to_be_clausified_167) ).
fof(c_0_175,axiom,
( lhs_atom167
| ~ $true ),
file('<stdin>',to_be_clausified_166) ).
fof(c_0_176,axiom,
( lhs_atom166
| ~ $true ),
file('<stdin>',to_be_clausified_165) ).
fof(c_0_177,axiom,
( lhs_atom165
| ~ $true ),
file('<stdin>',to_be_clausified_164) ).
fof(c_0_178,axiom,
( lhs_atom164
| ~ $true ),
file('<stdin>',to_be_clausified_163) ).
fof(c_0_179,axiom,
( lhs_atom163
| ~ $true ),
file('<stdin>',to_be_clausified_162) ).
fof(c_0_180,axiom,
( lhs_atom162
| ~ $true ),
file('<stdin>',to_be_clausified_161) ).
fof(c_0_181,axiom,
( lhs_atom161
| ~ $true ),
file('<stdin>',to_be_clausified_160) ).
fof(c_0_182,axiom,
( lhs_atom160
| ~ $true ),
file('<stdin>',to_be_clausified_159) ).
fof(c_0_183,axiom,
( lhs_atom159
| ~ $true ),
file('<stdin>',to_be_clausified_158) ).
fof(c_0_184,axiom,
( lhs_atom158
| ~ $true ),
file('<stdin>',to_be_clausified_157) ).
fof(c_0_185,axiom,
( lhs_atom157
| ~ $true ),
file('<stdin>',to_be_clausified_156) ).
fof(c_0_186,axiom,
( lhs_atom156
| ~ $true ),
file('<stdin>',to_be_clausified_155) ).
fof(c_0_187,axiom,
( lhs_atom155
| ~ $true ),
file('<stdin>',to_be_clausified_154) ).
fof(c_0_188,axiom,
( lhs_atom154
| ~ $true ),
file('<stdin>',to_be_clausified_153) ).
fof(c_0_189,axiom,
( lhs_atom153
| ~ $true ),
file('<stdin>',to_be_clausified_152) ).
fof(c_0_190,axiom,
( lhs_atom152
| ~ $true ),
file('<stdin>',to_be_clausified_151) ).
fof(c_0_191,axiom,
( lhs_atom151
| ~ $true ),
file('<stdin>',to_be_clausified_150) ).
fof(c_0_192,axiom,
( lhs_atom150
| ~ $true ),
file('<stdin>',to_be_clausified_149) ).
fof(c_0_193,axiom,
( lhs_atom138
| ~ $true ),
file('<stdin>',to_be_clausified_137) ).
fof(c_0_194,axiom,
( lhs_atom129
| ~ $true ),
file('<stdin>',to_be_clausified_128) ).
fof(c_0_195,axiom,
( lhs_atom83
| ~ $true ),
file('<stdin>',to_be_clausified_82) ).
fof(c_0_196,plain,
! [X14,X7,X24,X4,X6,X2] : lhs_atom67(X14,X7,X24,X4,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_197,plain,
! [X14,X7,X12,X13,X6,X2] : lhs_atom60(X14,X7,X12,X13,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_198,plain,
! [X18,X19,X20,X21,X6,X2] : lhs_atom20(X18,X19,X20,X21,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_199,plain,
! [X3,X14,X7,X4,X6,X2] : lhs_atom11(X3,X14,X7,X4,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_200,plain,
! [X34,X31,X32,X6,X2] : lhs_atom116(X34,X31,X32,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_201,plain,
! [X4,X11,X5,X6,X2] : lhs_atom111(X4,X11,X5,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_202,plain,
! [X4,X11,X5,X6,X2] : lhs_atom98(X4,X11,X5,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_203,plain,
! [X4,X1,X11,X6,X2] : lhs_atom74(X4,X1,X11,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_204,plain,
! [X3,X24,X4,X6,X2] : lhs_atom48(X3,X24,X4,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_205,plain,
! [X4,X11,X5,X6,X2] : lhs_atom47(X4,X11,X5,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_206,plain,
! [X23,X7,X12,X22,X2] : lhs_atom46(X23,X7,X12,X22,X2),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_207,plain,
! [X14,X7,X4,X22,X2] : lhs_atom28(X14,X7,X4,X22,X2),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_208,plain,
! [X14,X7,X4,X6,X2] : lhs_atom26(X14,X7,X4,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_209,plain,
! [X16,X17,X1,X6,X2] : lhs_atom17(X16,X17,X1,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_210,plain,
! [X4,X1,X5,X6,X2] : lhs_atom8(X4,X1,X5,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_211,plain,
! [X12,X11,X5,X6,X2] : lhs_atom6(X12,X11,X5,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_212,plain,
! [X7,X8,X9,X6,X2] : lhs_atom3(X7,X8,X9,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_213,plain,
! [X3,X4,X5,X6,X2] : lhs_atom2(X3,X4,X5,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_214,plain,
! [X14,X7,X5,X2] : lhs_atom147(X14,X7,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_215,plain,
! [X4,X1,X22,X2] : lhs_atom128(X4,X1,X22,X2),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_216,plain,
! [X1,X11,X5,X2] : lhs_atom122(X1,X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_217,plain,
! [X1,X11,X5,X2] : lhs_atom121(X1,X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_218,plain,
! [X15,X12,X6,X2] : lhs_atom113(X15,X12,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_219,plain,
! [X10,X11,X5,X2] : lhs_atom105(X10,X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_220,plain,
! [X10,X11,X5,X2] : lhs_atom104(X10,X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_221,plain,
! [X10,X11,X5,X2] : lhs_atom101(X10,X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_222,plain,
! [X24,X4,X6,X2] : lhs_atom97(X24,X4,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_223,plain,
! [X23,X7,X6,X2] : lhs_atom89(X23,X7,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_224,plain,
! [X7,X4,X6,X2] : lhs_atom82(X7,X4,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_225,plain,
! [X1,X10,X11,X2] : lhs_atom76(X1,X10,X11,X2),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_226,plain,
! [X1,X11,X5,X2] : lhs_atom75(X1,X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_227,plain,
! [X7,X4,X6,X2] : lhs_atom70(X7,X4,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_228,plain,
! [X10,X11,X5,X2] : lhs_atom65(X10,X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_229,plain,
! [X10,X11,X5,X2] : lhs_atom64(X10,X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_230,plain,
! [X1,X11,X5,X2] : lhs_atom59(X1,X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_231,plain,
! [X3,X4,X6,X2] : lhs_atom56(X3,X4,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_232,plain,
! [X3,X4,X6,X2] : lhs_atom55(X3,X4,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_233,plain,
! [X3,X4,X6,X2] : lhs_atom49(X3,X4,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_37]) ).
fof(c_0_234,plain,
! [X10,X11,X5,X2] : lhs_atom45(X10,X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_235,plain,
! [X10,X11,X5,X2] : lhs_atom39(X10,X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_236,plain,
! [X10,X11,X5,X2] : lhs_atom33(X10,X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_237,plain,
! [X10,X11,X5,X2] : lhs_atom32(X10,X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_238,plain,
! [X7,X4,X22,X2] : lhs_atom29(X7,X4,X22,X2),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_239,plain,
! [X7,X4,X6,X2] : lhs_atom27(X7,X4,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_240,plain,
! [X7,X4,X6,X2] : lhs_atom25(X7,X4,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_241,plain,
! [X16,X17,X6,X2] : lhs_atom22(X16,X17,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_242,plain,
! [X19,X20,X6,X2] : lhs_atom21(X19,X20,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_243,plain,
! [X10,X11,X5,X2] : lhs_atom19(X10,X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_47]) ).
fof(c_0_244,plain,
! [X10,X11,X5,X2] : lhs_atom18(X10,X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_245,plain,
! [X12,X5,X6,X2] : lhs_atom16(X12,X5,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_246,plain,
! [X10,X11,X5,X2] : lhs_atom12(X10,X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_247,plain,
! [X10,X11,X5,X2] : lhs_atom10(X10,X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_248,plain,
! [X10,X11,X5,X2] : lhs_atom9(X10,X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_52]) ).
fof(c_0_249,plain,
! [X10,X11,X5,X2] : lhs_atom5(X10,X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_250,plain,
! [X10,X11,X5,X2] : lhs_atom4(X10,X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_251,plain,
! [X23,X7,X2] : lhs_atom148(X23,X7,X2),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_252,plain,
! [X7,X11,X2] : lhs_atom146(X7,X11,X2),
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_253,plain,
! [X1,X11,X2] : lhs_atom145(X1,X11,X2),
inference(fof_simplification,[status(thm)],[c_0_57]) ).
fof(c_0_254,plain,
! [X7,X5,X2] : lhs_atom144(X7,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_255,plain,
! [X1,X5,X2] : lhs_atom143(X1,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_59]) ).
fof(c_0_256,plain,
! [X7,X5,X2] : lhs_atom142(X7,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_257,plain,
! [X1,X5,X2] : lhs_atom137(X1,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_258,plain,
! [X20,X36,X2] : lhs_atom133(X20,X36,X2),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_259,plain,
! [X7,X5,X2] : lhs_atom132(X7,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_260,plain,
! [X1,X5,X2] : lhs_atom126(X1,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_261,plain,
! [X1,X5,X2] : lhs_atom125(X1,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_65]) ).
fof(c_0_262,plain,
! [X4,X1,X2] : lhs_atom124(X4,X1,X2),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_263,plain,
! [X7,X4,X2] : lhs_atom119(X7,X4,X2),
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_264,plain,
! [X4,X6,X2] : lhs_atom112(X4,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_68]) ).
fof(c_0_265,plain,
! [X4,X5,X2] : lhs_atom110(X4,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_69]) ).
fof(c_0_266,plain,
! [X11,X5,X2] : lhs_atom108(X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_70]) ).
fof(c_0_267,plain,
! [X11,X5,X2] : lhs_atom103(X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_71]) ).
fof(c_0_268,plain,
! [X11,X5,X2] : lhs_atom102(X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_269,plain,
! [X11,X5,X2] : lhs_atom100(X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_73]) ).
fof(c_0_270,plain,
! [X11,X5,X2] : lhs_atom99(X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_74]) ).
fof(c_0_271,plain,
! [X4,X6,X2] : lhs_atom96(X4,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_75]) ).
fof(c_0_272,plain,
! [X7,X4,X2] : lhs_atom94(X7,X4,X2),
inference(fof_simplification,[status(thm)],[c_0_76]) ).
fof(c_0_273,plain,
! [X31,X32,X6] : lhs_atom84(X31,X32,X6),
inference(fof_simplification,[status(thm)],[c_0_77]) ).
fof(c_0_274,plain,
! [X26,X27,X28] : lhs_atom78(X26,X27,X28),
inference(fof_simplification,[status(thm)],[c_0_78]) ).
fof(c_0_275,plain,
! [X26,X27,X28] : lhs_atom77(X26,X27,X28),
inference(fof_simplification,[status(thm)],[c_0_79]) ).
fof(c_0_276,plain,
! [X24,X6,X2] : lhs_atom71(X24,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_80]) ).
fof(c_0_277,plain,
! [X12,X6,X2] : lhs_atom69(X12,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_278,plain,
! [X12,X6,X2] : lhs_atom68(X12,X6,X2),
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_279,plain,
! [X11,X5,X2] : lhs_atom63(X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_280,plain,
! [X11,X5,X2] : lhs_atom62(X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_281,plain,
! [X1,X11,X2] : lhs_atom58(X1,X11,X2),
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_282,plain,
! [X11,X5,X2] : lhs_atom38(X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_86]) ).
fof(c_0_283,plain,
! [X11,X5,X2] : lhs_atom37(X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_87]) ).
fof(c_0_284,plain,
! [X11,X5,X2] : lhs_atom36(X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_88]) ).
fof(c_0_285,plain,
! [X11,X5,X2] : lhs_atom35(X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_286,plain,
! [X11,X5,X2] : lhs_atom34(X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_287,plain,
! [X11,X5,X2] : lhs_atom31(X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_288,plain,
! [X11,X5,X2] : lhs_atom30(X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_289,plain,
! [X7,X2] : lhs_atom196(X7,X2),
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_290,plain,
! [X36,X2] : lhs_atom141(X36,X2),
inference(fof_simplification,[status(thm)],[c_0_94]) ).
fof(c_0_291,plain,
! [X7,X2] : lhs_atom140(X7,X2),
inference(fof_simplification,[status(thm)],[c_0_95]) ).
fof(c_0_292,plain,
! [X1,X2] : lhs_atom136(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_96]) ).
fof(c_0_293,plain,
! [X35,X2] : lhs_atom135(X35,X2),
inference(fof_simplification,[status(thm)],[c_0_97]) ).
fof(c_0_294,plain,
! [X7,X2] : lhs_atom134(X7,X2),
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_295,plain,
! [X7,X2] : lhs_atom131(X7,X2),
inference(fof_simplification,[status(thm)],[c_0_99]) ).
fof(c_0_296,plain,
! [X7,X2] : lhs_atom123(X7,X2),
inference(fof_simplification,[status(thm)],[c_0_100]) ).
fof(c_0_297,plain,
! [X7,X2] : lhs_atom120(X7,X2),
inference(fof_simplification,[status(thm)],[c_0_101]) ).
fof(c_0_298,plain,
! [X7,X2] : lhs_atom118(X7,X2),
inference(fof_simplification,[status(thm)],[c_0_102]) ).
fof(c_0_299,plain,
! [X7,X2] : lhs_atom117(X7,X2),
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_300,plain,
! [X23,X2] : lhs_atom115(X23,X2),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_301,plain,
! [X33,X2] : lhs_atom114(X33,X2),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_302,plain,
! [X5,X2] : lhs_atom109(X5,X2),
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_303,plain,
! [X14,X2] : lhs_atom107(X14,X2),
inference(fof_simplification,[status(thm)],[c_0_107]) ).
fof(c_0_304,plain,
! [X33,X2] : lhs_atom106(X33,X2),
inference(fof_simplification,[status(thm)],[c_0_108]) ).
fof(c_0_305,plain,
! [X5,X2] : lhs_atom93(X5,X2),
inference(fof_simplification,[status(thm)],[c_0_109]) ).
fof(c_0_306,plain,
! [X5,X2] : lhs_atom92(X5,X2),
inference(fof_simplification,[status(thm)],[c_0_110]) ).
fof(c_0_307,plain,
! [X11,X2] : lhs_atom91(X11,X2),
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_308,plain,
! [X5,X2] : lhs_atom90(X5,X2),
inference(fof_simplification,[status(thm)],[c_0_112]) ).
fof(c_0_309,plain,
! [X25,X18] : lhs_atom88(X25,X18),
inference(fof_simplification,[status(thm)],[c_0_113]) ).
fof(c_0_310,plain,
! [X7,X2] : lhs_atom87(X7,X2),
inference(fof_simplification,[status(thm)],[c_0_114]) ).
fof(c_0_311,plain,
! [X12,X6] : lhs_atom86(X12,X6),
inference(fof_simplification,[status(thm)],[c_0_115]) ).
fof(c_0_312,plain,
! [X6,X2] : lhs_atom85(X6,X2),
inference(fof_simplification,[status(thm)],[c_0_116]) ).
fof(c_0_313,plain,
! [X7,X2] : lhs_atom81(X7,X2),
inference(fof_simplification,[status(thm)],[c_0_117]) ).
fof(c_0_314,plain,
! [X29,X30] : lhs_atom80(X29,X30),
inference(fof_simplification,[status(thm)],[c_0_118]) ).
fof(c_0_315,plain,
! [X29,X30] : lhs_atom79(X29,X30),
inference(fof_simplification,[status(thm)],[c_0_119]) ).
fof(c_0_316,plain,
! [X5,X2] : lhs_atom72(X5,X2),
inference(fof_simplification,[status(thm)],[c_0_120]) ).
fof(c_0_317,plain,
! [X7,X2] : lhs_atom61(X7,X2),
inference(fof_simplification,[status(thm)],[c_0_121]) ).
fof(c_0_318,plain,
! [X25,X18] : lhs_atom57(X25,X18),
inference(fof_simplification,[status(thm)],[c_0_122]) ).
fof(c_0_319,plain,
! [X5,X2] : lhs_atom54(X5,X2),
inference(fof_simplification,[status(thm)],[c_0_123]) ).
fof(c_0_320,plain,
! [X11,X2] : lhs_atom53(X11,X2),
inference(fof_simplification,[status(thm)],[c_0_124]) ).
fof(c_0_321,plain,
! [X5,X2] : lhs_atom52(X5,X2),
inference(fof_simplification,[status(thm)],[c_0_125]) ).
fof(c_0_322,plain,
! [X5,X2] : lhs_atom51(X5,X2),
inference(fof_simplification,[status(thm)],[c_0_126]) ).
fof(c_0_323,plain,
! [X5,X2] : lhs_atom44(X5,X2),
inference(fof_simplification,[status(thm)],[c_0_127]) ).
fof(c_0_324,plain,
! [X7,X2] : lhs_atom43(X7,X2),
inference(fof_simplification,[status(thm)],[c_0_128]) ).
fof(c_0_325,plain,
! [X5,X2] : lhs_atom42(X5,X2),
inference(fof_simplification,[status(thm)],[c_0_129]) ).
fof(c_0_326,plain,
! [X7,X2] : lhs_atom13(X7,X2),
inference(fof_simplification,[status(thm)],[c_0_130]) ).
fof(c_0_327,plain,
! [X13,X6] : lhs_atom7(X13,X6),
inference(fof_simplification,[status(thm)],[c_0_131]) ).
fof(c_0_328,plain,
! [X1,X2] : lhs_atom1(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_132]) ).
fof(c_0_329,plain,
! [X26] : lhs_atom149(X26),
inference(fof_simplification,[status(thm)],[c_0_133]) ).
fof(c_0_330,plain,
! [X37] : lhs_atom139(X37),
inference(fof_simplification,[status(thm)],[c_0_134]) ).
fof(c_0_331,plain,
! [X26] : lhs_atom130(X26),
inference(fof_simplification,[status(thm)],[c_0_135]) ).
fof(c_0_332,plain,
! [X35] : lhs_atom127(X35),
inference(fof_simplification,[status(thm)],[c_0_136]) ).
fof(c_0_333,plain,
! [X2] : lhs_atom95(X2),
inference(fof_simplification,[status(thm)],[c_0_137]) ).
fof(c_0_334,plain,
! [X2] : lhs_atom73(X2),
inference(fof_simplification,[status(thm)],[c_0_138]) ).
fof(c_0_335,plain,
! [X2] : lhs_atom66(X2),
inference(fof_simplification,[status(thm)],[c_0_139]) ).
fof(c_0_336,plain,
! [X2] : lhs_atom50(X2),
inference(fof_simplification,[status(thm)],[c_0_140]) ).
fof(c_0_337,plain,
! [X15] : lhs_atom41(X15),
inference(fof_simplification,[status(thm)],[c_0_141]) ).
fof(c_0_338,plain,
! [X15] : lhs_atom40(X15),
inference(fof_simplification,[status(thm)],[c_0_142]) ).
fof(c_0_339,plain,
! [X7] : lhs_atom24(X7),
inference(fof_simplification,[status(thm)],[c_0_143]) ).
fof(c_0_340,plain,
! [X15] : lhs_atom23(X15),
inference(fof_simplification,[status(thm)],[c_0_144]) ).
fof(c_0_341,plain,
! [X15] : lhs_atom15(X15),
inference(fof_simplification,[status(thm)],[c_0_145]) ).
fof(c_0_342,plain,
! [X7] : lhs_atom14(X7),
inference(fof_simplification,[status(thm)],[c_0_146]) ).
fof(c_0_343,plain,
lhs_atom195,
inference(fof_simplification,[status(thm)],[c_0_147]) ).
fof(c_0_344,plain,
lhs_atom194,
inference(fof_simplification,[status(thm)],[c_0_148]) ).
fof(c_0_345,plain,
lhs_atom193,
inference(fof_simplification,[status(thm)],[c_0_149]) ).
fof(c_0_346,plain,
lhs_atom192,
inference(fof_simplification,[status(thm)],[c_0_150]) ).
fof(c_0_347,plain,
lhs_atom191,
inference(fof_simplification,[status(thm)],[c_0_151]) ).
fof(c_0_348,plain,
lhs_atom190,
inference(fof_simplification,[status(thm)],[c_0_152]) ).
fof(c_0_349,plain,
lhs_atom189,
inference(fof_simplification,[status(thm)],[c_0_153]) ).
fof(c_0_350,plain,
lhs_atom188,
inference(fof_simplification,[status(thm)],[c_0_154]) ).
fof(c_0_351,plain,
lhs_atom187,
inference(fof_simplification,[status(thm)],[c_0_155]) ).
fof(c_0_352,plain,
lhs_atom186,
inference(fof_simplification,[status(thm)],[c_0_156]) ).
fof(c_0_353,plain,
lhs_atom185,
inference(fof_simplification,[status(thm)],[c_0_157]) ).
fof(c_0_354,plain,
lhs_atom184,
inference(fof_simplification,[status(thm)],[c_0_158]) ).
fof(c_0_355,plain,
lhs_atom183,
inference(fof_simplification,[status(thm)],[c_0_159]) ).
fof(c_0_356,plain,
lhs_atom182,
inference(fof_simplification,[status(thm)],[c_0_160]) ).
fof(c_0_357,plain,
lhs_atom181,
inference(fof_simplification,[status(thm)],[c_0_161]) ).
fof(c_0_358,plain,
lhs_atom180,
inference(fof_simplification,[status(thm)],[c_0_162]) ).
fof(c_0_359,plain,
lhs_atom179,
inference(fof_simplification,[status(thm)],[c_0_163]) ).
fof(c_0_360,plain,
lhs_atom178,
inference(fof_simplification,[status(thm)],[c_0_164]) ).
fof(c_0_361,plain,
lhs_atom177,
inference(fof_simplification,[status(thm)],[c_0_165]) ).
fof(c_0_362,plain,
lhs_atom176,
inference(fof_simplification,[status(thm)],[c_0_166]) ).
fof(c_0_363,plain,
lhs_atom175,
inference(fof_simplification,[status(thm)],[c_0_167]) ).
fof(c_0_364,plain,
lhs_atom174,
inference(fof_simplification,[status(thm)],[c_0_168]) ).
fof(c_0_365,plain,
lhs_atom173,
inference(fof_simplification,[status(thm)],[c_0_169]) ).
fof(c_0_366,plain,
lhs_atom172,
inference(fof_simplification,[status(thm)],[c_0_170]) ).
fof(c_0_367,plain,
lhs_atom171,
inference(fof_simplification,[status(thm)],[c_0_171]) ).
fof(c_0_368,plain,
lhs_atom170,
inference(fof_simplification,[status(thm)],[c_0_172]) ).
fof(c_0_369,plain,
lhs_atom169,
inference(fof_simplification,[status(thm)],[c_0_173]) ).
fof(c_0_370,plain,
lhs_atom168,
inference(fof_simplification,[status(thm)],[c_0_174]) ).
fof(c_0_371,plain,
lhs_atom167,
inference(fof_simplification,[status(thm)],[c_0_175]) ).
fof(c_0_372,plain,
lhs_atom166,
inference(fof_simplification,[status(thm)],[c_0_176]) ).
fof(c_0_373,plain,
lhs_atom165,
inference(fof_simplification,[status(thm)],[c_0_177]) ).
fof(c_0_374,plain,
lhs_atom164,
inference(fof_simplification,[status(thm)],[c_0_178]) ).
fof(c_0_375,plain,
lhs_atom163,
inference(fof_simplification,[status(thm)],[c_0_179]) ).
fof(c_0_376,plain,
lhs_atom162,
inference(fof_simplification,[status(thm)],[c_0_180]) ).
fof(c_0_377,plain,
lhs_atom161,
inference(fof_simplification,[status(thm)],[c_0_181]) ).
fof(c_0_378,plain,
lhs_atom160,
inference(fof_simplification,[status(thm)],[c_0_182]) ).
fof(c_0_379,plain,
lhs_atom159,
inference(fof_simplification,[status(thm)],[c_0_183]) ).
fof(c_0_380,plain,
lhs_atom158,
inference(fof_simplification,[status(thm)],[c_0_184]) ).
fof(c_0_381,plain,
lhs_atom157,
inference(fof_simplification,[status(thm)],[c_0_185]) ).
fof(c_0_382,plain,
lhs_atom156,
inference(fof_simplification,[status(thm)],[c_0_186]) ).
fof(c_0_383,plain,
lhs_atom155,
inference(fof_simplification,[status(thm)],[c_0_187]) ).
fof(c_0_384,plain,
lhs_atom154,
inference(fof_simplification,[status(thm)],[c_0_188]) ).
fof(c_0_385,plain,
lhs_atom153,
inference(fof_simplification,[status(thm)],[c_0_189]) ).
fof(c_0_386,plain,
lhs_atom152,
inference(fof_simplification,[status(thm)],[c_0_190]) ).
fof(c_0_387,plain,
lhs_atom151,
inference(fof_simplification,[status(thm)],[c_0_191]) ).
fof(c_0_388,plain,
lhs_atom150,
inference(fof_simplification,[status(thm)],[c_0_192]) ).
fof(c_0_389,plain,
lhs_atom138,
inference(fof_simplification,[status(thm)],[c_0_193]) ).
fof(c_0_390,plain,
lhs_atom129,
inference(fof_simplification,[status(thm)],[c_0_194]) ).
fof(c_0_391,plain,
lhs_atom83,
inference(fof_simplification,[status(thm)],[c_0_195]) ).
fof(c_0_392,plain,
! [X25,X26,X27,X28,X29,X30] : lhs_atom67(X25,X26,X27,X28,X29,X30),
inference(variable_rename,[status(thm)],[c_0_196]) ).
fof(c_0_393,plain,
! [X15,X16,X17,X18,X19,X20] : lhs_atom60(X15,X16,X17,X18,X19,X20),
inference(variable_rename,[status(thm)],[c_0_197]) ).
fof(c_0_394,plain,
! [X22,X23,X24,X25,X26,X27] : lhs_atom20(X22,X23,X24,X25,X26,X27),
inference(variable_rename,[status(thm)],[c_0_198]) ).
fof(c_0_395,plain,
! [X15,X16,X17,X18,X19,X20] : lhs_atom11(X15,X16,X17,X18,X19,X20),
inference(variable_rename,[status(thm)],[c_0_199]) ).
fof(c_0_396,plain,
! [X35,X36,X37,X38,X39] : lhs_atom116(X35,X36,X37,X38,X39),
inference(variable_rename,[status(thm)],[c_0_200]) ).
fof(c_0_397,plain,
! [X12,X13,X14,X15,X16] : lhs_atom111(X12,X13,X14,X15,X16),
inference(variable_rename,[status(thm)],[c_0_201]) ).
fof(c_0_398,plain,
! [X12,X13,X14,X15,X16] : lhs_atom98(X12,X13,X14,X15,X16),
inference(variable_rename,[status(thm)],[c_0_202]) ).
fof(c_0_399,plain,
! [X12,X13,X14,X15,X16] : lhs_atom74(X12,X13,X14,X15,X16),
inference(variable_rename,[status(thm)],[c_0_203]) ).
fof(c_0_400,plain,
! [X25,X26,X27,X28,X29] : lhs_atom48(X25,X26,X27,X28,X29),
inference(variable_rename,[status(thm)],[c_0_204]) ).
fof(c_0_401,plain,
! [X12,X13,X14,X15,X16] : lhs_atom47(X12,X13,X14,X15,X16),
inference(variable_rename,[status(thm)],[c_0_205]) ).
fof(c_0_402,plain,
! [X24,X25,X26,X27,X28] : lhs_atom46(X24,X25,X26,X27,X28),
inference(variable_rename,[status(thm)],[c_0_206]) ).
fof(c_0_403,plain,
! [X23,X24,X25,X26,X27] : lhs_atom28(X23,X24,X25,X26,X27),
inference(variable_rename,[status(thm)],[c_0_207]) ).
fof(c_0_404,plain,
! [X15,X16,X17,X18,X19] : lhs_atom26(X15,X16,X17,X18,X19),
inference(variable_rename,[status(thm)],[c_0_208]) ).
fof(c_0_405,plain,
! [X18,X19,X20,X21,X22] : lhs_atom17(X18,X19,X20,X21,X22),
inference(variable_rename,[status(thm)],[c_0_209]) ).
fof(c_0_406,plain,
! [X7,X8,X9,X10,X11] : lhs_atom8(X7,X8,X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_210]) ).
fof(c_0_407,plain,
! [X13,X14,X15,X16,X17] : lhs_atom6(X13,X14,X15,X16,X17),
inference(variable_rename,[status(thm)],[c_0_211]) ).
fof(c_0_408,plain,
! [X10,X11,X12,X13,X14] : lhs_atom3(X10,X11,X12,X13,X14),
inference(variable_rename,[status(thm)],[c_0_212]) ).
fof(c_0_409,plain,
! [X7,X8,X9,X10,X11] : lhs_atom2(X7,X8,X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_213]) ).
fof(c_0_410,plain,
! [X15,X16,X17,X18] : lhs_atom147(X15,X16,X17,X18),
inference(variable_rename,[status(thm)],[c_0_214]) ).
fof(c_0_411,plain,
! [X23,X24,X25,X26] : lhs_atom128(X23,X24,X25,X26),
inference(variable_rename,[status(thm)],[c_0_215]) ).
fof(c_0_412,plain,
! [X12,X13,X14,X15] : lhs_atom122(X12,X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_216]) ).
fof(c_0_413,plain,
! [X12,X13,X14,X15] : lhs_atom121(X12,X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_217]) ).
fof(c_0_414,plain,
! [X16,X17,X18,X19] : lhs_atom113(X16,X17,X18,X19),
inference(variable_rename,[status(thm)],[c_0_218]) ).
fof(c_0_415,plain,
! [X12,X13,X14,X15] : lhs_atom105(X12,X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_219]) ).
fof(c_0_416,plain,
! [X12,X13,X14,X15] : lhs_atom104(X12,X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_220]) ).
fof(c_0_417,plain,
! [X12,X13,X14,X15] : lhs_atom101(X12,X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_221]) ).
fof(c_0_418,plain,
! [X25,X26,X27,X28] : lhs_atom97(X25,X26,X27,X28),
inference(variable_rename,[status(thm)],[c_0_222]) ).
fof(c_0_419,plain,
! [X24,X25,X26,X27] : lhs_atom89(X24,X25,X26,X27),
inference(variable_rename,[status(thm)],[c_0_223]) ).
fof(c_0_420,plain,
! [X8,X9,X10,X11] : lhs_atom82(X8,X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_224]) ).
fof(c_0_421,plain,
! [X12,X13,X14,X15] : lhs_atom76(X12,X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_225]) ).
fof(c_0_422,plain,
! [X12,X13,X14,X15] : lhs_atom75(X12,X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_226]) ).
fof(c_0_423,plain,
! [X8,X9,X10,X11] : lhs_atom70(X8,X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_227]) ).
fof(c_0_424,plain,
! [X12,X13,X14,X15] : lhs_atom65(X12,X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_228]) ).
fof(c_0_425,plain,
! [X12,X13,X14,X15] : lhs_atom64(X12,X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_229]) ).
fof(c_0_426,plain,
! [X12,X13,X14,X15] : lhs_atom59(X12,X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_230]) ).
fof(c_0_427,plain,
! [X7,X8,X9,X10] : lhs_atom56(X7,X8,X9,X10),
inference(variable_rename,[status(thm)],[c_0_231]) ).
fof(c_0_428,plain,
! [X7,X8,X9,X10] : lhs_atom55(X7,X8,X9,X10),
inference(variable_rename,[status(thm)],[c_0_232]) ).
fof(c_0_429,plain,
! [X7,X8,X9,X10] : lhs_atom49(X7,X8,X9,X10),
inference(variable_rename,[status(thm)],[c_0_233]) ).
fof(c_0_430,plain,
! [X12,X13,X14,X15] : lhs_atom45(X12,X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_234]) ).
fof(c_0_431,plain,
! [X12,X13,X14,X15] : lhs_atom39(X12,X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_235]) ).
fof(c_0_432,plain,
! [X12,X13,X14,X15] : lhs_atom33(X12,X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_236]) ).
fof(c_0_433,plain,
! [X12,X13,X14,X15] : lhs_atom32(X12,X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_237]) ).
fof(c_0_434,plain,
! [X23,X24,X25,X26] : lhs_atom29(X23,X24,X25,X26),
inference(variable_rename,[status(thm)],[c_0_238]) ).
fof(c_0_435,plain,
! [X8,X9,X10,X11] : lhs_atom27(X8,X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_239]) ).
fof(c_0_436,plain,
! [X8,X9,X10,X11] : lhs_atom25(X8,X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_240]) ).
fof(c_0_437,plain,
! [X18,X19,X20,X21] : lhs_atom22(X18,X19,X20,X21),
inference(variable_rename,[status(thm)],[c_0_241]) ).
fof(c_0_438,plain,
! [X21,X22,X23,X24] : lhs_atom21(X21,X22,X23,X24),
inference(variable_rename,[status(thm)],[c_0_242]) ).
fof(c_0_439,plain,
! [X12,X13,X14,X15] : lhs_atom19(X12,X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_243]) ).
fof(c_0_440,plain,
! [X12,X13,X14,X15] : lhs_atom18(X12,X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_244]) ).
fof(c_0_441,plain,
! [X13,X14,X15,X16] : lhs_atom16(X13,X14,X15,X16),
inference(variable_rename,[status(thm)],[c_0_245]) ).
fof(c_0_442,plain,
! [X12,X13,X14,X15] : lhs_atom12(X12,X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_246]) ).
fof(c_0_443,plain,
! [X12,X13,X14,X15] : lhs_atom10(X12,X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_247]) ).
fof(c_0_444,plain,
! [X12,X13,X14,X15] : lhs_atom9(X12,X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_248]) ).
fof(c_0_445,plain,
! [X12,X13,X14,X15] : lhs_atom5(X12,X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_249]) ).
fof(c_0_446,plain,
! [X12,X13,X14,X15] : lhs_atom4(X12,X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_250]) ).
fof(c_0_447,plain,
! [X24,X25,X26] : lhs_atom148(X24,X25,X26),
inference(variable_rename,[status(thm)],[c_0_251]) ).
fof(c_0_448,plain,
! [X12,X13,X14] : lhs_atom146(X12,X13,X14),
inference(variable_rename,[status(thm)],[c_0_252]) ).
fof(c_0_449,plain,
! [X12,X13,X14] : lhs_atom145(X12,X13,X14),
inference(variable_rename,[status(thm)],[c_0_253]) ).
fof(c_0_450,plain,
! [X8,X9,X10] : lhs_atom144(X8,X9,X10),
inference(variable_rename,[status(thm)],[c_0_254]) ).
fof(c_0_451,plain,
! [X6,X7,X8] : lhs_atom143(X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_255]) ).
fof(c_0_452,plain,
! [X8,X9,X10] : lhs_atom142(X8,X9,X10),
inference(variable_rename,[status(thm)],[c_0_256]) ).
fof(c_0_453,plain,
! [X6,X7,X8] : lhs_atom137(X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_257]) ).
fof(c_0_454,plain,
! [X37,X38,X39] : lhs_atom133(X37,X38,X39),
inference(variable_rename,[status(thm)],[c_0_258]) ).
fof(c_0_455,plain,
! [X8,X9,X10] : lhs_atom132(X8,X9,X10),
inference(variable_rename,[status(thm)],[c_0_259]) ).
fof(c_0_456,plain,
! [X6,X7,X8] : lhs_atom126(X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_260]) ).
fof(c_0_457,plain,
! [X6,X7,X8] : lhs_atom125(X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_261]) ).
fof(c_0_458,plain,
! [X5,X6,X7] : lhs_atom124(X5,X6,X7),
inference(variable_rename,[status(thm)],[c_0_262]) ).
fof(c_0_459,plain,
! [X8,X9,X10] : lhs_atom119(X8,X9,X10),
inference(variable_rename,[status(thm)],[c_0_263]) ).
fof(c_0_460,plain,
! [X7,X8,X9] : lhs_atom112(X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_264]) ).
fof(c_0_461,plain,
! [X6,X7,X8] : lhs_atom110(X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_265]) ).
fof(c_0_462,plain,
! [X12,X13,X14] : lhs_atom108(X12,X13,X14),
inference(variable_rename,[status(thm)],[c_0_266]) ).
fof(c_0_463,plain,
! [X12,X13,X14] : lhs_atom103(X12,X13,X14),
inference(variable_rename,[status(thm)],[c_0_267]) ).
fof(c_0_464,plain,
! [X12,X13,X14] : lhs_atom102(X12,X13,X14),
inference(variable_rename,[status(thm)],[c_0_268]) ).
fof(c_0_465,plain,
! [X12,X13,X14] : lhs_atom100(X12,X13,X14),
inference(variable_rename,[status(thm)],[c_0_269]) ).
fof(c_0_466,plain,
! [X12,X13,X14] : lhs_atom99(X12,X13,X14),
inference(variable_rename,[status(thm)],[c_0_270]) ).
fof(c_0_467,plain,
! [X7,X8,X9] : lhs_atom96(X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_271]) ).
fof(c_0_468,plain,
! [X8,X9,X10] : lhs_atom94(X8,X9,X10),
inference(variable_rename,[status(thm)],[c_0_272]) ).
fof(c_0_469,plain,
! [X33,X34,X35] : lhs_atom84(X33,X34,X35),
inference(variable_rename,[status(thm)],[c_0_273]) ).
fof(c_0_470,plain,
! [X29,X30,X31] : lhs_atom78(X29,X30,X31),
inference(variable_rename,[status(thm)],[c_0_274]) ).
fof(c_0_471,plain,
! [X29,X30,X31] : lhs_atom77(X29,X30,X31),
inference(variable_rename,[status(thm)],[c_0_275]) ).
fof(c_0_472,plain,
! [X25,X26,X27] : lhs_atom71(X25,X26,X27),
inference(variable_rename,[status(thm)],[c_0_276]) ).
fof(c_0_473,plain,
! [X13,X14,X15] : lhs_atom69(X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_277]) ).
fof(c_0_474,plain,
! [X13,X14,X15] : lhs_atom68(X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_278]) ).
fof(c_0_475,plain,
! [X12,X13,X14] : lhs_atom63(X12,X13,X14),
inference(variable_rename,[status(thm)],[c_0_279]) ).
fof(c_0_476,plain,
! [X12,X13,X14] : lhs_atom62(X12,X13,X14),
inference(variable_rename,[status(thm)],[c_0_280]) ).
fof(c_0_477,plain,
! [X12,X13,X14] : lhs_atom58(X12,X13,X14),
inference(variable_rename,[status(thm)],[c_0_281]) ).
fof(c_0_478,plain,
! [X12,X13,X14] : lhs_atom38(X12,X13,X14),
inference(variable_rename,[status(thm)],[c_0_282]) ).
fof(c_0_479,plain,
! [X12,X13,X14] : lhs_atom37(X12,X13,X14),
inference(variable_rename,[status(thm)],[c_0_283]) ).
fof(c_0_480,plain,
! [X12,X13,X14] : lhs_atom36(X12,X13,X14),
inference(variable_rename,[status(thm)],[c_0_284]) ).
fof(c_0_481,plain,
! [X12,X13,X14] : lhs_atom35(X12,X13,X14),
inference(variable_rename,[status(thm)],[c_0_285]) ).
fof(c_0_482,plain,
! [X12,X13,X14] : lhs_atom34(X12,X13,X14),
inference(variable_rename,[status(thm)],[c_0_286]) ).
fof(c_0_483,plain,
! [X12,X13,X14] : lhs_atom31(X12,X13,X14),
inference(variable_rename,[status(thm)],[c_0_287]) ).
fof(c_0_484,plain,
! [X12,X13,X14] : lhs_atom30(X12,X13,X14),
inference(variable_rename,[status(thm)],[c_0_288]) ).
fof(c_0_485,plain,
! [X8,X9] : lhs_atom196(X8,X9),
inference(variable_rename,[status(thm)],[c_0_289]) ).
fof(c_0_486,plain,
! [X37,X38] : lhs_atom141(X37,X38),
inference(variable_rename,[status(thm)],[c_0_290]) ).
fof(c_0_487,plain,
! [X8,X9] : lhs_atom140(X8,X9),
inference(variable_rename,[status(thm)],[c_0_291]) ).
fof(c_0_488,plain,
! [X3,X4] : lhs_atom136(X3,X4),
inference(variable_rename,[status(thm)],[c_0_292]) ).
fof(c_0_489,plain,
! [X36,X37] : lhs_atom135(X36,X37),
inference(variable_rename,[status(thm)],[c_0_293]) ).
fof(c_0_490,plain,
! [X8,X9] : lhs_atom134(X8,X9),
inference(variable_rename,[status(thm)],[c_0_294]) ).
fof(c_0_491,plain,
! [X8,X9] : lhs_atom131(X8,X9),
inference(variable_rename,[status(thm)],[c_0_295]) ).
fof(c_0_492,plain,
! [X8,X9] : lhs_atom123(X8,X9),
inference(variable_rename,[status(thm)],[c_0_296]) ).
fof(c_0_493,plain,
! [X8,X9] : lhs_atom120(X8,X9),
inference(variable_rename,[status(thm)],[c_0_297]) ).
fof(c_0_494,plain,
! [X8,X9] : lhs_atom118(X8,X9),
inference(variable_rename,[status(thm)],[c_0_298]) ).
fof(c_0_495,plain,
! [X8,X9] : lhs_atom117(X8,X9),
inference(variable_rename,[status(thm)],[c_0_299]) ).
fof(c_0_496,plain,
! [X24,X25] : lhs_atom115(X24,X25),
inference(variable_rename,[status(thm)],[c_0_300]) ).
fof(c_0_497,plain,
! [X34,X35] : lhs_atom114(X34,X35),
inference(variable_rename,[status(thm)],[c_0_301]) ).
fof(c_0_498,plain,
! [X6,X7] : lhs_atom109(X6,X7),
inference(variable_rename,[status(thm)],[c_0_302]) ).
fof(c_0_499,plain,
! [X15,X16] : lhs_atom107(X15,X16),
inference(variable_rename,[status(thm)],[c_0_303]) ).
fof(c_0_500,plain,
! [X34,X35] : lhs_atom106(X34,X35),
inference(variable_rename,[status(thm)],[c_0_304]) ).
fof(c_0_501,plain,
! [X6,X7] : lhs_atom93(X6,X7),
inference(variable_rename,[status(thm)],[c_0_305]) ).
fof(c_0_502,plain,
! [X6,X7] : lhs_atom92(X6,X7),
inference(variable_rename,[status(thm)],[c_0_306]) ).
fof(c_0_503,plain,
! [X12,X13] : lhs_atom91(X12,X13),
inference(variable_rename,[status(thm)],[c_0_307]) ).
fof(c_0_504,plain,
! [X6,X7] : lhs_atom90(X6,X7),
inference(variable_rename,[status(thm)],[c_0_308]) ).
fof(c_0_505,plain,
! [X26,X27] : lhs_atom88(X26,X27),
inference(variable_rename,[status(thm)],[c_0_309]) ).
fof(c_0_506,plain,
! [X8,X9] : lhs_atom87(X8,X9),
inference(variable_rename,[status(thm)],[c_0_310]) ).
fof(c_0_507,plain,
! [X13,X14] : lhs_atom86(X13,X14),
inference(variable_rename,[status(thm)],[c_0_311]) ).
fof(c_0_508,plain,
! [X7,X8] : lhs_atom85(X7,X8),
inference(variable_rename,[status(thm)],[c_0_312]) ).
fof(c_0_509,plain,
! [X8,X9] : lhs_atom81(X8,X9),
inference(variable_rename,[status(thm)],[c_0_313]) ).
fof(c_0_510,plain,
! [X31,X32] : lhs_atom80(X31,X32),
inference(variable_rename,[status(thm)],[c_0_314]) ).
fof(c_0_511,plain,
! [X31,X32] : lhs_atom79(X31,X32),
inference(variable_rename,[status(thm)],[c_0_315]) ).
fof(c_0_512,plain,
! [X6,X7] : lhs_atom72(X6,X7),
inference(variable_rename,[status(thm)],[c_0_316]) ).
fof(c_0_513,plain,
! [X8,X9] : lhs_atom61(X8,X9),
inference(variable_rename,[status(thm)],[c_0_317]) ).
fof(c_0_514,plain,
! [X26,X27] : lhs_atom57(X26,X27),
inference(variable_rename,[status(thm)],[c_0_318]) ).
fof(c_0_515,plain,
! [X6,X7] : lhs_atom54(X6,X7),
inference(variable_rename,[status(thm)],[c_0_319]) ).
fof(c_0_516,plain,
! [X12,X13] : lhs_atom53(X12,X13),
inference(variable_rename,[status(thm)],[c_0_320]) ).
fof(c_0_517,plain,
! [X6,X7] : lhs_atom52(X6,X7),
inference(variable_rename,[status(thm)],[c_0_321]) ).
fof(c_0_518,plain,
! [X6,X7] : lhs_atom51(X6,X7),
inference(variable_rename,[status(thm)],[c_0_322]) ).
fof(c_0_519,plain,
! [X6,X7] : lhs_atom44(X6,X7),
inference(variable_rename,[status(thm)],[c_0_323]) ).
fof(c_0_520,plain,
! [X8,X9] : lhs_atom43(X8,X9),
inference(variable_rename,[status(thm)],[c_0_324]) ).
fof(c_0_521,plain,
! [X6,X7] : lhs_atom42(X6,X7),
inference(variable_rename,[status(thm)],[c_0_325]) ).
fof(c_0_522,plain,
! [X8,X9] : lhs_atom13(X8,X9),
inference(variable_rename,[status(thm)],[c_0_326]) ).
fof(c_0_523,plain,
! [X14,X15] : lhs_atom7(X14,X15),
inference(variable_rename,[status(thm)],[c_0_327]) ).
fof(c_0_524,plain,
! [X3,X4] : lhs_atom1(X3,X4),
inference(variable_rename,[status(thm)],[c_0_328]) ).
fof(c_0_525,plain,
! [X27] : lhs_atom149(X27),
inference(variable_rename,[status(thm)],[c_0_329]) ).
fof(c_0_526,plain,
! [X38] : lhs_atom139(X38),
inference(variable_rename,[status(thm)],[c_0_330]) ).
fof(c_0_527,plain,
! [X27] : lhs_atom130(X27),
inference(variable_rename,[status(thm)],[c_0_331]) ).
fof(c_0_528,plain,
! [X36] : lhs_atom127(X36),
inference(variable_rename,[status(thm)],[c_0_332]) ).
fof(c_0_529,plain,
! [X3] : lhs_atom95(X3),
inference(variable_rename,[status(thm)],[c_0_333]) ).
fof(c_0_530,plain,
! [X3] : lhs_atom73(X3),
inference(variable_rename,[status(thm)],[c_0_334]) ).
fof(c_0_531,plain,
! [X3] : lhs_atom66(X3),
inference(variable_rename,[status(thm)],[c_0_335]) ).
fof(c_0_532,plain,
! [X3] : lhs_atom50(X3),
inference(variable_rename,[status(thm)],[c_0_336]) ).
fof(c_0_533,plain,
! [X16] : lhs_atom41(X16),
inference(variable_rename,[status(thm)],[c_0_337]) ).
fof(c_0_534,plain,
! [X16] : lhs_atom40(X16),
inference(variable_rename,[status(thm)],[c_0_338]) ).
fof(c_0_535,plain,
! [X8] : lhs_atom24(X8),
inference(variable_rename,[status(thm)],[c_0_339]) ).
fof(c_0_536,plain,
! [X16] : lhs_atom23(X16),
inference(variable_rename,[status(thm)],[c_0_340]) ).
fof(c_0_537,plain,
! [X16] : lhs_atom15(X16),
inference(variable_rename,[status(thm)],[c_0_341]) ).
fof(c_0_538,plain,
! [X8] : lhs_atom14(X8),
inference(variable_rename,[status(thm)],[c_0_342]) ).
fof(c_0_539,plain,
lhs_atom195,
c_0_343 ).
fof(c_0_540,plain,
lhs_atom194,
c_0_344 ).
fof(c_0_541,plain,
lhs_atom193,
c_0_345 ).
fof(c_0_542,plain,
lhs_atom192,
c_0_346 ).
fof(c_0_543,plain,
lhs_atom191,
c_0_347 ).
fof(c_0_544,plain,
lhs_atom190,
c_0_348 ).
fof(c_0_545,plain,
lhs_atom189,
c_0_349 ).
fof(c_0_546,plain,
lhs_atom188,
c_0_350 ).
fof(c_0_547,plain,
lhs_atom187,
c_0_351 ).
fof(c_0_548,plain,
lhs_atom186,
c_0_352 ).
fof(c_0_549,plain,
lhs_atom185,
c_0_353 ).
fof(c_0_550,plain,
lhs_atom184,
c_0_354 ).
fof(c_0_551,plain,
lhs_atom183,
c_0_355 ).
fof(c_0_552,plain,
lhs_atom182,
c_0_356 ).
fof(c_0_553,plain,
lhs_atom181,
c_0_357 ).
fof(c_0_554,plain,
lhs_atom180,
c_0_358 ).
fof(c_0_555,plain,
lhs_atom179,
c_0_359 ).
fof(c_0_556,plain,
lhs_atom178,
c_0_360 ).
fof(c_0_557,plain,
lhs_atom177,
c_0_361 ).
fof(c_0_558,plain,
lhs_atom176,
c_0_362 ).
fof(c_0_559,plain,
lhs_atom175,
c_0_363 ).
fof(c_0_560,plain,
lhs_atom174,
c_0_364 ).
fof(c_0_561,plain,
lhs_atom173,
c_0_365 ).
fof(c_0_562,plain,
lhs_atom172,
c_0_366 ).
fof(c_0_563,plain,
lhs_atom171,
c_0_367 ).
fof(c_0_564,plain,
lhs_atom170,
c_0_368 ).
fof(c_0_565,plain,
lhs_atom169,
c_0_369 ).
fof(c_0_566,plain,
lhs_atom168,
c_0_370 ).
fof(c_0_567,plain,
lhs_atom167,
c_0_371 ).
fof(c_0_568,plain,
lhs_atom166,
c_0_372 ).
fof(c_0_569,plain,
lhs_atom165,
c_0_373 ).
fof(c_0_570,plain,
lhs_atom164,
c_0_374 ).
fof(c_0_571,plain,
lhs_atom163,
c_0_375 ).
fof(c_0_572,plain,
lhs_atom162,
c_0_376 ).
fof(c_0_573,plain,
lhs_atom161,
c_0_377 ).
fof(c_0_574,plain,
lhs_atom160,
c_0_378 ).
fof(c_0_575,plain,
lhs_atom159,
c_0_379 ).
fof(c_0_576,plain,
lhs_atom158,
c_0_380 ).
fof(c_0_577,plain,
lhs_atom157,
c_0_381 ).
fof(c_0_578,plain,
lhs_atom156,
c_0_382 ).
fof(c_0_579,plain,
lhs_atom155,
c_0_383 ).
fof(c_0_580,plain,
lhs_atom154,
c_0_384 ).
fof(c_0_581,plain,
lhs_atom153,
c_0_385 ).
fof(c_0_582,plain,
lhs_atom152,
c_0_386 ).
fof(c_0_583,plain,
lhs_atom151,
c_0_387 ).
fof(c_0_584,plain,
lhs_atom150,
c_0_388 ).
fof(c_0_585,plain,
lhs_atom138,
c_0_389 ).
fof(c_0_586,plain,
lhs_atom129,
c_0_390 ).
fof(c_0_587,plain,
lhs_atom83,
c_0_391 ).
cnf(c_0_588,plain,
lhs_atom67(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_392]) ).
cnf(c_0_589,plain,
lhs_atom60(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_393]) ).
cnf(c_0_590,plain,
lhs_atom20(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_394]) ).
cnf(c_0_591,plain,
lhs_atom11(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_395]) ).
cnf(c_0_592,plain,
lhs_atom116(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_396]) ).
cnf(c_0_593,plain,
lhs_atom111(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_397]) ).
cnf(c_0_594,plain,
lhs_atom98(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_398]) ).
cnf(c_0_595,plain,
lhs_atom74(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_399]) ).
cnf(c_0_596,plain,
lhs_atom48(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_400]) ).
cnf(c_0_597,plain,
lhs_atom47(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_401]) ).
cnf(c_0_598,plain,
lhs_atom46(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_402]) ).
cnf(c_0_599,plain,
lhs_atom28(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_403]) ).
cnf(c_0_600,plain,
lhs_atom26(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_404]) ).
cnf(c_0_601,plain,
lhs_atom17(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_405]) ).
cnf(c_0_602,plain,
lhs_atom8(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_406]) ).
cnf(c_0_603,plain,
lhs_atom6(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_407]) ).
cnf(c_0_604,plain,
lhs_atom3(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_408]) ).
cnf(c_0_605,plain,
lhs_atom2(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_409]) ).
cnf(c_0_606,plain,
lhs_atom147(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_410]) ).
cnf(c_0_607,plain,
lhs_atom128(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_411]) ).
cnf(c_0_608,plain,
lhs_atom122(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_412]) ).
cnf(c_0_609,plain,
lhs_atom121(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_413]) ).
cnf(c_0_610,plain,
lhs_atom113(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_414]) ).
cnf(c_0_611,plain,
lhs_atom105(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_415]) ).
cnf(c_0_612,plain,
lhs_atom104(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_416]) ).
cnf(c_0_613,plain,
lhs_atom101(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_417]) ).
cnf(c_0_614,plain,
lhs_atom97(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_418]) ).
cnf(c_0_615,plain,
lhs_atom89(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_419]) ).
cnf(c_0_616,plain,
lhs_atom82(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_420]) ).
cnf(c_0_617,plain,
lhs_atom76(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_421]) ).
cnf(c_0_618,plain,
lhs_atom75(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_422]) ).
cnf(c_0_619,plain,
lhs_atom70(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_423]) ).
cnf(c_0_620,plain,
lhs_atom65(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_424]) ).
cnf(c_0_621,plain,
lhs_atom64(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_425]) ).
cnf(c_0_622,plain,
lhs_atom59(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_426]) ).
cnf(c_0_623,plain,
lhs_atom56(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_427]) ).
cnf(c_0_624,plain,
lhs_atom55(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_428]) ).
cnf(c_0_625,plain,
lhs_atom49(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_429]) ).
cnf(c_0_626,plain,
lhs_atom45(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_430]) ).
cnf(c_0_627,plain,
lhs_atom39(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_431]) ).
cnf(c_0_628,plain,
lhs_atom33(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_432]) ).
cnf(c_0_629,plain,
lhs_atom32(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_433]) ).
cnf(c_0_630,plain,
lhs_atom29(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_434]) ).
cnf(c_0_631,plain,
lhs_atom27(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_435]) ).
cnf(c_0_632,plain,
lhs_atom25(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_436]) ).
cnf(c_0_633,plain,
lhs_atom22(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_437]) ).
cnf(c_0_634,plain,
lhs_atom21(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_438]) ).
cnf(c_0_635,plain,
lhs_atom19(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_439]) ).
cnf(c_0_636,plain,
lhs_atom18(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_440]) ).
cnf(c_0_637,plain,
lhs_atom16(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_441]) ).
cnf(c_0_638,plain,
lhs_atom12(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_442]) ).
cnf(c_0_639,plain,
lhs_atom10(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_443]) ).
cnf(c_0_640,plain,
lhs_atom9(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_444]) ).
cnf(c_0_641,plain,
lhs_atom5(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_445]) ).
cnf(c_0_642,plain,
lhs_atom4(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_446]) ).
cnf(c_0_643,plain,
lhs_atom148(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_447]) ).
cnf(c_0_644,plain,
lhs_atom146(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_448]) ).
cnf(c_0_645,plain,
lhs_atom145(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_449]) ).
cnf(c_0_646,plain,
lhs_atom144(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_450]) ).
cnf(c_0_647,plain,
lhs_atom143(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_451]) ).
cnf(c_0_648,plain,
lhs_atom142(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_452]) ).
cnf(c_0_649,plain,
lhs_atom137(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_453]) ).
cnf(c_0_650,plain,
lhs_atom133(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_454]) ).
cnf(c_0_651,plain,
lhs_atom132(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_455]) ).
cnf(c_0_652,plain,
lhs_atom126(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_456]) ).
cnf(c_0_653,plain,
lhs_atom125(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_457]) ).
cnf(c_0_654,plain,
lhs_atom124(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_458]) ).
cnf(c_0_655,plain,
lhs_atom119(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_459]) ).
cnf(c_0_656,plain,
lhs_atom112(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_460]) ).
cnf(c_0_657,plain,
lhs_atom110(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_461]) ).
cnf(c_0_658,plain,
lhs_atom108(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_462]) ).
cnf(c_0_659,plain,
lhs_atom103(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_463]) ).
cnf(c_0_660,plain,
lhs_atom102(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_464]) ).
cnf(c_0_661,plain,
lhs_atom100(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_465]) ).
cnf(c_0_662,plain,
lhs_atom99(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_466]) ).
cnf(c_0_663,plain,
lhs_atom96(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_467]) ).
cnf(c_0_664,plain,
lhs_atom94(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_468]) ).
cnf(c_0_665,plain,
lhs_atom84(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_469]) ).
cnf(c_0_666,plain,
lhs_atom78(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_470]) ).
cnf(c_0_667,plain,
lhs_atom77(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_471]) ).
cnf(c_0_668,plain,
lhs_atom71(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_472]) ).
cnf(c_0_669,plain,
lhs_atom69(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_473]) ).
cnf(c_0_670,plain,
lhs_atom68(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_474]) ).
cnf(c_0_671,plain,
lhs_atom63(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_475]) ).
cnf(c_0_672,plain,
lhs_atom62(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_476]) ).
cnf(c_0_673,plain,
lhs_atom58(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_477]) ).
cnf(c_0_674,plain,
lhs_atom38(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_478]) ).
cnf(c_0_675,plain,
lhs_atom37(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_479]) ).
cnf(c_0_676,plain,
lhs_atom36(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_480]) ).
cnf(c_0_677,plain,
lhs_atom35(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_481]) ).
cnf(c_0_678,plain,
lhs_atom34(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_482]) ).
cnf(c_0_679,plain,
lhs_atom31(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_483]) ).
cnf(c_0_680,plain,
lhs_atom30(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_484]) ).
cnf(c_0_681,plain,
lhs_atom196(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_485]) ).
cnf(c_0_682,plain,
lhs_atom141(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_486]) ).
cnf(c_0_683,plain,
lhs_atom140(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_487]) ).
cnf(c_0_684,plain,
lhs_atom136(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_488]) ).
cnf(c_0_685,plain,
lhs_atom135(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_489]) ).
cnf(c_0_686,plain,
lhs_atom134(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_490]) ).
cnf(c_0_687,plain,
lhs_atom131(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_491]) ).
cnf(c_0_688,plain,
lhs_atom123(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_492]) ).
cnf(c_0_689,plain,
lhs_atom120(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_493]) ).
cnf(c_0_690,plain,
lhs_atom118(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_494]) ).
cnf(c_0_691,plain,
lhs_atom117(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_495]) ).
cnf(c_0_692,plain,
lhs_atom115(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_496]) ).
cnf(c_0_693,plain,
lhs_atom114(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_497]) ).
cnf(c_0_694,plain,
lhs_atom109(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_498]) ).
cnf(c_0_695,plain,
lhs_atom107(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_499]) ).
cnf(c_0_696,plain,
lhs_atom106(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_500]) ).
cnf(c_0_697,plain,
lhs_atom93(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_501]) ).
cnf(c_0_698,plain,
lhs_atom92(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_502]) ).
cnf(c_0_699,plain,
lhs_atom91(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_503]) ).
cnf(c_0_700,plain,
lhs_atom90(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_504]) ).
cnf(c_0_701,plain,
lhs_atom88(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_505]) ).
cnf(c_0_702,plain,
lhs_atom87(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_506]) ).
cnf(c_0_703,plain,
lhs_atom86(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_507]) ).
cnf(c_0_704,plain,
lhs_atom85(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_508]) ).
cnf(c_0_705,plain,
lhs_atom81(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_509]) ).
cnf(c_0_706,plain,
lhs_atom80(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_510]) ).
cnf(c_0_707,plain,
lhs_atom79(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_511]) ).
cnf(c_0_708,plain,
lhs_atom72(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_512]) ).
cnf(c_0_709,plain,
lhs_atom61(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_513]) ).
cnf(c_0_710,plain,
lhs_atom57(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_514]) ).
cnf(c_0_711,plain,
lhs_atom54(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_515]) ).
cnf(c_0_712,plain,
lhs_atom53(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_516]) ).
cnf(c_0_713,plain,
lhs_atom52(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_517]) ).
cnf(c_0_714,plain,
lhs_atom51(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_518]) ).
cnf(c_0_715,plain,
lhs_atom44(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_519]) ).
cnf(c_0_716,plain,
lhs_atom43(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_520]) ).
cnf(c_0_717,plain,
lhs_atom42(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_521]) ).
cnf(c_0_718,plain,
lhs_atom13(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_522]) ).
cnf(c_0_719,plain,
lhs_atom7(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_523]) ).
cnf(c_0_720,plain,
lhs_atom1(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_524]) ).
cnf(c_0_721,plain,
lhs_atom149(X1),
inference(split_conjunct,[status(thm)],[c_0_525]) ).
cnf(c_0_722,plain,
lhs_atom139(X1),
inference(split_conjunct,[status(thm)],[c_0_526]) ).
cnf(c_0_723,plain,
lhs_atom130(X1),
inference(split_conjunct,[status(thm)],[c_0_527]) ).
cnf(c_0_724,plain,
lhs_atom127(X1),
inference(split_conjunct,[status(thm)],[c_0_528]) ).
cnf(c_0_725,plain,
lhs_atom95(X1),
inference(split_conjunct,[status(thm)],[c_0_529]) ).
cnf(c_0_726,plain,
lhs_atom73(X1),
inference(split_conjunct,[status(thm)],[c_0_530]) ).
cnf(c_0_727,plain,
lhs_atom66(X1),
inference(split_conjunct,[status(thm)],[c_0_531]) ).
cnf(c_0_728,plain,
lhs_atom50(X1),
inference(split_conjunct,[status(thm)],[c_0_532]) ).
cnf(c_0_729,plain,
lhs_atom41(X1),
inference(split_conjunct,[status(thm)],[c_0_533]) ).
cnf(c_0_730,plain,
lhs_atom40(X1),
inference(split_conjunct,[status(thm)],[c_0_534]) ).
cnf(c_0_731,plain,
lhs_atom24(X1),
inference(split_conjunct,[status(thm)],[c_0_535]) ).
cnf(c_0_732,plain,
lhs_atom23(X1),
inference(split_conjunct,[status(thm)],[c_0_536]) ).
cnf(c_0_733,plain,
lhs_atom15(X1),
inference(split_conjunct,[status(thm)],[c_0_537]) ).
cnf(c_0_734,plain,
lhs_atom14(X1),
inference(split_conjunct,[status(thm)],[c_0_538]) ).
cnf(c_0_735,plain,
lhs_atom195,
inference(split_conjunct,[status(thm)],[c_0_539]) ).
cnf(c_0_736,plain,
lhs_atom194,
inference(split_conjunct,[status(thm)],[c_0_540]) ).
cnf(c_0_737,plain,
lhs_atom193,
inference(split_conjunct,[status(thm)],[c_0_541]) ).
cnf(c_0_738,plain,
lhs_atom192,
inference(split_conjunct,[status(thm)],[c_0_542]) ).
cnf(c_0_739,plain,
lhs_atom191,
inference(split_conjunct,[status(thm)],[c_0_543]) ).
cnf(c_0_740,plain,
lhs_atom190,
inference(split_conjunct,[status(thm)],[c_0_544]) ).
cnf(c_0_741,plain,
lhs_atom189,
inference(split_conjunct,[status(thm)],[c_0_545]) ).
cnf(c_0_742,plain,
lhs_atom188,
inference(split_conjunct,[status(thm)],[c_0_546]) ).
cnf(c_0_743,plain,
lhs_atom187,
inference(split_conjunct,[status(thm)],[c_0_547]) ).
cnf(c_0_744,plain,
lhs_atom186,
inference(split_conjunct,[status(thm)],[c_0_548]) ).
cnf(c_0_745,plain,
lhs_atom185,
inference(split_conjunct,[status(thm)],[c_0_549]) ).
cnf(c_0_746,plain,
lhs_atom184,
inference(split_conjunct,[status(thm)],[c_0_550]) ).
cnf(c_0_747,plain,
lhs_atom183,
inference(split_conjunct,[status(thm)],[c_0_551]) ).
cnf(c_0_748,plain,
lhs_atom182,
inference(split_conjunct,[status(thm)],[c_0_552]) ).
cnf(c_0_749,plain,
lhs_atom181,
inference(split_conjunct,[status(thm)],[c_0_553]) ).
cnf(c_0_750,plain,
lhs_atom180,
inference(split_conjunct,[status(thm)],[c_0_554]) ).
cnf(c_0_751,plain,
lhs_atom179,
inference(split_conjunct,[status(thm)],[c_0_555]) ).
cnf(c_0_752,plain,
lhs_atom178,
inference(split_conjunct,[status(thm)],[c_0_556]) ).
cnf(c_0_753,plain,
lhs_atom177,
inference(split_conjunct,[status(thm)],[c_0_557]) ).
cnf(c_0_754,plain,
lhs_atom176,
inference(split_conjunct,[status(thm)],[c_0_558]) ).
cnf(c_0_755,plain,
lhs_atom175,
inference(split_conjunct,[status(thm)],[c_0_559]) ).
cnf(c_0_756,plain,
lhs_atom174,
inference(split_conjunct,[status(thm)],[c_0_560]) ).
cnf(c_0_757,plain,
lhs_atom173,
inference(split_conjunct,[status(thm)],[c_0_561]) ).
cnf(c_0_758,plain,
lhs_atom172,
inference(split_conjunct,[status(thm)],[c_0_562]) ).
cnf(c_0_759,plain,
lhs_atom171,
inference(split_conjunct,[status(thm)],[c_0_563]) ).
cnf(c_0_760,plain,
lhs_atom170,
inference(split_conjunct,[status(thm)],[c_0_564]) ).
cnf(c_0_761,plain,
lhs_atom169,
inference(split_conjunct,[status(thm)],[c_0_565]) ).
cnf(c_0_762,plain,
lhs_atom168,
inference(split_conjunct,[status(thm)],[c_0_566]) ).
cnf(c_0_763,plain,
lhs_atom167,
inference(split_conjunct,[status(thm)],[c_0_567]) ).
cnf(c_0_764,plain,
lhs_atom166,
inference(split_conjunct,[status(thm)],[c_0_568]) ).
cnf(c_0_765,plain,
lhs_atom165,
inference(split_conjunct,[status(thm)],[c_0_569]) ).
cnf(c_0_766,plain,
lhs_atom164,
inference(split_conjunct,[status(thm)],[c_0_570]) ).
cnf(c_0_767,plain,
lhs_atom163,
inference(split_conjunct,[status(thm)],[c_0_571]) ).
cnf(c_0_768,plain,
lhs_atom162,
inference(split_conjunct,[status(thm)],[c_0_572]) ).
cnf(c_0_769,plain,
lhs_atom161,
inference(split_conjunct,[status(thm)],[c_0_573]) ).
cnf(c_0_770,plain,
lhs_atom160,
inference(split_conjunct,[status(thm)],[c_0_574]) ).
cnf(c_0_771,plain,
lhs_atom159,
inference(split_conjunct,[status(thm)],[c_0_575]) ).
cnf(c_0_772,plain,
lhs_atom158,
inference(split_conjunct,[status(thm)],[c_0_576]) ).
cnf(c_0_773,plain,
lhs_atom157,
inference(split_conjunct,[status(thm)],[c_0_577]) ).
cnf(c_0_774,plain,
lhs_atom156,
inference(split_conjunct,[status(thm)],[c_0_578]) ).
cnf(c_0_775,plain,
lhs_atom155,
inference(split_conjunct,[status(thm)],[c_0_579]) ).
cnf(c_0_776,plain,
lhs_atom154,
inference(split_conjunct,[status(thm)],[c_0_580]) ).
cnf(c_0_777,plain,
lhs_atom153,
inference(split_conjunct,[status(thm)],[c_0_581]) ).
cnf(c_0_778,plain,
lhs_atom152,
inference(split_conjunct,[status(thm)],[c_0_582]) ).
cnf(c_0_779,plain,
lhs_atom151,
inference(split_conjunct,[status(thm)],[c_0_583]) ).
cnf(c_0_780,plain,
lhs_atom150,
inference(split_conjunct,[status(thm)],[c_0_584]) ).
cnf(c_0_781,plain,
lhs_atom138,
inference(split_conjunct,[status(thm)],[c_0_585]) ).
cnf(c_0_782,plain,
lhs_atom129,
inference(split_conjunct,[status(thm)],[c_0_586]) ).
cnf(c_0_783,plain,
lhs_atom83,
inference(split_conjunct,[status(thm)],[c_0_587]) ).
cnf(c_0_784,plain,
lhs_atom67(X1,X2,X3,X4,X5,X6),
c_0_588,
[final] ).
cnf(c_0_785,plain,
lhs_atom60(X1,X2,X3,X4,X5,X6),
c_0_589,
[final] ).
cnf(c_0_786,plain,
lhs_atom20(X1,X2,X3,X4,X5,X6),
c_0_590,
[final] ).
cnf(c_0_787,plain,
lhs_atom11(X1,X2,X3,X4,X5,X6),
c_0_591,
[final] ).
cnf(c_0_788,plain,
lhs_atom116(X1,X2,X3,X4,X5),
c_0_592,
[final] ).
cnf(c_0_789,plain,
lhs_atom111(X1,X2,X3,X4,X5),
c_0_593,
[final] ).
cnf(c_0_790,plain,
lhs_atom98(X1,X2,X3,X4,X5),
c_0_594,
[final] ).
cnf(c_0_791,plain,
lhs_atom74(X1,X2,X3,X4,X5),
c_0_595,
[final] ).
cnf(c_0_792,plain,
lhs_atom48(X1,X2,X3,X4,X5),
c_0_596,
[final] ).
cnf(c_0_793,plain,
lhs_atom47(X1,X2,X3,X4,X5),
c_0_597,
[final] ).
cnf(c_0_794,plain,
lhs_atom46(X1,X2,X3,X4,X5),
c_0_598,
[final] ).
cnf(c_0_795,plain,
lhs_atom28(X1,X2,X3,X4,X5),
c_0_599,
[final] ).
cnf(c_0_796,plain,
lhs_atom26(X1,X2,X3,X4,X5),
c_0_600,
[final] ).
cnf(c_0_797,plain,
lhs_atom17(X1,X2,X3,X4,X5),
c_0_601,
[final] ).
cnf(c_0_798,plain,
lhs_atom8(X1,X2,X3,X4,X5),
c_0_602,
[final] ).
cnf(c_0_799,plain,
lhs_atom6(X1,X2,X3,X4,X5),
c_0_603,
[final] ).
cnf(c_0_800,plain,
lhs_atom3(X1,X2,X3,X4,X5),
c_0_604,
[final] ).
cnf(c_0_801,plain,
lhs_atom2(X1,X2,X3,X4,X5),
c_0_605,
[final] ).
cnf(c_0_802,plain,
lhs_atom147(X1,X2,X3,X4),
c_0_606,
[final] ).
cnf(c_0_803,plain,
lhs_atom128(X1,X2,X3,X4),
c_0_607,
[final] ).
cnf(c_0_804,plain,
lhs_atom122(X1,X2,X3,X4),
c_0_608,
[final] ).
cnf(c_0_805,plain,
lhs_atom121(X1,X2,X3,X4),
c_0_609,
[final] ).
cnf(c_0_806,plain,
lhs_atom113(X1,X2,X3,X4),
c_0_610,
[final] ).
cnf(c_0_807,plain,
lhs_atom105(X1,X2,X3,X4),
c_0_611,
[final] ).
cnf(c_0_808,plain,
lhs_atom104(X1,X2,X3,X4),
c_0_612,
[final] ).
cnf(c_0_809,plain,
lhs_atom101(X1,X2,X3,X4),
c_0_613,
[final] ).
cnf(c_0_810,plain,
lhs_atom97(X1,X2,X3,X4),
c_0_614,
[final] ).
cnf(c_0_811,plain,
lhs_atom89(X1,X2,X3,X4),
c_0_615,
[final] ).
cnf(c_0_812,plain,
lhs_atom82(X1,X2,X3,X4),
c_0_616,
[final] ).
cnf(c_0_813,plain,
lhs_atom76(X1,X2,X3,X4),
c_0_617,
[final] ).
cnf(c_0_814,plain,
lhs_atom75(X1,X2,X3,X4),
c_0_618,
[final] ).
cnf(c_0_815,plain,
lhs_atom70(X1,X2,X3,X4),
c_0_619,
[final] ).
cnf(c_0_816,plain,
lhs_atom65(X1,X2,X3,X4),
c_0_620,
[final] ).
cnf(c_0_817,plain,
lhs_atom64(X1,X2,X3,X4),
c_0_621,
[final] ).
cnf(c_0_818,plain,
lhs_atom59(X1,X2,X3,X4),
c_0_622,
[final] ).
cnf(c_0_819,plain,
lhs_atom56(X1,X2,X3,X4),
c_0_623,
[final] ).
cnf(c_0_820,plain,
lhs_atom55(X1,X2,X3,X4),
c_0_624,
[final] ).
cnf(c_0_821,plain,
lhs_atom49(X1,X2,X3,X4),
c_0_625,
[final] ).
cnf(c_0_822,plain,
lhs_atom45(X1,X2,X3,X4),
c_0_626,
[final] ).
cnf(c_0_823,plain,
lhs_atom39(X1,X2,X3,X4),
c_0_627,
[final] ).
cnf(c_0_824,plain,
lhs_atom33(X1,X2,X3,X4),
c_0_628,
[final] ).
cnf(c_0_825,plain,
lhs_atom32(X1,X2,X3,X4),
c_0_629,
[final] ).
cnf(c_0_826,plain,
lhs_atom29(X1,X2,X3,X4),
c_0_630,
[final] ).
cnf(c_0_827,plain,
lhs_atom27(X1,X2,X3,X4),
c_0_631,
[final] ).
cnf(c_0_828,plain,
lhs_atom25(X1,X2,X3,X4),
c_0_632,
[final] ).
cnf(c_0_829,plain,
lhs_atom22(X1,X2,X3,X4),
c_0_633,
[final] ).
cnf(c_0_830,plain,
lhs_atom21(X1,X2,X3,X4),
c_0_634,
[final] ).
cnf(c_0_831,plain,
lhs_atom19(X1,X2,X3,X4),
c_0_635,
[final] ).
cnf(c_0_832,plain,
lhs_atom18(X1,X2,X3,X4),
c_0_636,
[final] ).
cnf(c_0_833,plain,
lhs_atom16(X1,X2,X3,X4),
c_0_637,
[final] ).
cnf(c_0_834,plain,
lhs_atom12(X1,X2,X3,X4),
c_0_638,
[final] ).
cnf(c_0_835,plain,
lhs_atom10(X1,X2,X3,X4),
c_0_639,
[final] ).
cnf(c_0_836,plain,
lhs_atom9(X1,X2,X3,X4),
c_0_640,
[final] ).
cnf(c_0_837,plain,
lhs_atom5(X1,X2,X3,X4),
c_0_641,
[final] ).
cnf(c_0_838,plain,
lhs_atom4(X1,X2,X3,X4),
c_0_642,
[final] ).
cnf(c_0_839,plain,
lhs_atom148(X1,X2,X3),
c_0_643,
[final] ).
cnf(c_0_840,plain,
lhs_atom146(X1,X2,X3),
c_0_644,
[final] ).
cnf(c_0_841,plain,
lhs_atom145(X1,X2,X3),
c_0_645,
[final] ).
cnf(c_0_842,plain,
lhs_atom144(X1,X2,X3),
c_0_646,
[final] ).
cnf(c_0_843,plain,
lhs_atom143(X1,X2,X3),
c_0_647,
[final] ).
cnf(c_0_844,plain,
lhs_atom142(X1,X2,X3),
c_0_648,
[final] ).
cnf(c_0_845,plain,
lhs_atom137(X1,X2,X3),
c_0_649,
[final] ).
cnf(c_0_846,plain,
lhs_atom133(X1,X2,X3),
c_0_650,
[final] ).
cnf(c_0_847,plain,
lhs_atom132(X1,X2,X3),
c_0_651,
[final] ).
cnf(c_0_848,plain,
lhs_atom126(X1,X2,X3),
c_0_652,
[final] ).
cnf(c_0_849,plain,
lhs_atom125(X1,X2,X3),
c_0_653,
[final] ).
cnf(c_0_850,plain,
lhs_atom124(X1,X2,X3),
c_0_654,
[final] ).
cnf(c_0_851,plain,
lhs_atom119(X1,X2,X3),
c_0_655,
[final] ).
cnf(c_0_852,plain,
lhs_atom112(X1,X2,X3),
c_0_656,
[final] ).
cnf(c_0_853,plain,
lhs_atom110(X1,X2,X3),
c_0_657,
[final] ).
cnf(c_0_854,plain,
lhs_atom108(X1,X2,X3),
c_0_658,
[final] ).
cnf(c_0_855,plain,
lhs_atom103(X1,X2,X3),
c_0_659,
[final] ).
cnf(c_0_856,plain,
lhs_atom102(X1,X2,X3),
c_0_660,
[final] ).
cnf(c_0_857,plain,
lhs_atom100(X1,X2,X3),
c_0_661,
[final] ).
cnf(c_0_858,plain,
lhs_atom99(X1,X2,X3),
c_0_662,
[final] ).
cnf(c_0_859,plain,
lhs_atom96(X1,X2,X3),
c_0_663,
[final] ).
cnf(c_0_860,plain,
lhs_atom94(X1,X2,X3),
c_0_664,
[final] ).
cnf(c_0_861,plain,
lhs_atom84(X1,X2,X3),
c_0_665,
[final] ).
cnf(c_0_862,plain,
lhs_atom78(X1,X2,X3),
c_0_666,
[final] ).
cnf(c_0_863,plain,
lhs_atom77(X1,X2,X3),
c_0_667,
[final] ).
cnf(c_0_864,plain,
lhs_atom71(X1,X2,X3),
c_0_668,
[final] ).
cnf(c_0_865,plain,
lhs_atom69(X1,X2,X3),
c_0_669,
[final] ).
cnf(c_0_866,plain,
lhs_atom68(X1,X2,X3),
c_0_670,
[final] ).
cnf(c_0_867,plain,
lhs_atom63(X1,X2,X3),
c_0_671,
[final] ).
cnf(c_0_868,plain,
lhs_atom62(X1,X2,X3),
c_0_672,
[final] ).
cnf(c_0_869,plain,
lhs_atom58(X1,X2,X3),
c_0_673,
[final] ).
cnf(c_0_870,plain,
lhs_atom38(X1,X2,X3),
c_0_674,
[final] ).
cnf(c_0_871,plain,
lhs_atom37(X1,X2,X3),
c_0_675,
[final] ).
cnf(c_0_872,plain,
lhs_atom36(X1,X2,X3),
c_0_676,
[final] ).
cnf(c_0_873,plain,
lhs_atom35(X1,X2,X3),
c_0_677,
[final] ).
cnf(c_0_874,plain,
lhs_atom34(X1,X2,X3),
c_0_678,
[final] ).
cnf(c_0_875,plain,
lhs_atom31(X1,X2,X3),
c_0_679,
[final] ).
cnf(c_0_876,plain,
lhs_atom30(X1,X2,X3),
c_0_680,
[final] ).
cnf(c_0_877,plain,
lhs_atom196(X1,X2),
c_0_681,
[final] ).
cnf(c_0_878,plain,
lhs_atom141(X1,X2),
c_0_682,
[final] ).
cnf(c_0_879,plain,
lhs_atom140(X1,X2),
c_0_683,
[final] ).
cnf(c_0_880,plain,
lhs_atom136(X1,X2),
c_0_684,
[final] ).
cnf(c_0_881,plain,
lhs_atom135(X1,X2),
c_0_685,
[final] ).
cnf(c_0_882,plain,
lhs_atom134(X1,X2),
c_0_686,
[final] ).
cnf(c_0_883,plain,
lhs_atom131(X1,X2),
c_0_687,
[final] ).
cnf(c_0_884,plain,
lhs_atom123(X1,X2),
c_0_688,
[final] ).
cnf(c_0_885,plain,
lhs_atom120(X1,X2),
c_0_689,
[final] ).
cnf(c_0_886,plain,
lhs_atom118(X1,X2),
c_0_690,
[final] ).
cnf(c_0_887,plain,
lhs_atom117(X1,X2),
c_0_691,
[final] ).
cnf(c_0_888,plain,
lhs_atom115(X1,X2),
c_0_692,
[final] ).
cnf(c_0_889,plain,
lhs_atom114(X1,X2),
c_0_693,
[final] ).
cnf(c_0_890,plain,
lhs_atom109(X1,X2),
c_0_694,
[final] ).
cnf(c_0_891,plain,
lhs_atom107(X1,X2),
c_0_695,
[final] ).
cnf(c_0_892,plain,
lhs_atom106(X1,X2),
c_0_696,
[final] ).
cnf(c_0_893,plain,
lhs_atom93(X1,X2),
c_0_697,
[final] ).
cnf(c_0_894,plain,
lhs_atom92(X1,X2),
c_0_698,
[final] ).
cnf(c_0_895,plain,
lhs_atom91(X1,X2),
c_0_699,
[final] ).
cnf(c_0_896,plain,
lhs_atom90(X1,X2),
c_0_700,
[final] ).
cnf(c_0_897,plain,
lhs_atom88(X1,X2),
c_0_701,
[final] ).
cnf(c_0_898,plain,
lhs_atom87(X1,X2),
c_0_702,
[final] ).
cnf(c_0_899,plain,
lhs_atom86(X1,X2),
c_0_703,
[final] ).
cnf(c_0_900,plain,
lhs_atom85(X1,X2),
c_0_704,
[final] ).
cnf(c_0_901,plain,
lhs_atom81(X1,X2),
c_0_705,
[final] ).
cnf(c_0_902,plain,
lhs_atom80(X1,X2),
c_0_706,
[final] ).
cnf(c_0_903,plain,
lhs_atom79(X1,X2),
c_0_707,
[final] ).
cnf(c_0_904,plain,
lhs_atom72(X1,X2),
c_0_708,
[final] ).
cnf(c_0_905,plain,
lhs_atom61(X1,X2),
c_0_709,
[final] ).
cnf(c_0_906,plain,
lhs_atom57(X1,X2),
c_0_710,
[final] ).
cnf(c_0_907,plain,
lhs_atom54(X1,X2),
c_0_711,
[final] ).
cnf(c_0_908,plain,
lhs_atom53(X1,X2),
c_0_712,
[final] ).
cnf(c_0_909,plain,
lhs_atom52(X1,X2),
c_0_713,
[final] ).
cnf(c_0_910,plain,
lhs_atom51(X1,X2),
c_0_714,
[final] ).
cnf(c_0_911,plain,
lhs_atom44(X1,X2),
c_0_715,
[final] ).
cnf(c_0_912,plain,
lhs_atom43(X1,X2),
c_0_716,
[final] ).
cnf(c_0_913,plain,
lhs_atom42(X1,X2),
c_0_717,
[final] ).
cnf(c_0_914,plain,
lhs_atom13(X1,X2),
c_0_718,
[final] ).
cnf(c_0_915,plain,
lhs_atom7(X1,X2),
c_0_719,
[final] ).
cnf(c_0_916,plain,
lhs_atom1(X1,X2),
c_0_720,
[final] ).
cnf(c_0_917,plain,
lhs_atom149(X1),
c_0_721,
[final] ).
cnf(c_0_918,plain,
lhs_atom139(X1),
c_0_722,
[final] ).
cnf(c_0_919,plain,
lhs_atom130(X1),
c_0_723,
[final] ).
cnf(c_0_920,plain,
lhs_atom127(X1),
c_0_724,
[final] ).
cnf(c_0_921,plain,
lhs_atom95(X1),
c_0_725,
[final] ).
cnf(c_0_922,plain,
lhs_atom73(X1),
c_0_726,
[final] ).
cnf(c_0_923,plain,
lhs_atom66(X1),
c_0_727,
[final] ).
cnf(c_0_924,plain,
lhs_atom50(X1),
c_0_728,
[final] ).
cnf(c_0_925,plain,
lhs_atom41(X1),
c_0_729,
[final] ).
cnf(c_0_926,plain,
lhs_atom40(X1),
c_0_730,
[final] ).
cnf(c_0_927,plain,
lhs_atom24(X1),
c_0_731,
[final] ).
cnf(c_0_928,plain,
lhs_atom23(X1),
c_0_732,
[final] ).
cnf(c_0_929,plain,
lhs_atom15(X1),
c_0_733,
[final] ).
cnf(c_0_930,plain,
lhs_atom14(X1),
c_0_734,
[final] ).
cnf(c_0_931,plain,
lhs_atom195,
c_0_735,
[final] ).
cnf(c_0_932,plain,
lhs_atom194,
c_0_736,
[final] ).
cnf(c_0_933,plain,
lhs_atom193,
c_0_737,
[final] ).
cnf(c_0_934,plain,
lhs_atom192,
c_0_738,
[final] ).
cnf(c_0_935,plain,
lhs_atom191,
c_0_739,
[final] ).
cnf(c_0_936,plain,
lhs_atom190,
c_0_740,
[final] ).
cnf(c_0_937,plain,
lhs_atom189,
c_0_741,
[final] ).
cnf(c_0_938,plain,
lhs_atom188,
c_0_742,
[final] ).
cnf(c_0_939,plain,
lhs_atom187,
c_0_743,
[final] ).
cnf(c_0_940,plain,
lhs_atom186,
c_0_744,
[final] ).
cnf(c_0_941,plain,
lhs_atom185,
c_0_745,
[final] ).
cnf(c_0_942,plain,
lhs_atom184,
c_0_746,
[final] ).
cnf(c_0_943,plain,
lhs_atom183,
c_0_747,
[final] ).
cnf(c_0_944,plain,
lhs_atom182,
c_0_748,
[final] ).
cnf(c_0_945,plain,
lhs_atom181,
c_0_749,
[final] ).
cnf(c_0_946,plain,
lhs_atom180,
c_0_750,
[final] ).
cnf(c_0_947,plain,
lhs_atom179,
c_0_751,
[final] ).
cnf(c_0_948,plain,
lhs_atom178,
c_0_752,
[final] ).
cnf(c_0_949,plain,
lhs_atom177,
c_0_753,
[final] ).
cnf(c_0_950,plain,
lhs_atom176,
c_0_754,
[final] ).
cnf(c_0_951,plain,
lhs_atom175,
c_0_755,
[final] ).
cnf(c_0_952,plain,
lhs_atom174,
c_0_756,
[final] ).
cnf(c_0_953,plain,
lhs_atom173,
c_0_757,
[final] ).
cnf(c_0_954,plain,
lhs_atom172,
c_0_758,
[final] ).
cnf(c_0_955,plain,
lhs_atom171,
c_0_759,
[final] ).
cnf(c_0_956,plain,
lhs_atom170,
c_0_760,
[final] ).
cnf(c_0_957,plain,
lhs_atom169,
c_0_761,
[final] ).
cnf(c_0_958,plain,
lhs_atom168,
c_0_762,
[final] ).
cnf(c_0_959,plain,
lhs_atom167,
c_0_763,
[final] ).
cnf(c_0_960,plain,
lhs_atom166,
c_0_764,
[final] ).
cnf(c_0_961,plain,
lhs_atom165,
c_0_765,
[final] ).
cnf(c_0_962,plain,
lhs_atom164,
c_0_766,
[final] ).
cnf(c_0_963,plain,
lhs_atom163,
c_0_767,
[final] ).
cnf(c_0_964,plain,
lhs_atom162,
c_0_768,
[final] ).
cnf(c_0_965,plain,
lhs_atom161,
c_0_769,
[final] ).
cnf(c_0_966,plain,
lhs_atom160,
c_0_770,
[final] ).
cnf(c_0_967,plain,
lhs_atom159,
c_0_771,
[final] ).
cnf(c_0_968,plain,
lhs_atom158,
c_0_772,
[final] ).
cnf(c_0_969,plain,
lhs_atom157,
c_0_773,
[final] ).
cnf(c_0_970,plain,
lhs_atom156,
c_0_774,
[final] ).
cnf(c_0_971,plain,
lhs_atom155,
c_0_775,
[final] ).
cnf(c_0_972,plain,
lhs_atom154,
c_0_776,
[final] ).
cnf(c_0_973,plain,
lhs_atom153,
c_0_777,
[final] ).
cnf(c_0_974,plain,
lhs_atom152,
c_0_778,
[final] ).
cnf(c_0_975,plain,
lhs_atom151,
c_0_779,
[final] ).
cnf(c_0_976,plain,
lhs_atom150,
c_0_780,
[final] ).
cnf(c_0_977,plain,
lhs_atom138,
c_0_781,
[final] ).
cnf(c_0_978,plain,
lhs_atom129,
c_0_782,
[final] ).
cnf(c_0_979,plain,
lhs_atom83,
c_0_783,
[final] ).
% End CNF derivation
cnf(c_0_784_0,axiom,
c_Map_Omap__add(X4,c_Fun_Ofun__upd(X3,X2,hAPP(c_Option_Ooption_OSome(X5),X1),X6,tc_Option_Ooption(X5)),X6,X5) = c_Fun_Ofun__upd(c_Map_Omap__add(X4,X3,X6,X5),X2,hAPP(c_Option_Ooption_OSome(X5),X1),X6,tc_Option_Ooption(X5)),
inference(unfold_definition,[status(thm)],[c_0_784,def_lhs_atom67]) ).
cnf(c_0_785_0,axiom,
c_Fun_Ofun__upd(c_Map_Orestrict__map(X3,X4,X6,X5),X2,X1,X6,tc_Option_Ooption(X5)) = c_Fun_Ofun__upd(c_Map_Orestrict__map(X3,c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X6),X2),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool))),tc_fun(X6,tc_bool)),X6,X5),X2,X1,X6,tc_Option_Ooption(X5)),
inference(unfold_definition,[status(thm)],[c_0_785,def_lhs_atom60]) ).
cnf(c_0_786_0,axiom,
hAPP(hAPP(c_COMBC(X3,X5,X4,X6),X2),X1) = hAPP(hAPP(X3,X1),X2),
inference(unfold_definition,[status(thm)],[c_0_786,def_lhs_atom20]) ).
cnf(c_0_787_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_787,def_lhs_atom11]) ).
cnf(c_0_788_0,axiom,
c_Map_Omap__add(X3,c_Map_Omap__add(X2,X1,X5,X4),X5,X4) = c_Map_Omap__add(c_Map_Omap__add(X3,X2,X5,X4),X1,X5,X4),
inference(unfold_definition,[status(thm)],[c_0_788,def_lhs_atom116]) ).
cnf(c_0_789_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_789,def_lhs_atom111]) ).
cnf(c_0_790_0,axiom,
c_Set_Ovimage(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X3),X2),X5,X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X5,tc_bool)),c_Set_Ovimage(X1,X3,X5,X4)),c_Set_Ovimage(X1,X2,X5,X4)),
inference(unfold_definition,[status(thm)],[c_0_790,def_lhs_atom98]) ).
cnf(c_0_791_0,axiom,
c_Set_Ovimage(X1,hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X5,X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X5,tc_bool)),c_Set_Ovimage(X1,hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))),X5,X4)),c_Set_Ovimage(X1,X3,X5,X4)),
inference(unfold_definition,[status(thm)],[c_0_791,def_lhs_atom74]) ).
cnf(c_0_792_0,axiom,
c_Finite__Set_Ofold__image(X3,X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X5,X4) = X1,
inference(unfold_definition,[status(thm)],[c_0_792,def_lhs_atom48]) ).
cnf(c_0_793_0,axiom,
c_Set_Ovimage(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X3),X2),X5,X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X5,tc_bool)),c_Set_Ovimage(X1,X3,X5,X4)),c_Set_Ovimage(X1,X2,X5,X4)),
inference(unfold_definition,[status(thm)],[c_0_793,def_lhs_atom47]) ).
cnf(c_0_794_0,axiom,
hAPP(c_Fun_Ofun__upd(X3,X1,hAPP(c_Option_Ooption_OSome(X5),X2),X4,tc_Option_Ooption(X5)),X1) = hAPP(c_Option_Ooption_OSome(X5),X2),
inference(unfold_definition,[status(thm)],[c_0_794,def_lhs_atom46]) ).
cnf(c_0_795_0,axiom,
hAPP(c_Fun_Ofun__upd(X3,X2,X1,X5,X4),X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_795,def_lhs_atom28]) ).
cnf(c_0_796_0,axiom,
hAPP(c_Fun_Ofun__upd(X3,X2,X1,X4,X5),X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_796,def_lhs_atom26]) ).
cnf(c_0_797_0,axiom,
c_Option_Ooption_Ooption__case(X2,X1,hAPP(c_Option_Ooption_OSome(X4),X3),X5,X4) = hAPP(X1,X3),
inference(unfold_definition,[status(thm)],[c_0_797,def_lhs_atom17]) ).
cnf(c_0_798_0,axiom,
c_Map_Orestrict__map(X1,hAPP(hAPP(c_Set_Oinsert(X5),X2),X3),X5,X4) = c_Fun_Ofun__upd(c_Map_Orestrict__map(X1,X3,X5,X4),X2,hAPP(X1,X2),X5,tc_Option_Ooption(X4)),
inference(unfold_definition,[status(thm)],[c_0_798,def_lhs_atom8]) ).
cnf(c_0_799_0,axiom,
c_Map_Orestrict__map(c_Map_Orestrict__map(X1,X3,X5,X4),X2,X5,X4) = c_Map_Orestrict__map(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X5,tc_bool)),X3),X2),X5,X4),
inference(unfold_definition,[status(thm)],[c_0_799,def_lhs_atom6]) ).
cnf(c_0_800_0,axiom,
c_Fun_Ofun__upd(X2,X3,hAPP(c_Option_Ooption_OSome(X4),X1),X5,tc_Option_Ooption(X4)) != c_COMBK(c_Option_Ooption_ONone(X4),tc_Option_Ooption(X4),X5),
inference(unfold_definition,[status(thm)],[c_0_800,def_lhs_atom3]) ).
cnf(c_0_801_0,axiom,
c_Finite__Set_Ofold(X2,X1,X3,X4,X5) = c_The(c_Finite__Set_Ofold__graph(X2,X1,X3,X4,X5),X5),
inference(unfold_definition,[status(thm)],[c_0_801,def_lhs_atom2]) ).
cnf(c_0_802_0,axiom,
hAPP(hAPP(c_Set_Oinsert(X4),X2),hAPP(hAPP(c_Set_Oinsert(X4),X1),X3)) = hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Set_Oinsert(X4),X2),X3)),
inference(unfold_definition,[status(thm)],[c_0_802,def_lhs_atom147]) ).
cnf(c_0_803_0,axiom,
hBOOL(hAPP(hAPP(c_in(X3),X2),c_Set_Ovimage(X1,hAPP(hAPP(c_Set_Oinsert(X4),hAPP(X1,X2)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))),X3,X4))),
inference(unfold_definition,[status(thm)],[c_0_803,def_lhs_atom128]) ).
cnf(c_0_804_0,axiom,
c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X4),X1),X2),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X4,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_804,def_lhs_atom122]) ).
cnf(c_0_805_0,axiom,
c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X4),X1),X2),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))),tc_fun(X4,tc_bool)),X2,tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_805,def_lhs_atom121]) ).
cnf(c_0_806_0,axiom,
c_Map_Odom(c_Map_Omap__add(X2,X1,X4,X3),X4,X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),c_Map_Odom(X1,X4,X3)),c_Map_Odom(X2,X4,X3)),
inference(unfold_definition,[status(thm)],[c_0_806,def_lhs_atom113]) ).
cnf(c_0_807_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X2),X1)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X3),X1)),
inference(unfold_definition,[status(thm)],[c_0_807,def_lhs_atom105]) ).
cnf(c_0_808_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X3),X2)),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X2),X1)),
inference(unfold_definition,[status(thm)],[c_0_808,def_lhs_atom104]) ).
cnf(c_0_809_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X3),X2),X1,tc_fun(X4,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X4,tc_bool))),c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X4,tc_bool))),
inference(unfold_definition,[status(thm)],[c_0_809,def_lhs_atom101]) ).
cnf(c_0_810_0,axiom,
c_Map_Omap__le(X2,c_Map_Omap__add(X1,X2,X4,X3),X4,X3),
inference(unfold_definition,[status(thm)],[c_0_810,def_lhs_atom97]) ).
cnf(c_0_811_0,axiom,
c_Map_Odom(c_Fun_Ofun__upd(c_COMBK(c_Option_Ooption_ONone(X3),tc_Option_Ooption(X3),X4),X2,hAPP(c_Option_Ooption_OSome(X3),X1),X4,tc_Option_Ooption(X3)),X4,X3) = hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))),
inference(unfold_definition,[status(thm)],[c_0_811,def_lhs_atom89]) ).
cnf(c_0_812_0,axiom,
c_Map_Odom(c_Fun_Ofun__upd(X2,X1,c_Option_Ooption_ONone(X3),X4,tc_Option_Ooption(X3)),X4,X3) = c_HOL_Ominus__class_Ominus(c_Map_Odom(X2,X4,X3),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_812,def_lhs_atom82]) ).
cnf(c_0_813_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X4),X1),X3)),X2) = hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X3),X2)),
inference(unfold_definition,[status(thm)],[c_0_813,def_lhs_atom76]) ).
cnf(c_0_814_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X3),hAPP(hAPP(c_Set_Oinsert(X4),X1),X2)) = hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X3),X2)),
inference(unfold_definition,[status(thm)],[c_0_814,def_lhs_atom75]) ).
cnf(c_0_815_0,axiom,
c_Map_Omap__le(c_Fun_Ofun__upd(X2,X1,c_Option_Ooption_ONone(X3),X4,tc_Option_Ooption(X3)),X2,X4,X3),
inference(unfold_definition,[status(thm)],[c_0_815,def_lhs_atom70]) ).
cnf(c_0_816_0,axiom,
c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X2),X1),tc_fun(X4,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X4,tc_bool))),c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X4,tc_bool))),
inference(unfold_definition,[status(thm)],[c_0_816,def_lhs_atom65]) ).
cnf(c_0_817_0,axiom,
c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X2),X1),tc_fun(X4,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X4,tc_bool))),c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X4,tc_bool))),
inference(unfold_definition,[status(thm)],[c_0_817,def_lhs_atom64]) ).
cnf(c_0_818_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X4),X1),X3)),hAPP(hAPP(c_Set_Oinsert(X4),X1),X2)) = hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X3),X2)),
inference(unfold_definition,[status(thm)],[c_0_818,def_lhs_atom59]) ).
cnf(c_0_819_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_819,def_lhs_atom56]) ).
cnf(c_0_820_0,axiom,
hBOOL(hAPP(c_Finite__Set_Ofold__graph(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4,X3),X1)),
inference(unfold_definition,[status(thm)],[c_0_820,def_lhs_atom55]) ).
cnf(c_0_821_0,axiom,
c_Finite__Set_Ofold(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X4) = X1,
inference(unfold_definition,[status(thm)],[c_0_821,def_lhs_atom49]) ).
cnf(c_0_822_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X3),X2),X1,tc_fun(X4,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X3),c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X4,tc_bool))),
inference(unfold_definition,[status(thm)],[c_0_822,def_lhs_atom45]) ).
cnf(c_0_823_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X3),X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X2),X1))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X1),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X3),X2)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X2),X1))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X1),X3)),
inference(unfold_definition,[status(thm)],[c_0_823,def_lhs_atom39]) ).
cnf(c_0_824_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X2),X1)),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X1),X3)),
inference(unfold_definition,[status(thm)],[c_0_824,def_lhs_atom33]) ).
cnf(c_0_825_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X2),X1)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X3),X2)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X3),X1)),
inference(unfold_definition,[status(thm)],[c_0_825,def_lhs_atom32]) ).
cnf(c_0_826_0,axiom,
c_Fun_Ofun__upd(X2,X1,hAPP(X2,X1),X3,X4) = X2,
inference(unfold_definition,[status(thm)],[c_0_826,def_lhs_atom29]) ).
cnf(c_0_827_0,axiom,
c_Fun_Ofun__upd(X2,X1,hAPP(X2,X1),X4,X3) = X2,
inference(unfold_definition,[status(thm)],[c_0_827,def_lhs_atom27]) ).
cnf(c_0_828_0,axiom,
c_Fun_Ofun__upd(X2,X1,hAPP(X2,X1),X3,X4) = X2,
inference(unfold_definition,[status(thm)],[c_0_828,def_lhs_atom25]) ).
cnf(c_0_829_0,axiom,
c_Option_Ooption_Ooption__case(X2,X1,c_Option_Ooption_ONone(X3),X4,X3) = X2,
inference(unfold_definition,[status(thm)],[c_0_829,def_lhs_atom22]) ).
cnf(c_0_830_0,axiom,
hAPP(c_COMBK(X2,X4,X3),X1) = X2,
inference(unfold_definition,[status(thm)],[c_0_830,def_lhs_atom21]) ).
cnf(c_0_831_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X2),X1)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X3),X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X3),X1)),
inference(unfold_definition,[status(thm)],[c_0_831,def_lhs_atom19]) ).
cnf(c_0_832_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X2),X1)),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X1),X3)),
inference(unfold_definition,[status(thm)],[c_0_832,def_lhs_atom18]) ).
cnf(c_0_833_0,axiom,
c_Map_Odom(c_Map_Orestrict__map(X1,X2,X4,X3),X4,X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),c_Map_Odom(X1,X4,X3)),X2),
inference(unfold_definition,[status(thm)],[c_0_833,def_lhs_atom16]) ).
cnf(c_0_834_0,axiom,
c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X3),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X2),X1),tc_fun(X4,tc_bool)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X3),X1),X2,tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_834,def_lhs_atom12]) ).
cnf(c_0_835_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X4,tc_bool))),X1) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X3),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X2),X1),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_835,def_lhs_atom10]) ).
cnf(c_0_836_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X1),c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X4,tc_bool))) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X1),X2),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_836,def_lhs_atom9]) ).
cnf(c_0_837_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X2),X1)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X3),X1)),
inference(unfold_definition,[status(thm)],[c_0_837,def_lhs_atom5]) ).
cnf(c_0_838_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X3),X2)),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X2),X1)),
inference(unfold_definition,[status(thm)],[c_0_838,def_lhs_atom4]) ).
cnf(c_0_839_0,axiom,
hAPP(hAPP(c_Set_Oinsert(X3),X1),hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) = hAPP(hAPP(c_Set_Oinsert(X3),X2),hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))),
inference(unfold_definition,[status(thm)],[c_0_839,def_lhs_atom148]) ).
cnf(c_0_840_0,axiom,
hBOOL(hAPP(hAPP(c_in(X3),X1),hAPP(hAPP(c_Set_Oinsert(X3),X1),X2))),
inference(unfold_definition,[status(thm)],[c_0_840,def_lhs_atom146]) ).
cnf(c_0_841_0,axiom,
hBOOL(hAPP(hAPP(c_in(X3),X1),hAPP(hAPP(c_Set_Oinsert(X3),X1),X2))),
inference(unfold_definition,[status(thm)],[c_0_841,def_lhs_atom145]) ).
cnf(c_0_842_0,axiom,
hBOOL(hAPP(hAPP(c_in(X3),X1),hAPP(hAPP(c_Set_Oinsert(X3),X1),X2))),
inference(unfold_definition,[status(thm)],[c_0_842,def_lhs_atom144]) ).
cnf(c_0_843_0,axiom,
hAPP(hAPP(c_Set_Oinsert(X3),X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_843,def_lhs_atom143]) ).
cnf(c_0_844_0,axiom,
hAPP(hAPP(c_Set_Oinsert(X3),X1),hAPP(hAPP(c_Set_Oinsert(X3),X1),X2)) = hAPP(hAPP(c_Set_Oinsert(X3),X1),X2),
inference(unfold_definition,[status(thm)],[c_0_844,def_lhs_atom142]) ).
cnf(c_0_845_0,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != hAPP(hAPP(c_Set_Oinsert(X3),X1),X2),
inference(unfold_definition,[status(thm)],[c_0_845,def_lhs_atom137]) ).
cnf(c_0_846_0,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),c_Hoare__Mirabelle_Otriple_Otriple(X1,c_Com_Ocom_OSKIP,X1,X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))),X3),
inference(unfold_definition,[status(thm)],[c_0_846,def_lhs_atom133]) ).
cnf(c_0_847_0,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X1),X2),X1)),
inference(unfold_definition,[status(thm)],[c_0_847,def_lhs_atom132]) ).
cnf(c_0_848_0,axiom,
hAPP(hAPP(c_Set_Oinsert(X3),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))),X2),
inference(unfold_definition,[status(thm)],[c_0_848,def_lhs_atom126]) ).
cnf(c_0_849_0,axiom,
hAPP(hAPP(c_Set_Oinsert(X3),X1),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))) = hAPP(hAPP(c_Set_Oinsert(X3),X1),X2),
inference(unfold_definition,[status(thm)],[c_0_849,def_lhs_atom125]) ).
cnf(c_0_850_0,axiom,
hAPP(c_Finite__Set_Ofold1(X1,X3),hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) = X2,
inference(unfold_definition,[status(thm)],[c_0_850,def_lhs_atom124]) ).
cnf(c_0_851_0,axiom,
hBOOL(hAPP(c_Finite__Set_Ofold1Set(X2,hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),X3),X1)),
inference(unfold_definition,[status(thm)],[c_0_851,def_lhs_atom119]) ).
cnf(c_0_852_0,axiom,
c_Map_Omap__le(X1,X1,X3,X2),
inference(unfold_definition,[status(thm)],[c_0_852,def_lhs_atom112]) ).
cnf(c_0_853_0,axiom,
hAPP(c_Finite__Set_Ofold1(X1,X3),X2) = c_The(c_Finite__Set_Ofold1Set(X1,X2,X3),X3),
inference(unfold_definition,[status(thm)],[c_0_853,def_lhs_atom110]) ).
cnf(c_0_854_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_854,def_lhs_atom108]) ).
cnf(c_0_855_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool))),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X2),
inference(unfold_definition,[status(thm)],[c_0_855,def_lhs_atom103]) ).
cnf(c_0_856_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool))) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),X1),
inference(unfold_definition,[status(thm)],[c_0_856,def_lhs_atom102]) ).
cnf(c_0_857_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X2),
inference(unfold_definition,[status(thm)],[c_0_857,def_lhs_atom100]) ).
cnf(c_0_858_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),X1)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),X1),
inference(unfold_definition,[status(thm)],[c_0_858,def_lhs_atom99]) ).
cnf(c_0_859_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_859,def_lhs_atom96]) ).
cnf(c_0_860_0,axiom,
~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X1)),
inference(unfold_definition,[status(thm)],[c_0_860,def_lhs_atom94]) ).
cnf(c_0_861_0,axiom,
hAPP(c_Map_Omap__add(X2,X1,t_a,X3),v_x) = c_Option_Ooption_Ooption__case(hAPP(X2,v_x),c_Option_Ooption_OSome(X3),hAPP(X1,v_x),tc_Option_Ooption(X3),X3),
inference(unfold_definition,[status(thm)],[c_0_861,def_lhs_atom84]) ).
cnf(c_0_862_0,axiom,
c_Com_Ocom_OSemi(X3,X2) != c_Com_Ocom_OBODY(X1),
inference(unfold_definition,[status(thm)],[c_0_862,def_lhs_atom78]) ).
cnf(c_0_863_0,axiom,
c_Com_Ocom_OBODY(X1) != c_Com_Ocom_OSemi(X3,X2),
inference(unfold_definition,[status(thm)],[c_0_863,def_lhs_atom77]) ).
cnf(c_0_864_0,axiom,
c_Map_Omap__le(c_COMBK(c_Option_Ooption_ONone(X2),tc_Option_Ooption(X2),X3),X1,X3,X2),
inference(unfold_definition,[status(thm)],[c_0_864,def_lhs_atom71]) ).
cnf(c_0_865_0,axiom,
c_Map_Omap__add(X1,c_COMBK(c_Option_Ooption_ONone(X2),tc_Option_Ooption(X2),X3),X3,X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_865,def_lhs_atom69]) ).
cnf(c_0_866_0,axiom,
c_Map_Omap__add(c_COMBK(c_Option_Ooption_ONone(X2),tc_Option_Ooption(X2),X3),X1,X3,X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_866,def_lhs_atom68]) ).
cnf(c_0_867_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X1)) = X2,
inference(unfold_definition,[status(thm)],[c_0_867,def_lhs_atom63]) ).
cnf(c_0_868_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_868,def_lhs_atom62]) ).
cnf(c_0_869_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X3),X1),X2))),
inference(unfold_definition,[status(thm)],[c_0_869,def_lhs_atom58]) ).
cnf(c_0_870_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X1,tc_fun(X3,tc_bool))),X2)),
inference(unfold_definition,[status(thm)],[c_0_870,def_lhs_atom38]) ).
cnf(c_0_871_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X2),
inference(unfold_definition,[status(thm)],[c_0_871,def_lhs_atom37]) ).
cnf(c_0_872_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),X1))),
inference(unfold_definition,[status(thm)],[c_0_872,def_lhs_atom36]) ).
cnf(c_0_873_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),X1))),
inference(unfold_definition,[status(thm)],[c_0_873,def_lhs_atom35]) ).
cnf(c_0_874_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X1)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X1),
inference(unfold_definition,[status(thm)],[c_0_874,def_lhs_atom34]) ).
cnf(c_0_875_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X1)),X1)),
inference(unfold_definition,[status(thm)],[c_0_875,def_lhs_atom31]) ).
cnf(c_0_876_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X1)),X2)),
inference(unfold_definition,[status(thm)],[c_0_876,def_lhs_atom30]) ).
cnf(c_0_877_0,axiom,
hBOOL(hAPP(hAPP(c_fequal(X2),X1),X1)),
inference(unfold_definition,[status(thm)],[c_0_877,def_lhs_atom196]) ).
cnf(c_0_878_0,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X2),
inference(unfold_definition,[status(thm)],[c_0_878,def_lhs_atom141]) ).
cnf(c_0_879_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X1)),
inference(unfold_definition,[status(thm)],[c_0_879,def_lhs_atom140]) ).
cnf(c_0_880_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_880,def_lhs_atom136]) ).
cnf(c_0_881_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_881,def_lhs_atom135]) ).
cnf(c_0_882_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_882,def_lhs_atom134]) ).
cnf(c_0_883_0,axiom,
hBOOL(hAPP(hAPP(c_in(X2),X1),hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))))),
inference(unfold_definition,[status(thm)],[c_0_883,def_lhs_atom131]) ).
cnf(c_0_884_0,axiom,
c_Set_Ocontents(hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_884,def_lhs_atom123]) ).
cnf(c_0_885_0,axiom,
c_The(hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_885,def_lhs_atom120]) ).
cnf(c_0_886_0,axiom,
c_Option_Othe(hAPP(c_Option_Ooption_OSome(X2),X1),X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_886,def_lhs_atom118]) ).
cnf(c_0_887_0,axiom,
c_The(hAPP(c_fequal(X2),X1),X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_887,def_lhs_atom117]) ).
cnf(c_0_888_0,axiom,
hAPP(c_Option_Ooption_OSome(X2),X1) != c_Option_Ooption_ONone(X2),
inference(unfold_definition,[status(thm)],[c_0_888,def_lhs_atom115]) ).
cnf(c_0_889_0,axiom,
hAPP(c_Option_Ooption_OSome(X2),X1) != c_Option_Ooption_ONone(X2),
inference(unfold_definition,[status(thm)],[c_0_889,def_lhs_atom114]) ).
cnf(c_0_890_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X1) = X1,
inference(unfold_definition,[status(thm)],[c_0_890,def_lhs_atom109]) ).
cnf(c_0_891_0,axiom,
c_Option_Ooption_ONone(X2) != hAPP(c_Option_Ooption_OSome(X2),X1),
inference(unfold_definition,[status(thm)],[c_0_891,def_lhs_atom107]) ).
cnf(c_0_892_0,axiom,
c_Option_Ooption_ONone(X2) != hAPP(c_Option_Ooption_OSome(X2),X1),
inference(unfold_definition,[status(thm)],[c_0_892,def_lhs_atom106]) ).
cnf(c_0_893_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_893,def_lhs_atom93]) ).
cnf(c_0_894_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = X1,
inference(unfold_definition,[status(thm)],[c_0_894,def_lhs_atom92]) ).
cnf(c_0_895_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X1) = X1,
inference(unfold_definition,[status(thm)],[c_0_895,def_lhs_atom91]) ).
cnf(c_0_896_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_896,def_lhs_atom90]) ).
cnf(c_0_897_0,axiom,
hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),X2)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),X1)),v_x) = hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),X2),X1)),
inference(unfold_definition,[status(thm)],[c_0_897,def_lhs_atom88]) ).
cnf(c_0_898_0,axiom,
c_Option_Oset(hAPP(c_Option_Ooption_OSome(X2),X1),X2) = hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),
inference(unfold_definition,[status(thm)],[c_0_898,def_lhs_atom87]) ).
cnf(c_0_899_0,axiom,
hAPP(c_Map_Orestrict__map(X1,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a,X2),v_x) = c_Option_Ooption_ONone(X2),
inference(unfold_definition,[status(thm)],[c_0_899,def_lhs_atom86]) ).
cnf(c_0_900_0,axiom,
c_Map_Odom(c_COMBK(c_Option_Ooption_ONone(X1),tc_Option_Ooption(X1),X2),X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_900,def_lhs_atom85]) ).
cnf(c_0_901_0,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2))),
inference(unfold_definition,[status(thm)],[c_0_901,def_lhs_atom81]) ).
cnf(c_0_902_0,axiom,
c_Com_Ocom_OSemi(X2,X1) != c_Com_Ocom_OSKIP,
inference(unfold_definition,[status(thm)],[c_0_902,def_lhs_atom80]) ).
cnf(c_0_903_0,axiom,
c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X2,X1),
inference(unfold_definition,[status(thm)],[c_0_903,def_lhs_atom79]) ).
cnf(c_0_904_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_904,def_lhs_atom72]) ).
cnf(c_0_905_0,axiom,
hBOOL(hAPP(hAPP(c_in(X2),X1),c_Option_Oset(hAPP(c_Option_Ooption_OSome(X2),X1),X2))),
inference(unfold_definition,[status(thm)],[c_0_905,def_lhs_atom61]) ).
cnf(c_0_906_0,axiom,
hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),X2)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),X1)),v_x) = hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),X2),X1)),
inference(unfold_definition,[status(thm)],[c_0_906,def_lhs_atom57]) ).
cnf(c_0_907_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X1)),
inference(unfold_definition,[status(thm)],[c_0_907,def_lhs_atom54]) ).
cnf(c_0_908_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_908,def_lhs_atom53]) ).
cnf(c_0_909_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_909,def_lhs_atom52]) ).
cnf(c_0_910_0,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X2,tc_bool)),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))),
inference(unfold_definition,[status(thm)],[c_0_910,def_lhs_atom51]) ).
cnf(c_0_911_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1),X1)),
inference(unfold_definition,[status(thm)],[c_0_911,def_lhs_atom44]) ).
cnf(c_0_912_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1),X1)),
inference(unfold_definition,[status(thm)],[c_0_912,def_lhs_atom43]) ).
cnf(c_0_913_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X1) = X1,
inference(unfold_definition,[status(thm)],[c_0_913,def_lhs_atom42]) ).
cnf(c_0_914_0,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X2,tc_bool)),X1),X1)),
inference(unfold_definition,[status(thm)],[c_0_914,def_lhs_atom13]) ).
cnf(c_0_915_0,axiom,
hAPP(c_Map_Orestrict__map(c_COMBK(c_Option_Ooption_ONone(X2),tc_Option_Ooption(X2),t_a),X1,t_a,X2),v_x) = c_Option_Ooption_ONone(X2),
inference(unfold_definition,[status(thm)],[c_0_915,def_lhs_atom7]) ).
cnf(c_0_916_0,axiom,
c_The(hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1),X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_916,def_lhs_atom1]) ).
cnf(c_0_917_0,axiom,
c_Com_Ocom_OSKIP != c_Com_Ocom_OBODY(X1),
inference(unfold_definition,[status(thm)],[c_0_917,def_lhs_atom149]) ).
cnf(c_0_918_0,axiom,
hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X1),X1)),
inference(unfold_definition,[status(thm)],[c_0_918,def_lhs_atom139]) ).
cnf(c_0_919_0,axiom,
c_Com_Ocom_OBODY(X1) != c_Com_Ocom_OSKIP,
inference(unfold_definition,[status(thm)],[c_0_919,def_lhs_atom130]) ).
cnf(c_0_920_0,axiom,
c_Hoare__Mirabelle_OMGT(X1) = c_Hoare__Mirabelle_Otriple_Otriple(c_fequal(tc_Com_Ostate),X1,c_Natural_Oevalc(X1),tc_Com_Ostate),
inference(unfold_definition,[status(thm)],[c_0_920,def_lhs_atom127]) ).
cnf(c_0_921_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_921,def_lhs_atom95]) ).
cnf(c_0_922_0,axiom,
c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
inference(unfold_definition,[status(thm)],[c_0_922,def_lhs_atom73]) ).
cnf(c_0_923_0,axiom,
c_Option_Oset(c_Option_Ooption_ONone(X1),X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_923,def_lhs_atom66]) ).
cnf(c_0_924_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
inference(unfold_definition,[status(thm)],[c_0_924,def_lhs_atom50]) ).
cnf(c_0_925_0,axiom,
X1 != c_Suc(X1),
inference(unfold_definition,[status(thm)],[c_0_925,def_lhs_atom41]) ).
cnf(c_0_926_0,axiom,
c_Suc(X1) != X1,
inference(unfold_definition,[status(thm)],[c_0_926,def_lhs_atom40]) ).
cnf(c_0_927_0,axiom,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X1))),
inference(unfold_definition,[status(thm)],[c_0_927,def_lhs_atom24]) ).
cnf(c_0_928_0,axiom,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X1))),
inference(unfold_definition,[status(thm)],[c_0_928,def_lhs_atom23]) ).
cnf(c_0_929_0,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X1)),
inference(unfold_definition,[status(thm)],[c_0_929,def_lhs_atom15]) ).
cnf(c_0_930_0,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X1)),
inference(unfold_definition,[status(thm)],[c_0_930,def_lhs_atom14]) ).
cnf(c_0_931_0,axiom,
class_HOL_Oord(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_931,def_lhs_atom195]) ).
cnf(c_0_932_0,axiom,
class_HOL_Ominus(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_932,def_lhs_atom194]) ).
cnf(c_0_933_0,axiom,
class_Orderings_Obot(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_933,def_lhs_atom193]) ).
cnf(c_0_934_0,axiom,
class_Orderings_Oorder(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_934,def_lhs_atom192]) ).
cnf(c_0_935_0,axiom,
class_Lattices_Olattice(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_935,def_lhs_atom191]) ).
cnf(c_0_936_0,axiom,
class_Orderings_Opreorder(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_936,def_lhs_atom190]) ).
cnf(c_0_937_0,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_937,def_lhs_atom189]) ).
cnf(c_0_938_0,axiom,
class_Lattices_Obounded__lattice(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_938,def_lhs_atom188]) ).
cnf(c_0_939_0,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_939,def_lhs_atom187]) ).
cnf(c_0_940_0,axiom,
class_Lattices_Olower__semilattice(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_940,def_lhs_atom186]) ).
cnf(c_0_941_0,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_941,def_lhs_atom185]) ).
cnf(c_0_942_0,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_942,def_lhs_atom184]) ).
cnf(c_0_943_0,axiom,
class_HOL_Oord(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_943,def_lhs_atom183]) ).
cnf(c_0_944_0,axiom,
class_HOL_Ominus(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_944,def_lhs_atom182]) ).
cnf(c_0_945_0,axiom,
class_Orderings_Obot(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_945,def_lhs_atom181]) ).
cnf(c_0_946_0,axiom,
class_Orderings_Oorder(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_946,def_lhs_atom180]) ).
cnf(c_0_947_0,axiom,
class_Lattices_Olattice(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_947,def_lhs_atom179]) ).
cnf(c_0_948_0,axiom,
class_Orderings_Olinorder(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_948,def_lhs_atom178]) ).
cnf(c_0_949_0,axiom,
class_Orderings_Opreorder(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_949,def_lhs_atom177]) ).
cnf(c_0_950_0,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_950,def_lhs_atom176]) ).
cnf(c_0_951_0,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_951,def_lhs_atom175]) ).
cnf(c_0_952_0,axiom,
class_Lattices_Odistrib__lattice(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_952,def_lhs_atom174]) ).
cnf(c_0_953_0,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_953,def_lhs_atom173]) ).
cnf(c_0_954_0,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_954,def_lhs_atom172]) ).
cnf(c_0_955_0,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_955,def_lhs_atom171]) ).
cnf(c_0_956_0,axiom,
class_Lattices_Olower__semilattice(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_956,def_lhs_atom170]) ).
cnf(c_0_957_0,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_957,def_lhs_atom169]) ).
cnf(c_0_958_0,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_958,def_lhs_atom168]) ).
cnf(c_0_959_0,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_959,def_lhs_atom167]) ).
cnf(c_0_960_0,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_960,def_lhs_atom166]) ).
cnf(c_0_961_0,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_961,def_lhs_atom165]) ).
cnf(c_0_962_0,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_962,def_lhs_atom164]) ).
cnf(c_0_963_0,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_963,def_lhs_atom163]) ).
cnf(c_0_964_0,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_964,def_lhs_atom162]) ).
cnf(c_0_965_0,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_965,def_lhs_atom161]) ).
cnf(c_0_966_0,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_966,def_lhs_atom160]) ).
cnf(c_0_967_0,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_967,def_lhs_atom159]) ).
cnf(c_0_968_0,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_968,def_lhs_atom158]) ).
cnf(c_0_969_0,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_969,def_lhs_atom157]) ).
cnf(c_0_970_0,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_970,def_lhs_atom156]) ).
cnf(c_0_971_0,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_971,def_lhs_atom155]) ).
cnf(c_0_972_0,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_972,def_lhs_atom154]) ).
cnf(c_0_973_0,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_973,def_lhs_atom153]) ).
cnf(c_0_974_0,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_974,def_lhs_atom152]) ).
cnf(c_0_975_0,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_975,def_lhs_atom151]) ).
cnf(c_0_976_0,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
inference(unfold_definition,[status(thm)],[c_0_976,def_lhs_atom150]) ).
cnf(c_0_977_0,axiom,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = hAPP(hAPP(c_in(t_a),v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),
inference(unfold_definition,[status(thm)],[c_0_977,def_lhs_atom138]) ).
cnf(c_0_978_0,axiom,
c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname),
inference(unfold_definition,[status(thm)],[c_0_978,def_lhs_atom129]) ).
cnf(c_0_979_0,axiom,
c_Hoare__Mirabelle_OMGT(v_c) = c_Hoare__Mirabelle_Otriple_Otriple(c_fequal(tc_Com_Ostate),v_c,c_Natural_Oevalc(v_c),tc_Com_Ostate),
inference(unfold_definition,[status(thm)],[c_0_979,def_lhs_atom83]) ).
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0_001,axiom,
! [X47,X48,X49,X50,X51,X52,X53,X54,X3] :
( c_Complete__Lattice_Ocomplete__lattice(X53,X54,c_COMBC(X49,X3,X3,tc_bool),c_COMBC(X50,X3,X3,tc_bool),X48,X51,X47,X52,X3)
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
file('<stdin>',cls_complete__lattice_Odual__complete__lattice_0) ).
fof(c_0_1_002,axiom,
! [X47,X48,X49,X50,X51,X52,X53,X54,X13,X9,X3] :
( hAPP(hAPP(X48,X13),hAPP(X53,X9)) = c_Finite__Set_Ofold(X48,X13,X9,X3,X3)
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
file('<stdin>',cls_complete__lattice_Osup__Sup__fold__sup_0) ).
fof(c_0_2_003,axiom,
! [X47,X48,X49,X50,X51,X52,X53,X54,X13,X9,X3] :
( hAPP(hAPP(X51,X13),hAPP(X54,X9)) = c_Finite__Set_Ofold(X51,X13,X9,X3,X3)
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
file('<stdin>',cls_complete__lattice_Oinf__Inf__fold__inf_0) ).
fof(c_0_3_004,axiom,
! [X47,X48,X49,X50,X51,X52,X53,X54,X9,X3] :
( hAPP(X53,X9) = c_Finite__Set_Ofold(X48,X52,X9,X3,X3)
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
file('<stdin>',cls_complete__lattice_OSup__fold__sup_0) ).
fof(c_0_4_005,axiom,
! [X47,X48,X49,X50,X51,X52,X53,X54,X9,X3] :
( hAPP(X54,X9) = c_Finite__Set_Ofold(X51,X47,X9,X3,X3)
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
file('<stdin>',cls_complete__lattice_OInf__fold__inf_0) ).
fof(c_0_5_006,axiom,
! [X47,X48,X49,X50,X51,X52,X19,X8,X53,X54,X3] :
( hAPP(X54,hAPP(hAPP(c_Set_Oinsert(X3),X8),hAPP(hAPP(c_Set_Oinsert(X3),X19),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))))) = hAPP(hAPP(X51,X8),X19)
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
file('<stdin>',cls_complete__lattice_OInf__binary_0) ).
fof(c_0_6_007,axiom,
! [X47,X48,X49,X50,X51,X52,X19,X8,X53,X54,X3] :
( hAPP(X53,hAPP(hAPP(c_Set_Oinsert(X3),X8),hAPP(hAPP(c_Set_Oinsert(X3),X19),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))))) = hAPP(hAPP(X48,X8),X19)
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
file('<stdin>',cls_complete__lattice_OSup__binary_0) ).
fof(c_0_7_008,axiom,
! [X12,X47,X48,X49,X50,X51,X52,X53,X54,X9,X3] :
( hBOOL(hAPP(hAPP(X49,hAPP(X54,X9)),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
file('<stdin>',cls_complete__lattice_OInf__lower_0) ).
fof(c_0_8_009,axiom,
! [X12,X47,X48,X49,X50,X51,X52,X53,X54,X9,X3] :
( hBOOL(hAPP(hAPP(X49,X12),hAPP(X53,X9)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
file('<stdin>',cls_complete__lattice_OSup__upper_0) ).
fof(c_0_9_010,axiom,
! [X47,X48,X49,X50,X51,X52,X8,X53,X54,X3] :
( hAPP(X54,hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) = X8
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
file('<stdin>',cls_complete__lattice_OInf__singleton_0) ).
fof(c_0_10_011,axiom,
! [X47,X48,X49,X50,X51,X52,X8,X53,X54,X3] :
( hAPP(X53,hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) = X8
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
file('<stdin>',cls_complete__lattice_OSup__singleton_0) ).
fof(c_0_11_012,axiom,
! [X47,X48,X49,X50,X51,X52,X8,X53,X54,X9,X3] :
( hAPP(X54,hAPP(hAPP(c_Set_Oinsert(X3),X8),X9)) = hAPP(hAPP(X51,X8),hAPP(X54,X9))
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
file('<stdin>',cls_complete__lattice_OInf__insert_0) ).
fof(c_0_12_013,axiom,
! [X47,X48,X49,X50,X51,X52,X8,X53,X54,X9,X3] :
( hAPP(X53,hAPP(hAPP(c_Set_Oinsert(X3),X8),X9)) = hAPP(hAPP(X48,X8),hAPP(X53,X9))
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
file('<stdin>',cls_complete__lattice_OSup__insert_0) ).
fof(c_0_13_014,axiom,
! [X47,X48,X49,X50,X51,X52,X53,X54,X9,X3] :
( c_Finite__Set_Olattice_OSup__fin(X48,X9,X3) = hAPP(X53,X9)
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
file('<stdin>',cls_complete__lattice_OSup__fin__Sup_0) ).
fof(c_0_14_015,axiom,
! [X47,X48,X49,X50,X51,X52,X53,X54,X9,X3] :
( c_Finite__Set_Olattice_OInf__fin(X51,X9,X3) = hAPP(X54,X9)
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
file('<stdin>',cls_complete__lattice_OInf__fin__Inf_0) ).
fof(c_0_15_016,axiom,
! [X47,X48,X49,X50,X51,X52,X53,X54,X3] :
( hAPP(X53,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) = X52
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
file('<stdin>',cls_complete__lattice_OSup__empty_0) ).
fof(c_0_16_017,axiom,
! [X47,X48,X49,X50,X51,X52,X53,X54,X3] :
( hAPP(X54,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) = X47
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
file('<stdin>',cls_complete__lattice_OInf__empty_0) ).
fof(c_0_17_018,axiom,
! [X23,X33,X18,X16] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X16,X18,X33,X23)),tc_fun(tc_Com_Ostate,tc_bool),t_a),X23,c_COMBK(hAPP(X33,v_sko__Hoare__Mirabelle__Xescape__1(X16,X18,X33,X23)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('<stdin>',cls_escape_1) ).
fof(c_0_18_019,axiom,
! [X57,X13,X9,X21,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X21)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X21),X57,c_HOL_Ozero__class_Ozero(X21),X9,X21,X3)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X21),X57,c_HOL_Ozero__class_Ozero(X21),X13,X21,X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X21),X57,c_HOL_Ozero__class_Ozero(X21),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13),X21,X3)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X21),X57,c_HOL_Ozero__class_Ozero(X21),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13),X21,X3))
| ~ c_Finite__Set_Ofinite(X13,X3)
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_comm__monoid__add_Ofold__image__Un__Int_0) ).
fof(c_0_19_020,axiom,
! [X17,X12,X23,X33,X18,X16] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X33,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X16,X18,X33,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X16,X18,X33,X23,X12,X17)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X12,X23,X17,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('<stdin>',cls_hoare__derivs_Ointros_I6_J_2) ).
fof(c_0_20_021,axiom,
! [X17,X12,X23,X33,X18,X16] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X33,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X16,X18,X33,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X16,X18,X33,X23,X12,X17)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X12,X23,X17,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('<stdin>',cls_conseq_2) ).
fof(c_0_21_022,axiom,
! [X57,X13,X9,X21,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X21)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X13,X3)
| ~ c_Finite__Set_Ofinite(X9,X3)
| c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X21),X57,c_HOL_Ozero__class_Ozero(X21),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13),X21,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X21),X57,c_HOL_Ozero__class_Ozero(X21),X9,X21,X3)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X21),X57,c_HOL_Ozero__class_Ozero(X21),X13,X21,X3)) ),
file('<stdin>',cls_comm__monoid__add_Ofold__Un__disjoint_0) ).
fof(c_0_22_023,axiom,
! [X17,X12,X23,X41,X33,X18,X16] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X17,X41),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X16,X18,X33,X23,X12,X17)))
| ~ hBOOL(hAPP(hAPP(X12,X41),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X16,X18,X33,X23)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X12,X23,X17,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('<stdin>',cls_conseq_1) ).
fof(c_0_23_024,axiom,
! [X17,X12,X23,X41,X33,X18,X16] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X17,X41),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X16,X18,X33,X23,X12,X17)))
| ~ hBOOL(hAPP(hAPP(X12,X41),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X16,X18,X33,X23)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X12,X23,X17,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('<stdin>',cls_hoare__derivs_Ointros_I6_J_1) ).
fof(c_0_24_025,axiom,
! [X70,X57,X8,X9,X21,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X21)
| c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X21),X57,X70,hAPP(hAPP(c_Set_Oinsert(X3),X8),X9),X21,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),hAPP(X57,X8)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X21),X57,X70,X9,X21,X3))
| hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_comm__monoid__add_Ofold__image__insert_0) ).
fof(c_0_25_026,axiom,
! [X70,X57,X8,X9,X21,X3] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X21)
| c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(X21),X57,X70,hAPP(hAPP(c_Set_Oinsert(X3),X8),X9),X21,X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X21),hAPP(X57,X8)),c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(X21),X57,X70,X9,X21,X3))
| hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_fold__image__insert_0) ).
fof(c_0_26_027,axiom,
! [X70,X37,X57,X8,X9,X21,X3] :
( c_Finite__Set_Ofold__image(X37,X57,X70,hAPP(hAPP(c_Set_Oinsert(X21),X8),X9),X3,X21) = hAPP(hAPP(X37,hAPP(X57,X8)),c_Finite__Set_Ofold__image(X37,X57,X70,X9,X3,X21))
| hBOOL(hAPP(hAPP(c_in(X21),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X21)
| ~ c_OrderedGroup_Oab__semigroup__mult(X37,X3) ),
file('<stdin>',cls_ab__semigroup__mult_Ofold__image__insert_0) ).
fof(c_0_27_028,axiom,
! [X12,X19,X8,X9,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X3),X8,hAPP(hAPP(c_Set_Oinsert(X3),X19),c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))),X3,X3),X12))
| hBOOL(hAPP(hAPP(c_in(X3),X19),X9))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X3),X19,X9,X3,X3),X12)) ),
file('<stdin>',cls_comm__monoid__add_Ofold__graph__permute__diff_0) ).
fof(c_0_28_029,axiom,
! [X12,X19,X8,X9,X3] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X3),X8,hAPP(hAPP(c_Set_Oinsert(X3),X19),c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))),X3,X3),X12))
| hBOOL(hAPP(hAPP(c_in(X3),X19),X9))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X3),X19,X9,X3,X3),X12)) ),
file('<stdin>',cls_fold__graph__permute__diff_0) ).
fof(c_0_29_030,axiom,
! [X12,X37,X19,X8,X9,X3] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X37,X8,hAPP(hAPP(c_Set_Oinsert(X3),X19),c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))),X3,X3),X12))
| hBOOL(hAPP(hAPP(c_in(X3),X19),X9))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X37,X19,X9,X3,X3),X12))
| ~ c_OrderedGroup_Oab__semigroup__mult(X37,X3) ),
file('<stdin>',cls_ab__semigroup__mult_Ofold__graph__permute__diff_0) ).
fof(c_0_30_031,axiom,
! [X90,X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X90)),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X90)),X24)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X8,X19,X3)),X90)),X23)),X24)) ),
file('<stdin>',cls_le__add__iff1_1) ).
fof(c_0_31_032,axiom,
! [X90,X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X90)),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X90)),X24)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X8,X19,X3)),X90)),X23)),X24)) ),
file('<stdin>',cls_less__add__iff1_1) ).
fof(c_0_32_033,axiom,
! [X70,X14,X12,X38,X9,X21,X3] :
( c_Nitpick_Ofold__graph_H(X38,X70,X9,hAPP(hAPP(X38,X12),X14),X3,X21)
| ~ c_Nitpick_Ofold__graph_H(X38,X70,c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X14,X3,X21)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9)) ),
file('<stdin>',cls_fold__graph_H_Ointros_I2_J_0) ).
fof(c_0_33_034,axiom,
! [X70,X14,X12,X38,X9,X21,X3] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X38,X70,X9,X3,X21),hAPP(hAPP(X38,X12),X14)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X38,X70,c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3,X21),X14)) ),
file('<stdin>',cls_Diff1__fold__graph_0) ).
fof(c_0_34_035,axiom,
! [X70,X14,X12,X38,X9,X21,X3] :
( X14 = X12
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X38,X70,X9,X3,X21),X14))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X38,X70,X9,X3,X21),X12))
| ~ c_Finite__Set_Ofun__left__comm(X38,X3,X21) ),
file('<stdin>',cls_fun__left__comm_Ofold__graph__determ_0) ).
fof(c_0_35_036,axiom,
! [X14,X12,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X3),X14),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3)),c_Finite__Set_Ocard(X9,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X14),X9))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_card__Diff2__less_0) ).
fof(c_0_36_037,axiom,
! [X90,X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X8,X19,X3)),X90)),X23)),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X90)),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X90)),X24))) ),
file('<stdin>',cls_le__add__iff1_0) ).
fof(c_0_37_038,axiom,
! [X90,X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X8,X19,X3)),X90)),X23)),X24))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X90)),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X90)),X24))) ),
file('<stdin>',cls_less__add__iff1_0) ).
fof(c_0_38_039,axiom,
! [X70,X14,X19,X9,X3] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X3),X70,hAPP(hAPP(c_Set_Oinsert(X3),X19),X9),X3,X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X70),X14)))
| hBOOL(hAPP(hAPP(c_in(X3),X19),X9))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X3),X19,X9,X3,X3),X14)) ),
file('<stdin>',cls_fold__graph__insert__swap_0) ).
fof(c_0_39_040,axiom,
! [X70,X14,X19,X9,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X3),X70,hAPP(hAPP(c_Set_Oinsert(X3),X19),X9),X3,X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X70),X14)))
| hBOOL(hAPP(hAPP(c_in(X3),X19),X9))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X3),X19,X9,X3,X3),X14)) ),
file('<stdin>',cls_comm__monoid__add_Ofold__graph__insert__swap_0) ).
fof(c_0_40_041,axiom,
! [X70,X17,X12,X38,X9,X87,X3] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X38,X70,X9,X87,X3),X17))
| hBOOL(hAPP(hAPP(c_in(X87),X12),X9))
| ~ c_Finite__Set_Ofun__left__comm(X38,X87,X3)
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X38,X70,hAPP(hAPP(c_Set_Oinsert(X87),X12),X9),X87,X3),hAPP(hAPP(X38,X12),X17))) ),
file('<stdin>',cls_fun__left__comm_Ofold__insert__aux_2) ).
fof(c_0_41_042,axiom,
! [X70,X14,X37,X19,X9,X3] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X37,X70,hAPP(hAPP(c_Set_Oinsert(X3),X19),X9),X3,X3),hAPP(hAPP(X37,X70),X14)))
| hBOOL(hAPP(hAPP(c_in(X3),X19),X9))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X37,X19,X9,X3,X3),X14))
| ~ c_OrderedGroup_Oab__semigroup__mult(X37,X3) ),
file('<stdin>',cls_ab__semigroup__mult_Ofold__graph__insert__swap_0) ).
fof(c_0_42_043,axiom,
! [X70,X14,X12,X38,X9,X21,X3] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X38,X70,hAPP(hAPP(c_Set_Oinsert(X3),X12),X9),X3,X21),hAPP(hAPP(X38,X12),X14)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X38,X70,X9,X3,X21),X14))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9)) ),
file('<stdin>',cls_fold__graph_OinsertI_0) ).
fof(c_0_43_044,axiom,
! [X20,X34,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X34),X20))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X34)),hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X20))) ),
file('<stdin>',cls_pred__subset__eq_0) ).
fof(c_0_44_045,axiom,
! [X23,X39,X33,X40,X18,X16] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X33,v_sko__Hoare__Mirabelle__Xconseq12__1(X18,X40,X33,X39)),v_sko__Hoare__Mirabelle__Xconseq12__3(X18,X40,X33,X39)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X40,X23,X39,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('<stdin>',cls_conseq12_2) ).
fof(c_0_45_046,axiom,
! [X49,X50,X51,X19,X8,X9,X3] :
( hBOOL(hAPP(hAPP(X49,c_Finite__Set_Ofold(X51,X19,X9,X3,X3)),hAPP(hAPP(X51,X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
file('<stdin>',cls_lower__semilattice_Ofold__inf__le__inf_0) ).
fof(c_0_46_047,axiom,
! [X90,X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X90)),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X90)),X24)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X19,X8,X3)),X90)),X24))) ),
file('<stdin>',cls_le__add__iff2_1) ).
fof(c_0_47_048,axiom,
! [X90,X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X90)),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X90)),X24)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X19,X8,X3)),X90)),X24))) ),
file('<stdin>',cls_less__add__iff2_1) ).
fof(c_0_48_049,axiom,
! [X32,X33,X18,X16,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),c_Hoare__Mirabelle_Otriple_Otriple(X18,c_Com_Ocom_OBODY(X32),X33,X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),c_Hoare__Mirabelle_Otriple_Otriple(X18,c_Com_Ocom_OBODY(X32),X33,X3)),X16),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),c_Hoare__Mirabelle_Otriple_Otriple(X18,c_Option_Othe(hAPP(c_Com_Obody,X32),tc_Com_Ocom),X33,X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))),X3) ),
file('<stdin>',cls_BodyN_0) ).
fof(c_0_49_050,axiom,
! [X19,X8,X9,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X3),X19,X9,X3,X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_fold__inf__le__inf_0) ).
fof(c_0_50_051,axiom,
! [X24,X23,X34,X33,X18,X16,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),c_Hoare__Mirabelle_Otriple_Otriple(X18,c_Com_Ocom_OSemi(X23,X24),X34,X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),c_Hoare__Mirabelle_Otriple_Otriple(X33,X24,X34,X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))),X3) ),
file('<stdin>',cls_Comp_0) ).
fof(c_0_51_052,axiom,
! [X90,X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X19,X8,X3)),X90)),X24)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X90)),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X90)),X24))) ),
file('<stdin>',cls_le__add__iff2_0) ).
fof(c_0_52_053,axiom,
! [X90,X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X19,X8,X3)),X90)),X24)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X90)),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X90)),X24))) ),
file('<stdin>',cls_less__add__iff2_0) ).
fof(c_0_53_054,axiom,
! [X70,X14,X38,X9,X21,X3] :
( c_Finite__Set_Ofold(X38,X70,X9,X3,X21) = X14
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X38,X70,X9,X3,X21),X14))
| ~ c_Finite__Set_Ofun__left__comm(X38,X3,X21) ),
file('<stdin>',cls_fun__left__comm_Ofold__equality_0) ).
fof(c_0_54_055,axiom,
! [X23,X39,X33,X40,X18,X16] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X18,v_sko__Hoare__Mirabelle__Xconseq12__1(X18,X40,X33,X39)),v_sko__Hoare__Mirabelle__Xconseq12__2(X18,X40,X33,X39)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X40,X23,X39,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('<stdin>',cls_conseq12_0) ).
fof(c_0_55_056,axiom,
! [X23,X41,X39,X33,X40,X18,X16] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X39,X41),v_sko__Hoare__Mirabelle__Xconseq12__3(X18,X40,X33,X39)))
| ~ hBOOL(hAPP(hAPP(X40,X41),v_sko__Hoare__Mirabelle__Xconseq12__2(X18,X40,X33,X39)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X40,X23,X39,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('<stdin>',cls_conseq12_1) ).
fof(c_0_56_057,axiom,
! [X12,X38,X8,X9,X3] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X38,hAPP(hAPP(c_Set_Oinsert(X3),X8),X9),X3),X12))
| hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X38,X8,X9,X3,X3),X12)) ),
file('<stdin>',cls_fold1Set_Ointros_0) ).
fof(c_0_57_058,axiom,
! [X70,X12,X38,X21,X3] :
( X12 = X70
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X38,X70,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X21),X12)) ),
file('<stdin>',cls_empty__fold__graphE_0) ).
fof(c_0_58_059,axiom,
! [X93,X94,X8,X18] :
( ~ hBOOL(hAPP(X18,c_Option_Ooption_Ooption__case(X94,X93,hAPP(c_Option_Ooption_OSome(t_b),X8),t_a,t_b)))
| hBOOL(hAPP(X18,hAPP(X93,X8))) ),
file('<stdin>',cls_option_Osplit_1) ).
fof(c_0_59_060,axiom,
! [X17,X93,X94,X18] :
( ~ hBOOL(hAPP(X18,c_Option_Ooption_Ooption__case(X94,X93,hAPP(c_Option_Ooption_OSome(t_b),X17),t_a,t_b)))
| hBOOL(hAPP(X18,hAPP(X93,X17))) ),
file('<stdin>',cls_option_Osplit__asm_1) ).
fof(c_0_60_061,axiom,
! [X93,X94,X18] :
( ~ hBOOL(hAPP(X18,c_Option_Ooption_Ooption__case(X94,X93,c_Option_Ooption_ONone(t_b),t_a,t_b)))
| hBOOL(hAPP(X18,X94)) ),
file('<stdin>',cls_option_Osplit_0) ).
fof(c_0_61_062,axiom,
! [X70,X12,X38,X9,X21,X3] :
( c_Finite__Set_Ofinite(X9,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X38,X70,X9,X3,X21),X12)) ),
file('<stdin>',cls_fold__graph__imp__finite_0) ).
fof(c_0_62_063,axiom,
! [X20,X34,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X34)),hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X20)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X34),X20)) ),
file('<stdin>',cls_pred__subset__eq_1) ).
fof(c_0_63_064,axiom,
! [X42,X24,X23,X19,X8,X21,X3] :
( c_Fun_Ofun__upd(c_Fun_Ofun__upd(X42,X8,X19,X3,X21),X23,X24,X3,X21) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X42,X23,X24,X3,X21),X8,X19,X3,X21)
| X8 = X23 ),
file('<stdin>',cls_fun__upd__twist_0) ).
fof(c_0_64_065,axiom,
! [X32,X33,X18,X16,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),c_Hoare__Mirabelle_Otriple_Otriple(X18,c_Com_Ocom_OBODY(X32),X33,X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),c_Hoare__Mirabelle_Otriple_Otriple(X18,c_Option_Othe(hAPP(c_Com_Obody,X32),tc_Com_Ocom),X33,X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))),X3) ),
file('<stdin>',cls_weak__Body_0) ).
fof(c_0_65_066,axiom,
! [X23,X33,X18] :
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,tc_Com_Ostate)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,tc_Com_Ostate)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(X23)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))),tc_Com_Ostate) ),
file('<stdin>',cls_MGF__complete_0) ).
fof(c_0_66_067,axiom,
! [X38,X9,X21,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_Finite__Set_Osetsum(X38,X9,X21,X3) = c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X3),X38,c_HOL_Ozero__class_Ozero(X3),X9,X3,X21)
| ~ c_Finite__Set_Ofinite(X9,X21) ),
file('<stdin>',cls_setsum__def_0) ).
fof(c_0_67_068,axiom,
! [X23,X33,X40,X18,X16] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X40,v_sko__Hoare__Mirabelle__Xconseq1__1(X18,X40)),v_sko__Hoare__Mirabelle__Xconseq1__2(X18,X40)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X40,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('<stdin>',cls_conseq1_1) ).
fof(c_0_68_069,axiom,
! [X23,X39,X33,X18,X16] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X33,v_sko__Hoare__Mirabelle__Xconseq2__1(X33,X39)),v_sko__Hoare__Mirabelle__Xconseq2__2(X33,X39)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X39,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('<stdin>',cls_conseq2_1) ).
fof(c_0_69_070,axiom,
! [X23,X39,X33,X18,X16] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X39,v_sko__Hoare__Mirabelle__Xconseq2__1(X33,X39)),v_sko__Hoare__Mirabelle__Xconseq2__2(X33,X39)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X39,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('<stdin>',cls_conseq2_0) ).
fof(c_0_70_071,axiom,
! [X23,X33,X40,X18,X16] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X18,v_sko__Hoare__Mirabelle__Xconseq1__1(X18,X40)),v_sko__Hoare__Mirabelle__Xconseq1__2(X18,X40)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X40,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('<stdin>',cls_conseq1_0) ).
fof(c_0_71_072,axiom,
! [X14,X12,X42,X72,X21,X3] :
( c_Map_Orestrict__map(c_Fun_Ofun__upd(X42,X12,X14,X3,tc_Option_Ooption(X21)),X72,X3,X21) = c_Fun_Ofun__upd(c_Map_Orestrict__map(X42,c_HOL_Ominus__class_Ominus(X72,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3,X21),X12,X14,X3,tc_Option_Ooption(X21))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X72)) ),
file('<stdin>',cls_restrict__fun__upd_0) ).
fof(c_0_72_073,axiom,
! [X14,X12,X61,X62,X21,X3] :
( c_Map_Omap__le(c_Fun_Ofun__upd(X62,X12,c_Option_Ooption_ONone(X21),X3,tc_Option_Ooption(X21)),c_Fun_Ofun__upd(X61,X12,hAPP(c_Option_Ooption_OSome(X21),X14),X3,tc_Option_Ooption(X21)),X3,X21)
| ~ c_Map_Omap__le(X62,X61,X3,X21) ),
file('<stdin>',cls_map__le__imp__upd__le_0) ).
fof(c_0_73_074,axiom,
! [X19,X8,X9,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X8),X19)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X3),X19,X9,X3,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_sup__le__fold__sup_0) ).
fof(c_0_74_075,axiom,
! [X57,X38,X19,X8,X21,X3] :
( c_Map_Omap__le(c_Fun_Ofun__upd(X38,X8,X19,X3,tc_Option_Ooption(X21)),c_Fun_Ofun__upd(X57,X8,X19,X3,tc_Option_Ooption(X21)),X3,X21)
| ~ c_Map_Omap__le(X38,X57,X3,X21) ),
file('<stdin>',cls_map__le__upd_0) ).
fof(c_0_75_076,axiom,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))),X13))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),X13)) ),
file('<stdin>',cls_psubset__insert__iff_9) ).
fof(c_0_76_077,axiom,
! [X23,X33,X18,X16] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X18,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X16,X18,X33,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X16,X18,X33,X23))) ),
file('<stdin>',cls_hoare__derivs_Ointros_I6_J_0) ).
fof(c_0_77_078,axiom,
! [X23,X33,X18,X16] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X18,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X16,X18,X33,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X16,X18,X33,X23))) ),
file('<stdin>',cls_conseq_0) ).
fof(c_0_78_079,axiom,
! [X23,X33,X18,X16] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X18,v_sko__Hoare__Mirabelle__Xescape__1(X16,X18,X33,X23)),v_sko__Hoare__Mirabelle__Xescape__2(X16,X18,X33,X23))) ),
file('<stdin>',cls_escape_0) ).
fof(c_0_79_080,axiom,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))),X13))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),X13)) ),
file('<stdin>',cls_psubset__insert__iff_8) ).
fof(c_0_80_081,axiom,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))),X13))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X13)) ),
file('<stdin>',cls_psubset__insert__iff_5) ).
fof(c_0_81_082,axiom,
! [X70,X12,X38,X9,X21,X3] :
( c_Finite__Set_Ofold(X38,X70,X9,X3,X21) = hAPP(hAPP(X38,X12),c_Finite__Set_Ofold(X38,X70,c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3,X21))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_Finite__Set_Ofun__left__comm(X38,X3,X21) ),
file('<stdin>',cls_fun__left__comm_Ofold__rec_0) ).
fof(c_0_82_083,axiom,
! [X70,X12,X38,X9,X21,X3] :
( c_Finite__Set_Ofold(X38,X70,hAPP(hAPP(c_Set_Oinsert(X3),X12),X9),X3,X21) = hAPP(hAPP(X38,X12),c_Finite__Set_Ofold(X38,X70,c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3,X21))
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_Finite__Set_Ofun__left__comm(X38,X3,X21) ),
file('<stdin>',cls_fun__left__comm_Ofold__insert__remove_0) ).
fof(c_0_83_084,axiom,
! [X12,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3)),c_Finite__Set_Ocard(X9,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_card__Diff1__less_0) ).
fof(c_0_84_085,axiom,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))),X13)) ),
file('<stdin>',cls_subset__insert__iff_4) ).
fof(c_0_85_086,axiom,
! [X57,X13,X9,X21,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X21)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),c_Finite__Set_Osetsum(X57,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13),X3,X21)),c_Finite__Set_Osetsum(X57,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13),X3,X21)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),c_Finite__Set_Osetsum(X57,X9,X3,X21)),c_Finite__Set_Osetsum(X57,X13,X3,X21))
| ~ c_Finite__Set_Ofinite(X13,X3)
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_setsum__Un__Int_0) ).
fof(c_0_86_087,axiom,
! [X57,X13,X9,X21,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X21)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X21),c_Finite__Set_Osetprod(X57,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13),X3,X21)),c_Finite__Set_Osetprod(X57,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13),X3,X21)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X21),c_Finite__Set_Osetprod(X57,X9,X3,X21)),c_Finite__Set_Osetprod(X57,X13,X3,X21))
| ~ c_Finite__Set_Ofinite(X13,X3)
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_setprod__Un__Int_0) ).
fof(c_0_87_088,axiom,
! [X73,X42,X74,X75,X21,X3] :
( c_Map_Omap__add(c_Fun_Ofun__upd(X75,X42,hAPP(c_Option_Ooption_OSome(X21),X73),X3,tc_Option_Ooption(X21)),X74,X3,X21) = c_Fun_Ofun__upd(c_Map_Omap__add(X75,X74,X3,X21),X42,hAPP(c_Option_Ooption_OSome(X21),X73),X3,tc_Option_Ooption(X21))
| hBOOL(hAPP(hAPP(c_in(X3),X42),c_Map_Odom(X74,X3,X21))) ),
file('<stdin>',cls_map__add__upd__left_0) ).
fof(c_0_88_089,axiom,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))),X13))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X13)) ),
file('<stdin>',cls_psubset__insert__iff_4) ).
fof(c_0_89_090,axiom,
! [X38,X13,X9,X21,X3] :
( ~ class_OrderedGroup_Oab__group__add(X21)
| c_Finite__Set_Osetsum(X38,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13),X3,X21) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),c_Finite__Set_Osetsum(X38,X9,X3,X21)),c_Finite__Set_Osetsum(X38,X13,X3,X21)),c_Finite__Set_Osetsum(X38,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13),X3,X21),X21)
| ~ c_Finite__Set_Ofinite(X13,X3)
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_setsum__Un_0) ).
fof(c_0_90_091,axiom,
! [X37,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),hAPP(c_Finite__Set_Ofold1(X37,X3),X9)),X9))
| ~ hBOOL(hAPP(hAPP(c_in(X3),hAPP(hAPP(X37,c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1(X37,X3)),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2(X37,X3))),hAPP(hAPP(c_Set_Oinsert(X3),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1(X37,X3)),hAPP(hAPP(c_Set_Oinsert(X3),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2(X37,X3)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))))))
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_OrderedGroup_Oab__semigroup__mult(X37,X3) ),
file('<stdin>',cls_ab__semigroup__mult_Ofold1__in_0) ).
fof(c_0_91_092,axiom,
! [X14,X12,X42,X72,X21,X3] :
( c_Fun_Ofun__upd(c_Map_Orestrict__map(X42,X72,X3,X21),X12,X14,X3,tc_Option_Ooption(X21)) = c_Fun_Ofun__upd(c_Map_Orestrict__map(X42,c_HOL_Ominus__class_Ominus(X72,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3,X21),X12,X14,X3,tc_Option_Ooption(X21))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X72)) ),
file('<stdin>',cls_fun__upd__restrict__conv_0) ).
fof(c_0_92_093,axiom,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| X12 = c_HOL_Ozero__class_Ozero(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X12)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X14),X14))),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_sum__squares__le__zero__iff_0) ).
fof(c_0_93_094,axiom,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| X14 = c_HOL_Ozero__class_Ozero(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X12)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X14),X14))),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_sum__squares__le__zero__iff_1) ).
fof(c_0_94_095,axiom,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X12)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X14),X14))),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_not__sum__squares__lt__zero_0) ).
fof(c_0_95_096,axiom,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))),X13)) ),
file('<stdin>',cls_diff__single__insert_0) ).
fof(c_0_96_097,axiom,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))),X13)) ),
file('<stdin>',cls_subset__insert__iff_3) ).
fof(c_0_97_098,axiom,
! [X49,X50,X51,X19,X8,X9,X3] :
( c_Finite__Set_Ofold(X51,X19,hAPP(hAPP(c_Set_Oinsert(X3),X8),X9),X3,X3) = hAPP(hAPP(X51,X8),c_Finite__Set_Ofold(X51,X19,X9,X3,X3))
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
file('<stdin>',cls_lower__semilattice_Ofold__inf__insert_0) ).
fof(c_0_98_099,axiom,
! [X14,X12,X42,X19,X8,X21,X3] :
( hAPP(c_Fun_Ofun__upd(X42,X8,hAPP(c_Option_Ooption_OSome(X3),X19),X21,tc_Option_Ooption(X3)),X12) != hAPP(c_Option_Ooption_OSome(X3),X14)
| hAPP(X42,X12) = hAPP(c_Option_Ooption_OSome(X3),X14)
| X19 = X14 ),
file('<stdin>',cls_map__upd__Some__unfold_2) ).
fof(c_0_99_100,axiom,
! [X14,X12,X42,X19,X8,X21,X3] :
( hAPP(c_Fun_Ofun__upd(X42,X8,hAPP(c_Option_Ooption_OSome(X3),X19),X21,tc_Option_Ooption(X3)),X12) != hAPP(c_Option_Ooption_OSome(X3),X14)
| hAPP(X42,X12) = hAPP(c_Option_Ooption_OSome(X3),X14)
| X12 = X8 ),
file('<stdin>',cls_map__upd__Some__unfold_0) ).
fof(c_0_100_101,axiom,
! [X14,X12,X42,X19,X87,X3] :
( X19 = X14
| hAPP(c_Fun_Ofun__upd(X42,X12,hAPP(c_Option_Ooption_OSome(X87),X19),X3,tc_Option_Ooption(X87)),X12) != hAPP(c_Option_Ooption_OSome(X87),X14) ),
file('<stdin>',cls_map__upd__Some__unfold_1) ).
fof(c_0_101_102,axiom,
! [X70,X12,X38,X9,X21,X3] :
( c_Finite__Set_Ofold(X38,X70,hAPP(hAPP(c_Set_Oinsert(X3),X12),X9),X3,X21) = hAPP(hAPP(X38,X12),c_Finite__Set_Ofold(X38,X70,X9,X3,X21))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_Finite__Set_Ofun__left__comm(X38,X3,X21) ),
file('<stdin>',cls_fun__left__comm_Ofold__insert_0) ).
fof(c_0_102_103,axiom,
! [X14,X12,X55,X42,X8,X21,X3] :
( c_Fun_Ofun__upd(X42,X8,hAPP(c_Option_Ooption_OSome(X21),X12),X3,tc_Option_Ooption(X21)) != c_Fun_Ofun__upd(X55,X8,hAPP(c_Option_Ooption_OSome(X21),X14),X3,tc_Option_Ooption(X21))
| X12 = X14 ),
file('<stdin>',cls_map__upd__eqD1_0) ).
fof(c_0_103_104,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3)))),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_sum__squares__le__zero__iff_2) ).
fof(c_0_104_105,axiom,
! [X70,X12,X38,X9,X21,X3] :
( hAPP(hAPP(X38,X12),c_Finite__Set_Ofold(X38,X70,X9,X3,X21)) = c_Finite__Set_Ofold(X38,hAPP(hAPP(X38,X12),X70),X9,X3,X21)
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_Finite__Set_Ofun__left__comm(X38,X3,X21) ),
file('<stdin>',cls_fun__left__comm_Ofold__fun__comm_0) ).
fof(c_0_105_106,axiom,
! [X19,X8,X9,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X3),X19,hAPP(hAPP(c_Set_Oinsert(X3),X8),X9),X3,X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X8),c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X3),X19,X9,X3,X3))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_fold__inf__insert_0) ).
fof(c_0_106_107,axiom,
! [X19,X8,X9,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X3),X19,hAPP(hAPP(c_Set_Oinsert(X3),X8),X9),X3,X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X8),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X3),X19,X9,X3,X3))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_fold__sup__insert_0) ).
fof(c_0_107_108,axiom,
! [X38,X13,X9,X21,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X21,tc_bool)),c_Set_Ovimage(X38,X9,X21,X3)),c_Set_Ovimage(X38,X13,X21,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
file('<stdin>',cls_vimage__mono_0) ).
fof(c_0_108_109,axiom,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X13))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13))) ),
file('<stdin>',cls_psubset__insert__iff_1) ).
fof(c_0_109_110,axiom,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Olattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X70))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X14),X70)))) ),
file('<stdin>',cls_distrib__inf__le_0) ).
fof(c_0_110_111,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X70))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X14),X70)))) ),
file('<stdin>',cls_min__max_Odistrib__inf__le_0) ).
fof(c_0_111_112,axiom,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13))) ),
file('<stdin>',cls_subset__insert__iff_0) ).
fof(c_0_112_113,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))))) ),
file('<stdin>',cls_sum__squares__gt__zero__iff_0) ).
fof(c_0_113_114,axiom,
! [X38,X19,X8,X21,X3] :
( hAPP(X38,X8) = X19
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),c_Set_Ovimage(X38,hAPP(hAPP(c_Set_Oinsert(X21),X19),c_Orderings_Obot__class_Obot(tc_fun(X21,tc_bool))),X3,X21))) ),
file('<stdin>',cls_vimage__singleton__eq_0) ).
fof(c_0_114_115,axiom,
! [X14,X12,X42,X72,X21,X3] :
( c_Map_Orestrict__map(c_Fun_Ofun__upd(X42,X12,X14,X3,tc_Option_Ooption(X21)),X72,X3,X21) = c_Map_Orestrict__map(X42,X72,X3,X21)
| hBOOL(hAPP(hAPP(c_in(X3),X12),X72)) ),
file('<stdin>',cls_restrict__fun__upd_1) ).
fof(c_0_115_116,axiom,
! [X72,X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X80),X72)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X13),X72))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X80)) ),
file('<stdin>',cls_Un__mono_0) ).
fof(c_0_116_117,axiom,
! [X72,X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X80),X72)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X13),X72))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X80)) ),
file('<stdin>',cls_Int__mono_0) ).
fof(c_0_117_118,axiom,
! [X70,X12,X38,X9,X21,X3] :
( c_Finite__Set_Ofold(X38,X70,hAPP(hAPP(c_Set_Oinsert(X3),X12),X9),X3,X21) = c_Finite__Set_Ofold(X38,hAPP(hAPP(X38,X12),X70),X9,X3,X21)
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_Finite__Set_Ofun__left__comm(X38,X3,X21) ),
file('<stdin>',cls_fun__left__comm_Ofold__insert2_0) ).
fof(c_0_118_119,axiom,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Olattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X14),X70))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X70)))) ),
file('<stdin>',cls_distrib__sup__le_0) ).
fof(c_0_119_120,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X14),X70))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X70)))) ),
file('<stdin>',cls_min__max_Odistrib__sup__le_0) ).
fof(c_0_120_121,axiom,
! [X90,X24,X19,X8,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X90)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X19,X8,X3)),X90)),X24)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X90)),X24) ),
file('<stdin>',cls_eq__add__iff2_1) ).
fof(c_0_121_122,axiom,
! [X90,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X90)),X23) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X90)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X8,X19,X3)),X90)),X23)) ),
file('<stdin>',cls_eq__add__iff1_1) ).
fof(c_0_122_123,axiom,
! [X12,X42,X72,X21,X3] :
( c_Fun_Ofun__upd(c_Map_Orestrict__map(X42,X72,X3,X21),X12,c_Option_Ooption_ONone(X21),X3,tc_Option_Ooption(X21)) = c_Map_Orestrict__map(X42,c_HOL_Ominus__class_Ominus(X72,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3,X21)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X72)) ),
file('<stdin>',cls_fun__upd__None__restrict_0) ).
fof(c_0_123_124,axiom,
! [X63,X57,X38,X21,X3] :
( c_Map_Omap__le(c_Map_Omap__add(X38,X57,X3,X21),X63,X3,X21)
| ~ c_Map_Omap__le(X38,c_Map_Omap__add(X38,X57,X3,X21),X3,X21)
| ~ c_Map_Omap__le(X57,X63,X3,X21)
| ~ c_Map_Omap__le(X38,X63,X3,X21) ),
file('<stdin>',cls_map__add__le__mapI_0) ).
fof(c_0_124_125,axiom,
! [X14,X12,X38,X21,X3] :
( c_Map_Odom(c_Fun_Ofun__upd(X38,X12,X14,X3,tc_Option_Ooption(X21)),X3,X21) = hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Map_Odom(X38,X3,X21))
| X14 = c_Option_Ooption_ONone(X21) ),
file('<stdin>',cls_dom__fun__upd_1) ).
fof(c_0_125_126,axiom,
! [X14,X12,X42,X19,X8,X21,X3] :
( hAPP(X42,X12) != hAPP(c_Option_Ooption_OSome(X3),X14)
| X12 = X8
| hAPP(c_Fun_Ofun__upd(X42,X8,hAPP(c_Option_Ooption_OSome(X3),X19),X21,tc_Option_Ooption(X3)),X12) = hAPP(c_Option_Ooption_OSome(X3),X14) ),
file('<stdin>',cls_map__upd__Some__unfold_4) ).
fof(c_0_126_127,axiom,
! [X45,X46,X21,X3] :
( c_Map_Omap__le(X46,X45,X3,X21)
| hBOOL(hAPP(hAPP(c_in(X3),c_Map_Osko__Map__Xmap__le__def__1__1(X46,X45,X3,X21)),c_Map_Odom(X46,X3,X21))) ),
file('<stdin>',cls_map__le__def_1) ).
fof(c_0_127_128,axiom,
! [X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X80))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13)),X80)) ),
file('<stdin>',cls_Un__subset__iff_0) ).
fof(c_0_128_129,axiom,
! [X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X13),X80))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13)),X80)) ),
file('<stdin>',cls_Un__subset__iff_1) ).
fof(c_0_129_130,axiom,
! [X70,X14,X12,X38,X21,X3] :
( hAPP(c_Fun_Ofun__upd(X38,X12,X14,X21,X3),X70) = hAPP(X38,X70)
| X70 = X12 ),
file('<stdin>',cls_fun__upd__apply_1) ).
fof(c_0_130_131,axiom,
! [X70,X14,X12,X38,X21,X3] :
( hAPP(c_Fun_Ofun__upd(X38,X12,X14,X3,X21),X70) = hAPP(X38,X70)
| X70 = X12 ),
file('<stdin>',cls_fun__upd__other_0) ).
fof(c_0_131_132,axiom,
! [X57,X13,X9,X21,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X21)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X13,X3)
| ~ c_Finite__Set_Ofinite(X9,X3)
| c_Finite__Set_Osetsum(X57,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13),X3,X21) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),c_Finite__Set_Osetsum(X57,X9,X3,X21)),c_Finite__Set_Osetsum(X57,X13,X3,X21)) ),
file('<stdin>',cls_setsum__Un__disjoint_0) ).
fof(c_0_132_133,axiom,
! [X57,X13,X9,X21,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X21)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X13,X3)
| ~ c_Finite__Set_Ofinite(X9,X3)
| c_Finite__Set_Osetprod(X57,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13),X3,X21) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X21),c_Finite__Set_Osetprod(X57,X9,X3,X21)),c_Finite__Set_Osetprod(X57,X13,X3,X21)) ),
file('<stdin>',cls_setprod__Un__disjoint_0) ).
fof(c_0_133_134,axiom,
! [X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13)),X80))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X13),X80))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X80)) ),
file('<stdin>',cls_Un__subset__iff_2) ).
fof(c_0_134_135,axiom,
! [X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13)),X80))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X13),X80))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X80)) ),
file('<stdin>',cls_Un__least_0) ).
fof(c_0_135_136,axiom,
! [X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X13),X80)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(X3,tc_bool))),X80)) ),
file('<stdin>',cls_Diff__subset__conv_0) ).
fof(c_0_136_137,axiom,
! [X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(X3,tc_bool))),X80))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X13),X80))) ),
file('<stdin>',cls_Diff__subset__conv_1) ).
fof(c_0_137_138,axiom,
! [X38,X8,X9,X21,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X21)
| c_Finite__Set_Osetsum(X38,X9,X3,X21) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),hAPP(X38,X8)),c_Finite__Set_Osetsum(X38,c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3,X21))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_setsum__diff1_H_0) ).
fof(c_0_138_139,axiom,
! [X72,X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(X3,tc_bool))),c_HOL_Ominus__class_Ominus(X80,X72,tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X72),X13))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X80)) ),
file('<stdin>',cls_Diff__mono_0) ).
fof(c_0_139_140,axiom,
! [X80,X13,X9,X3] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13)),X80) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X13),X80))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X80),X9)) ),
file('<stdin>',cls_Un__Int__assoc__eq_0) ).
fof(c_0_140_141,axiom,
! [X12,X42,X72,X21,X3] :
( c_Fun_Ofun__upd(c_Map_Orestrict__map(X42,X72,X3,X21),X12,c_Option_Ooption_ONone(X21),X3,tc_Option_Ooption(X21)) = c_Map_Orestrict__map(X42,X72,X3,X21)
| hBOOL(hAPP(hAPP(c_in(X3),X12),X72)) ),
file('<stdin>',cls_fun__upd__None__restrict_1) ).
fof(c_0_141_142,axiom,
! [X38,X8,X9,X21,X3] :
( hBOOL(hAPP(hAPP(c_in(X21),hAPP(X38,X8)),X9))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),c_Set_Ovimage(X38,X9,X3,X21))) ),
file('<stdin>',cls_vimageD_0) ).
fof(c_0_142_143,axiom,
! [X38,X8,X13,X21,X3] :
( hBOOL(hAPP(hAPP(c_in(X21),hAPP(X38,X8)),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),c_Set_Ovimage(X38,X13,X3,X21))) ),
file('<stdin>',cls_vimageE_0) ).
fof(c_0_143_144,axiom,
! [X90,X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X90)),X23) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X90)),X24)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X8,X19,X3)),X90)),X23) = X24 ),
file('<stdin>',cls_eq__add__iff1_0) ).
fof(c_0_144_145,axiom,
! [X90,X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X90)),X23) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X90)),X24)
| X23 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X19,X8,X3)),X90)),X24) ),
file('<stdin>',cls_eq__add__iff2_0) ).
fof(c_0_145_146,axiom,
! [X38,X13,X9,X21,X3] :
( ~ class_OrderedGroup_Oab__group__add(X21)
| c_Finite__Set_Osetsum(X38,c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(X3,tc_bool)),X3,X21) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X38,X9,X3,X21),c_Finite__Set_Osetsum(X38,X13,X3,X21),X21)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X13),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_setsum__diff_0) ).
fof(c_0_146_147,axiom,
! [X14,X12,X38,X21,X3] :
( c_Fun_Ofun__upd(X38,X12,X14,X3,X21) != X38
| hAPP(X38,X12) = X14 ),
file('<stdin>',cls_fun__upd__idem__iff_0) ).
fof(c_0_147_148,axiom,
! [X24,X23,X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X24))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X23,X24,X3))) ),
file('<stdin>',cls_atLeastatMost__psubset__iff_2) ).
fof(c_0_148_149,axiom,
! [X90,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Osemiring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X90)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X90)),X23)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),X90)),X23) ),
file('<stdin>',cls_combine__common__factor_0) ).
fof(c_0_149_150,axiom,
! [X45,X46,X21,X3] :
( hAPP(X46,c_Map_Osko__Map__Xmap__le__def__1__1(X46,X45,X3,X21)) != hAPP(X45,c_Map_Osko__Map__Xmap__le__def__1__1(X46,X45,X3,X21))
| c_Map_Omap__le(X46,X45,X3,X21) ),
file('<stdin>',cls_map__le__def_2) ).
fof(c_0_150_151,axiom,
! [X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X80),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X80),X13))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X80),X9)) ),
file('<stdin>',cls_Int__greatest_0) ).
fof(c_0_151_152,axiom,
! [X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X80),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X80),X13))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X80),X9)) ),
file('<stdin>',cls_Int__subset__iff_2) ).
fof(c_0_152_153,axiom,
! [X20,X34,X3] :
( hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X34) != hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X20)
| X34 = X20 ),
file('<stdin>',cls_pred__equals__eq_0) ).
fof(c_0_153_154,axiom,
! [X24,X23,X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X23),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X23,X24,X3))) ),
file('<stdin>',cls_atLeastatMost__subset__iff_0) ).
fof(c_0_154_155,axiom,
! [X24,X23,X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X23,X24,X3))) ),
file('<stdin>',cls_atLeastatMost__subset__iff_1) ).
fof(c_0_155_156,axiom,
! [X24,X23,X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X23),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X23,X24,X3))) ),
file('<stdin>',cls_atLeastatMost__psubset__iff_0) ).
fof(c_0_156_157,axiom,
! [X24,X23,X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X23,X24,X3))) ),
file('<stdin>',cls_atLeastatMost__psubset__iff_1) ).
fof(c_0_157_158,axiom,
! [X38,X19,X8,X3] :
( X8 = X19
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X38,hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),X3),X19)) ),
file('<stdin>',cls_fold1Set__sing_0) ).
fof(c_0_158_159,axiom,
! [X12,X38,X9,X21,X3] :
( hBOOL(hAPP(X9,hAPP(X38,X12)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X38,X9,X3,X21),X12)) ),
file('<stdin>',cls_vimage__code_0) ).
fof(c_0_159_160,axiom,
! [X57,X38,X21,X3] :
( c_Map_Omap__add(X38,X57,X3,X21) = c_Map_Omap__add(X57,X38,X3,X21)
| ~ c_Map_Omap__le(X38,c_Map_Omap__add(X38,X57,X3,X21),X3,X21) ),
file('<stdin>',cls_map__le__iff__map__add__commute_0) ).
fof(c_0_160_161,axiom,
! [X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X80),X13))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X80),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13))) ),
file('<stdin>',cls_Int__subset__iff_1) ).
fof(c_0_161_162,axiom,
! [X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X80),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X80),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13))) ),
file('<stdin>',cls_Int__subset__iff_0) ).
fof(c_0_162_163,axiom,
! [X24,X23,X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X23,X24,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X23),X24))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X23),X8)) ),
file('<stdin>',cls_atLeastatMost__psubset__iff_6) ).
fof(c_0_163_164,axiom,
! [X24,X23,X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X23,X24,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X23),X24))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X23),X8)) ),
file('<stdin>',cls_atLeastatMost__psubset__iff_5) ).
fof(c_0_164_165,axiom,
! [X80,X13,X9,X3] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13)),X80) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X13),X80))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X80),X9)) ),
file('<stdin>',cls_Un__Int__assoc__eq_1) ).
fof(c_0_165_166,axiom,
! [X38,X8,X9,X21,X3] :
( ~ class_Ring__and__Field_Oring(X21)
| c_Finite__Set_Osetsum(X38,c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3,X21) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X38,X9,X3,X21),hAPP(X38,X8),X21)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_setsum__diff1__ring_0) ).
fof(c_0_166_167,axiom,
! [X38,X8,X9,X21,X3] :
( ~ class_OrderedGroup_Oab__group__add(X21)
| c_Finite__Set_Osetsum(X38,c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3,X21) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X38,X9,X3,X21),hAPP(X38,X8),X21)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_setsum__diff1_0) ).
fof(c_0_167_168,axiom,
! [X24,X23,X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X23),X24))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X23,X24,X3))) ),
file('<stdin>',cls_atLeastatMost__psubset__iff_3) ).
fof(c_0_168_169,axiom,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X12)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X14),X14))))
| X12 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_sum__squares__gt__zero__iff_1) ).
fof(c_0_169_170,axiom,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X12)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X14),X14))))
| X14 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_sum__squares__gt__zero__iff_2) ).
fof(c_0_170_171,axiom,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X12)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X14),X14)))) ),
file('<stdin>',cls_sum__squares__ge__zero_0) ).
fof(c_0_171_172,axiom,
! [X57,X38,X21,X3] :
( c_Map_Omap__add(X38,X57,X3,X21) != c_Map_Omap__add(X57,X38,X3,X21)
| c_Map_Omap__le(X38,c_Map_Omap__add(X38,X57,X3,X21),X3,X21) ),
file('<stdin>',cls_map__le__iff__map__add__commute_1) ).
fof(c_0_172_173,axiom,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),X13)) ),
file('<stdin>',cls_psubset__insert__iff_7) ).
fof(c_0_173_174,axiom,
! [X8,X9,X3] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X3),X3),hAPP(hAPP(c_Set_Oinsert(X3),X8),X9)) = c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(X3),X8,X9,X3,X3)
| hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_fold1__eq__fold_0) ).
fof(c_0_174_175,axiom,
! [X8,X9,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X3),X3),hAPP(hAPP(c_Set_Oinsert(X3),X8),X9)) = c_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(X3),X8,X9,X3,X3)
| hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_comm__monoid__add_Ofold1__eq__fold_0) ).
fof(c_0_175_176,axiom,
! [X37,X8,X9,X3] :
( hAPP(c_Finite__Set_Ofold1(X37,X3),hAPP(hAPP(c_Set_Oinsert(X3),X8),X9)) = c_Finite__Set_Ofold(X37,X8,X9,X3,X3)
| hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_OrderedGroup_Oab__semigroup__mult(X37,X3) ),
file('<stdin>',cls_ab__semigroup__mult_Ofold1__eq__fold_0) ).
fof(c_0_176_177,axiom,
! [X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X24)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),X24))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19)) ),
file('<stdin>',cls_mult__strict__mono_0) ).
fof(c_0_177_178,axiom,
! [X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X24)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X23),X24))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19)) ),
file('<stdin>',cls_mult__less__le__imp__less_0) ).
fof(c_0_178_179,axiom,
! [X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X24)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X8))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
file('<stdin>',cls_mult__le__less__imp__less_0) ).
fof(c_0_179_180,axiom,
! [X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X24)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),X24))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19)) ),
file('<stdin>',cls_mult__strict__mono_H_0) ).
fof(c_0_180_181,axiom,
! [X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__semiring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X24)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X23),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
file('<stdin>',cls_mult__mono_0) ).
fof(c_0_181_182,axiom,
! [X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__semiring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X24)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X23),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
file('<stdin>',cls_mult__mono_H_0) ).
fof(c_0_182_183,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19))) ),
file('<stdin>',cls_mult__left__less__imp__less_0) ).
fof(c_0_183_184,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23))) ),
file('<stdin>',cls_mult__right__less__imp__less_0) ).
fof(c_0_184_185,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19))) ),
file('<stdin>',cls_mult__less__imp__less__left_0) ).
fof(c_0_185_186,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23))) ),
file('<stdin>',cls_mult__less__imp__less__right_0) ).
fof(c_0_186_187,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X23)) ),
file('<stdin>',cls_mult__le__cancel__left__pos_0) ).
fof(c_0_187_188,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19))) ),
file('<stdin>',cls_mult__left__le__imp__le_0) ).
fof(c_0_188_189,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23))) ),
file('<stdin>',cls_mult__right__le__imp__le_0) ).
fof(c_0_189_190,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X23)) ),
file('<stdin>',cls_mult__less__cancel__left__pos_0) ).
fof(c_0_190_191,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_mult__le__cancel__left__neg_0) ).
fof(c_0_191_192,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X8))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_mult__less__cancel__left__neg_0) ).
fof(c_0_192_193,axiom,
! [X38,X8,X13,X21,X3] :
( hBOOL(hAPP(hAPP(c_in(X21),X8),c_Set_Ovimage(X38,X13,X21,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),hAPP(X38,X8)),X13)) ),
file('<stdin>',cls_vimageI_0) ).
fof(c_0_193_194,axiom,
! [X38,X8,X9,X21,X3] :
( hBOOL(hAPP(hAPP(c_in(X21),X8),c_Set_Ovimage(X38,X9,X21,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),hAPP(X38,X8)),X9)) ),
file('<stdin>',cls_vimageI2_0) ).
fof(c_0_194_195,axiom,
! [X38,X8,X13,X21,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X8),c_Set_Ovimage(X38,X13,X3,X21)))
| ~ hBOOL(hAPP(hAPP(c_in(X21),hAPP(X38,X8)),X13)) ),
file('<stdin>',cls_vimage__eq_1) ).
fof(c_0_195_196,axiom,
! [X63,X57,X38,X21,X3] :
( c_Map_Omap__le(X57,X63,X3,X21)
| ~ c_Map_Omap__le(c_Map_Omap__add(X38,X57,X3,X21),X63,X3,X21) ),
file('<stdin>',cls_map__add__le__mapE_0) ).
fof(c_0_196_197,axiom,
! [X13,X9,X3] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13) = c_Finite__Set_Ofold(c_Set_Oinsert(X3),X13,X9,X3,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_union__fold__insert_0) ).
fof(c_0_197_198,axiom,
! [X8,X9,X3] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X3),X3),hAPP(hAPP(c_Set_Oinsert(X3),X8),X9)) = c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(X3),X8,X9,X3,X3)
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_fold1__eq__fold__idem_0) ).
fof(c_0_198_199,axiom,
! [X37,X8,X9,X3] :
( hAPP(c_Finite__Set_Ofold1(X37,X3),hAPP(hAPP(c_Set_Oinsert(X3),X8),X9)) = c_Finite__Set_Ofold(X37,X8,X9,X3,X3)
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X37,X3) ),
file('<stdin>',cls_ab__semigroup__idem__mult_Ofold1__eq__fold__idem_0) ).
fof(c_0_199_200,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),c_HOL_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19))) ),
file('<stdin>',cls_mult__less__cancel__left__disj_0) ).
fof(c_0_200_201,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),c_HOL_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23))) ),
file('<stdin>',cls_mult__less__cancel__right__disj_0) ).
fof(c_0_201_202,axiom,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X3),X12),X9)),X13)) ),
file('<stdin>',cls_insert__subset_1) ).
fof(c_0_202_203,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X8))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23))) ),
file('<stdin>',cls_mult__less__cancel__right__disj_1) ).
fof(c_0_203_204,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X8))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19))) ),
file('<stdin>',cls_mult__less__cancel__left__disj_1) ).
fof(c_0_204_205,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),c_HOL_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23))) ),
file('<stdin>',cls_mult__less__cancel__right__disj_2) ).
fof(c_0_205_206,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),c_HOL_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19))) ),
file('<stdin>',cls_mult__less__cancel__left__disj_2) ).
fof(c_0_206_207,axiom,
! [X12,X9,X3] :
( c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3)) = c_Finite__Set_Ocard(X9,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_card__Suc__Diff1_0) ).
fof(c_0_207_208,axiom,
! [X8,X72,X80,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X3),X8),X80)),hAPP(hAPP(c_Set_Oinsert(X3),X8),X72)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X80),X72)) ),
file('<stdin>',cls_insert__mono_0) ).
fof(c_0_208_209,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X8))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19))) ),
file('<stdin>',cls_mult__less__cancel__left__disj_3) ).
fof(c_0_209_210,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X8))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23))) ),
file('<stdin>',cls_mult__less__cancel__right__disj_3) ).
fof(c_0_210_211,axiom,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X3),X12),X9)),X13))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X13)) ),
file('<stdin>',cls_insert__subset_2) ).
fof(c_0_211_212,axiom,
! [X57,X38,X21,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Map_Odom(X38,X3,X21)),c_Map_Odom(X57,X3,X21)))
| ~ c_Map_Omap__le(X38,X57,X3,X21) ),
file('<stdin>',cls_map__le__implies__dom__le_0) ).
fof(c_0_212_213,axiom,
! [X13,X9,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X13),c_Complete__Lattice_OInf__class_OInf(X9,X3)) = c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X3),X13,X9,X3,X3)
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_inf__Inf__fold__inf_0) ).
fof(c_0_213_214,axiom,
! [X13,X9,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X13),c_Complete__Lattice_OSup__class_OSup(X9,X3)) = c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X3),X13,X9,X3,X3)
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_sup__Sup__fold__sup_0) ).
fof(c_0_214_215,axiom,
! [X12,X6,X56,X21,X3] :
( hAPP(X6,X56) != hAPP(c_Option_Ooption_OSome(X3),X12)
| c_Fun_Ofun__upd(X6,X56,hAPP(c_Option_Ooption_OSome(X3),X12),X21,tc_Option_Ooption(X3)) = X6 ),
file('<stdin>',cls_map__upd__triv_0) ).
fof(c_0_215_216,axiom,
! [X12,X9,X3] :
( c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(X3),X12),X9),X3) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_card__insert_0) ).
fof(c_0_216_217,axiom,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X13))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13))) ),
file('<stdin>',cls_psubset__insert__iff_2) ).
fof(c_0_217_218,axiom,
! [X23,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X23),X13))
| hBOOL(hAPP(hAPP(c_in(X3),X23),X9))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X23),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13))) ),
file('<stdin>',cls_UnE_0) ).
fof(c_0_218_219,axiom,
! [X24,X23,X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X23,X24,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X23),X8)) ),
file('<stdin>',cls_atLeastatMost__subset__iff_3) ).
fof(c_0_219_220,axiom,
! [X61,X62,X21,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),c_Map_Odom(X62,X3,X21)),c_Map_Odom(X61,X3,X21)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_Map_Omap__add(X62,X61,X3,X21) = c_Map_Omap__add(X61,X62,X3,X21) ),
file('<stdin>',cls_map__add__comm_0) ).
fof(c_0_220_221,axiom,
! [X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Lattices_Olower__semilattice(c_COMBC(c_lessequals(X3),X3,X3,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(X3),X3,X3,tc_bool),c_Orderings_Oord__class_Omax(X3),X3) ),
file('<stdin>',cls_max__lattice_0) ).
fof(c_0_221_222,axiom,
! [X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Olower__semilattice(c_COMBC(c_lessequals(X3),X3,X3,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(X3),X3,X3,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X3),X3) ),
file('<stdin>',cls_dual__semilattice_0) ).
fof(c_0_222_223,axiom,
! [X9,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OSup__class_OSup(X9,X3) = c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X3),c_Orderings_Obot__class_Obot(X3),X9,X3,X3)
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_Sup__fold__sup_0) ).
fof(c_0_223_224,axiom,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X23))) ),
file('<stdin>',cls_add__le__cancel__right_0) ).
fof(c_0_224_225,axiom,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X8)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X19))) ),
file('<stdin>',cls_add__le__cancel__left_0) ).
fof(c_0_225_226,axiom,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X23))) ),
file('<stdin>',cls_add__less__cancel__right_0) ).
fof(c_0_226_227,axiom,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X8)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X19))) ),
file('<stdin>',cls_add__less__cancel__left_0) ).
fof(c_0_227_228,axiom,
! [X12,X9,X3] :
( X9 = hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))))) ),
file('<stdin>',cls_subset__singletonD_0) ).
fof(c_0_228_229,axiom,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X13))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13))) ),
file('<stdin>',cls_psubset__insert__iff_0) ).
fof(c_0_229_230,axiom,
! [X13,X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X3),X3),X13)),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X3),X3),X9)))
| ~ c_Finite__Set_Ofinite(X13,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_fold1__antimono_0) ).
fof(c_0_230_231,axiom,
! [X38,X8,X9,X21,X3] :
( ~ class_Ring__and__Field_Ofield(X21)
| c_Finite__Set_Osetprod(X38,c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3,X21) = c_Finite__Set_Osetprod(X38,X9,X3,X21)
| hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| hAPP(X38,X8) = c_HOL_Ozero__class_Ozero(X21)
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_setprod__diff1_1) ).
fof(c_0_231_232,axiom,
! [X24,X23,X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X23,X24,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X23),X24))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
file('<stdin>',cls_atLeastatMost__psubset__iff_4) ).
fof(c_0_232_233,axiom,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X12),X13))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X3),X12),X9)),X13)) ),
file('<stdin>',cls_insert__subset_0) ).
fof(c_0_233_234,axiom,
! [X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),X80))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X13),X80))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),X13)) ),
file('<stdin>',cls_psubset__trans_0) ).
fof(c_0_234_235,axiom,
! [X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X80))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X13),X80))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
file('<stdin>',cls_subset__trans_0) ).
fof(c_0_235_236,axiom,
! [X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),X80))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X13),X80))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),X13)) ),
file('<stdin>',cls_psubset__subset__trans_0) ).
fof(c_0_236_237,axiom,
! [X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),X80))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X13),X80))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
file('<stdin>',cls_subset__psubset__trans_0) ).
fof(c_0_237_238,axiom,
! [X38,X8,X9,X21,X3] :
( ~ class_OrderedGroup_Oab__group__add(X21)
| c_Finite__Set_Osetsum(X38,c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3,X21) = c_Finite__Set_Osetsum(X38,X9,X3,X21)
| hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_setsum__diff1_1) ).
fof(c_0_238_239,axiom,
! [X35,X36,X32] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OBODY(X32)),X36),X35))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Option_Othe(hAPP(c_Com_Obody,X32),tc_Com_Ocom)),X36),X35)) ),
file('<stdin>',cls_evalc_OBody_0) ).
fof(c_0_239_240,axiom,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13)))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9)) ),
file('<stdin>',cls_subset__insert_0) ).
fof(c_0_240_241,axiom,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13))) ),
file('<stdin>',cls_subset__insert__iff_1) ).
fof(c_0_241_242,axiom,
! [X23,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X23),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X23),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13))) ),
file('<stdin>',cls_IntE_1) ).
fof(c_0_242_243,axiom,
! [X23,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X23),X9))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X23),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13))) ),
file('<stdin>',cls_IntE_0) ).
fof(c_0_243_244,axiom,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X13)) ),
file('<stdin>',cls_psubset__insert__iff_3) ).
fof(c_0_244_245,axiom,
! [X38,X8,X9,X3] :
( c_Finite__Set_Osetsum(X38,c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3,tc_nat) = c_Finite__Set_Osetsum(X38,X9,X3,tc_nat)
| hBOOL(hAPP(hAPP(c_in(X3),X8),X9)) ),
file('<stdin>',cls_setsum__diff1__nat_1) ).
fof(c_0_245_246,axiom,
! [X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),X13))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(X9,X3)),c_Finite__Set_Ocard(X13,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| ~ c_Finite__Set_Ofinite(X13,X3) ),
file('<stdin>',cls_card__psubset_0) ).
fof(c_0_246_247,axiom,
! [X70,X14,X12,X95,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X95),X14)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X70)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X95),X70)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X14))
| X14 = X70
| X95 = X12 ),
file('<stdin>',cls_class__ringb_Oadd__mul__solve_0) ).
fof(c_0_247_248,axiom,
! [X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X24)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X24)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23))
| X23 = X24
| X8 = X19 ),
file('<stdin>',cls_class__ringb_Onoteq__reduce_0) ).
fof(c_0_248_249,axiom,
! [X12,X38,X9,X21,X3] :
( hBOOL(hAPP(c_Set_Ovimage(X38,X9,X3,X21),X12))
| ~ hBOOL(hAPP(X9,hAPP(X38,X12))) ),
file('<stdin>',cls_vimage__code_1) ).
fof(c_0_249_250,axiom,
! [X80,X13,X9,X3] :
( c_HOL_Ominus__class_Ominus(X13,c_HOL_Ominus__class_Ominus(X80,X9,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X9
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X13),X80))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
file('<stdin>',cls_double__diff_0) ).
fof(c_0_250_251,axiom,
! [X57,X38,X21,X3] :
( ~ class_HOL_Oord(X21)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,X21)),X38),X57))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,X21)),X57),X38))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,X21)),X38),X57)) ),
file('<stdin>',cls_less__fun__def_2) ).
fof(c_0_251_252,axiom,
! [X49,X50,X3] :
( c_Orderings_Olinorder(c_COMBC(X49,X3,X3,tc_bool),c_COMBC(X50,X3,X3,tc_bool),X3)
| ~ c_Orderings_Olinorder(X49,X50,X3) ),
file('<stdin>',cls_linorder_Odual__linorder_0) ).
fof(c_0_252_253,axiom,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X13))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),X13)) ),
file('<stdin>',cls_psubset__insert__iff_6) ).
fof(c_0_253_254,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X23)) ),
file('<stdin>',cls_mult__le__cancel__left__pos_1) ).
fof(c_0_254_255,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Omult__mono(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
file('<stdin>',cls_mult__right__mono_0) ).
fof(c_0_255_256,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Omult__mono(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
file('<stdin>',cls_mult__left__mono_0) ).
fof(c_0_256_257,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Omult__mono1(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
file('<stdin>',cls_mult__mono1_0) ).
fof(c_0_257_258,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X23)) ),
file('<stdin>',cls_mult__less__cancel__left__pos_1) ).
fof(c_0_258_259,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19)) ),
file('<stdin>',cls_mult__strict__left__mono_0) ).
fof(c_0_259_260,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X23)) ),
file('<stdin>',cls_mult__less__cancel__left__disj_4) ).
fof(c_0_260_261,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19)) ),
file('<stdin>',cls_mult__strict__right__mono_0) ).
fof(c_0_261_262,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X23)) ),
file('<stdin>',cls_mult__less__cancel__right__disj_4) ).
fof(c_0_262_263,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19)) ),
file('<stdin>',cls_mult__strict__left__mono__comm_0) ).
fof(c_0_263_264,axiom,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_mult__le__0__iff_1) ).
fof(c_0_264_265,axiom,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_mult__le__0__iff_3) ).
fof(c_0_265_266,axiom,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),c_HOL_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_mult__le__0__iff_0) ).
fof(c_0_266_267,axiom,
! [X38,X8,X58,X21,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X21)
| c_Finite__Set_Osetsum(X38,hAPP(hAPP(c_Set_Oinsert(X3),X8),X58),X3,X21) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),hAPP(X38,X8)),c_Finite__Set_Osetsum(X38,X58,X3,X21))
| hBOOL(hAPP(hAPP(c_in(X3),X8),X58))
| ~ c_Finite__Set_Ofinite(X58,X3) ),
file('<stdin>',cls_setsum__insert_0) ).
fof(c_0_267_268,axiom,
! [X38,X8,X9,X21,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X21)
| c_Finite__Set_Osetprod(X38,hAPP(hAPP(c_Set_Oinsert(X3),X8),X9),X3,X21) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X21),hAPP(X38,X8)),c_Finite__Set_Osetprod(X38,X9,X3,X21))
| hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_setprod__insert_0) ).
fof(c_0_268_269,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X8))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_mult__le__cancel__left__neg_1) ).
fof(c_0_269_270,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X23),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X8)) ),
file('<stdin>',cls_mult__right__mono__neg_0) ).
fof(c_0_270_271,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X23),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X8)) ),
file('<stdin>',cls_mult__left__mono__neg_0) ).
fof(c_0_271_272,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X8))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_mult__less__cancel__left__neg_1) ).
fof(c_0_272_273,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X8)) ),
file('<stdin>',cls_mult__strict__left__mono__neg_0) ).
fof(c_0_273_274,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X8))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_mult__less__cancel__left__disj_5) ).
fof(c_0_274_275,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X8)) ),
file('<stdin>',cls_mult__strict__right__mono__neg_0) ).
fof(c_0_275_276,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X8))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_mult__less__cancel__right__disj_5) ).
fof(c_0_276_277,axiom,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),c_HOL_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_mult__le__0__iff_2) ).
fof(c_0_277_278,axiom,
! [X13,X9,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X13 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X13,X3)
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X3),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X3),X3),X9)),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X3),X3),X13)) ),
file('<stdin>',cls_comm__monoid__add_Ofold1__Un_0) ).
fof(c_0_278_279,axiom,
! [X13,X9,X3] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X13 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X13,X3)
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X3),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X3),X3),X9)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X3),X3),X13)) ),
file('<stdin>',cls_fold1__Un_0) ).
fof(c_0_279_280,axiom,
! [X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Orderings_Olinorder(c_COMBC(c_lessequals(X3),X3,X3,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(X3),X3,X3,tc_bool),X3) ),
file('<stdin>',cls_dual__linorder_0) ).
fof(c_0_280_281,axiom,
! [X17,X12,X49,X50,X51,X9,X3] :
( hBOOL(hAPP(hAPP(X49,X12),X17))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X9))
| ~ hBOOL(hAPP(hAPP(X49,X12),hAPP(c_Finite__Set_Ofold1(X51,X3),X9)))
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
file('<stdin>',cls_lower__semilattice_Obelow__fold1__iff_0) ).
fof(c_0_281_282,axiom,
! [X24,X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X24)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X23),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
file('<stdin>',cls_add__mono_0) ).
fof(c_0_282_283,axiom,
! [X24,X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X24)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),X24))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19)) ),
file('<stdin>',cls_add__strict__mono_0) ).
fof(c_0_283_284,axiom,
! [X24,X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X24)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
file('<stdin>',cls_add__le__less__mono_0) ).
fof(c_0_284_285,axiom,
! [X24,X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X24)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X23),X24))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19)) ),
file('<stdin>',cls_add__less__le__mono_0) ).
fof(c_0_285_286,axiom,
! [X12,X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(c_Finite__Set_Olinorder__class_OMax(X3),X9) = X12
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(X9,X12,X3)),X12))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_Max__eqI_1) ).
fof(c_0_286_287,axiom,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9)) ),
file('<stdin>',cls_subset__insert_1) ).
fof(c_0_287_288,axiom,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9)) ),
file('<stdin>',cls_subset__insert__iff_2) ).
fof(c_0_288_289,axiom,
! [X24,X23,X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X23,X24,X3)))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
file('<stdin>',cls_atLeastatMost__subset__iff_2) ).
fof(c_0_289_290,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X70))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14)),X70)) ),
file('<stdin>',cls_min__le__iff__disj_0) ).
fof(c_0_290_291,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X70))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X70))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14)),X70)) ),
file('<stdin>',cls_min__less__iff__disj_0) ).
fof(c_0_291_292,axiom,
! [X42,X8,X21,X3] :
( hAPP(X42,X8) = hAPP(c_Option_Ooption_OSome(X21),c_Map_Osko__Map__XdomD__1__1(X8,X42,X3,X21))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),c_Map_Odom(X42,X3,X21))) ),
file('<stdin>',cls_domD_0) ).
fof(c_0_292_293,axiom,
! [X60,X61,X62,X21,X3] :
( c_Map_Omap__le(X62,X60,X3,X21)
| ~ c_Map_Omap__le(X61,X60,X3,X21)
| ~ c_Map_Omap__le(X62,X61,X3,X21) ),
file('<stdin>',cls_map__le__trans_0) ).
fof(c_0_293_294,axiom,
! [X42,X43,X44,X21,X3] :
( hAPP(c_Map_Omap__add(X44,X43,X3,X21),X42) = hAPP(X43,X42)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X42),c_Map_Odom(X43,X3,X21))) ),
file('<stdin>',cls_map__add__dom__app__simps_I1_J_0) ).
fof(c_0_294_295,axiom,
! [X23,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X23),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X23),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X23),X9)) ),
file('<stdin>',cls_Int__iff_2) ).
fof(c_0_295_296,axiom,
! [X23,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X23),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X23),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X23),X9)) ),
file('<stdin>',cls_IntI_0) ).
fof(c_0_296_297,axiom,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(X13,X12))
| hBOOL(hAPP(X9,X12))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13),X12)) ),
file('<stdin>',cls_sup1E_0) ).
fof(c_0_297_298,axiom,
! [X57,X38,X21,X3] :
( ~ class_HOL_Oord(X21)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,X21)),X57),X38))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,X21)),X38),X57)) ),
file('<stdin>',cls_less__fun__def_1) ).
fof(c_0_298_299,axiom,
! [X37,X13,X9,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X13 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X13,X3)
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_OrderedGroup_Oab__semigroup__mult(X37,X3)
| hAPP(c_Finite__Set_Ofold1(X37,X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13)) = hAPP(hAPP(X37,hAPP(c_Finite__Set_Ofold1(X37,X3),X9)),hAPP(c_Finite__Set_Ofold1(X37,X3),X13)) ),
file('<stdin>',cls_ab__semigroup__mult_Ofold1__Un_0) ).
fof(c_0_299_300,axiom,
! [X24,X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X24)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X23),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X23))) ),
file('<stdin>',cls_le__add__right__mono_0) ).
fof(c_0_300_301,axiom,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(X13,X12))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13),X12)) ),
file('<stdin>',cls_inf1E_1) ).
fof(c_0_301_302,axiom,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(X9,X12))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13),X12)) ),
file('<stdin>',cls_inf1E_0) ).
fof(c_0_302_303,axiom,
! [X49,X50,X51,X8,X9,X3] :
( hBOOL(hAPP(hAPP(X49,hAPP(c_Finite__Set_Ofold1(X51,X3),X9)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
file('<stdin>',cls_lower__semilattice_Ofold1__belowI_0) ).
fof(c_0_303_304,axiom,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ominus__class_Ominus(X8,X19,X3)),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_le__iff__diff__le__0_1) ).
fof(c_0_304_305,axiom,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ominus__class_Ominus(X8,X19,X3)),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_less__iff__diff__less__0_1) ).
fof(c_0_305_306,axiom,
! [X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X8)),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_0) ).
fof(c_0_306_307,axiom,
! [X8,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X8)),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_even__less__0__iff_0) ).
fof(c_0_307_308,axiom,
! [X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X8)),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
fof(c_0_308_309,axiom,
! [X19,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X19),X13)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
file('<stdin>',cls_subset__insertI2_0) ).
fof(c_0_309_310,axiom,
! [X83,X84,X86,X85,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X85),X86)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X84),X83)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X84),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X85),X86)),X83)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I15_J_0) ).
fof(c_0_310_311,axiom,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X8)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
file('<stdin>',cls_mult__pos__neg2_0) ).
fof(c_0_311_312,axiom,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
file('<stdin>',cls_mult__pos__neg_0) ).
fof(c_0_312_313,axiom,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_mult__neg__pos_0) ).
fof(c_0_313_314,axiom,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
file('<stdin>',cls_mult__le__0__iff_4) ).
fof(c_0_314_315,axiom,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_mult__le__0__iff_5) ).
fof(c_0_315_316,axiom,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
file('<stdin>',cls_split__mult__neg__le_0) ).
fof(c_0_316_317,axiom,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_split__mult__neg__le_1) ).
fof(c_0_317_318,axiom,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
file('<stdin>',cls_mult__nonneg__nonpos_0) ).
fof(c_0_318_319,axiom,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_mult__nonpos__nonneg_0) ).
fof(c_0_319_320,axiom,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X8)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
file('<stdin>',cls_mult__nonneg__nonpos2_0) ).
fof(c_0_320_321,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14)),X70)) ),
file('<stdin>',cls_min__max_Ole__sup__iff_1) ).
fof(c_0_321_322,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14)),X70)) ),
file('<stdin>',cls_min__max_Ole__sup__iff_0) ).
fof(c_0_322_323,axiom,
! [X12,X19,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X8),X19)),X12)) ),
file('<stdin>',cls_min__max_Ole__supE_1) ).
fof(c_0_323_324,axiom,
! [X12,X19,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X8),X19)),X12)) ),
file('<stdin>',cls_min__max_Ole__supE_0) ).
fof(c_0_324_325,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X70))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14)),X70)) ),
file('<stdin>',cls_max__less__iff__conj_0) ).
fof(c_0_325_326,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X70))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14)),X70)) ),
file('<stdin>',cls_max__less__iff__conj_1) ).
fof(c_0_326_327,axiom,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14)),X70)) ),
file('<stdin>',cls_le__sup__iff_1) ).
fof(c_0_327_328,axiom,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14)),X70)) ),
file('<stdin>',cls_le__sup__iff_0) ).
fof(c_0_328_329,axiom,
! [X12,X19,X8,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X8),X19)),X12)) ),
file('<stdin>',cls_le__supE_1) ).
fof(c_0_329_330,axiom,
! [X12,X19,X8,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X8),X19)),X12)) ),
file('<stdin>',cls_le__supE_0) ).
fof(c_0_330_331,axiom,
! [X12,X45,X46,X21,X3] :
( hAPP(X46,X12) = hAPP(X45,X12)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),c_Map_Odom(X46,X3,X21)))
| ~ c_Map_Omap__le(X46,X45,X3,X21) ),
file('<stdin>',cls_map__le__def_0) ).
fof(c_0_331_332,axiom,
! [X14,X12,X3] :
( X14 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),X3)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),X14)) ),
file('<stdin>',cls_Nitpick_OEx1__def_3) ).
fof(c_0_332_333,axiom,
! [X13,X9,X3] :
( X9 = X13
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X13),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
file('<stdin>',cls_equalityI_0) ).
fof(c_0_333_334,axiom,
! [X13,X9,X3] :
( X9 = X13
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X13),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
file('<stdin>',cls_set__eq__subset_2) ).
fof(c_0_334_335,axiom,
! [X12,X49,X50,X51,X19,X8,X3] :
( hBOOL(hAPP(hAPP(X50,hAPP(hAPP(X51,X8),X19)),X12))
| ~ hBOOL(hAPP(hAPP(X50,X19),X12))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
file('<stdin>',cls_lower__semilattice_Oless__infI2_0) ).
fof(c_0_335_336,axiom,
! [X12,X49,X50,X51,X19,X8,X3] :
( hBOOL(hAPP(hAPP(X50,hAPP(hAPP(X51,X8),X19)),X12))
| ~ hBOOL(hAPP(hAPP(X50,X8),X12))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
file('<stdin>',cls_lower__semilattice_Oless__infI1_0) ).
fof(c_0_336_337,axiom,
! [X12,X49,X50,X51,X19,X8,X3] :
( hBOOL(hAPP(hAPP(X49,hAPP(hAPP(X51,X8),X19)),X12))
| ~ hBOOL(hAPP(hAPP(X49,X8),X12))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
file('<stdin>',cls_lower__semilattice_Ole__infI1_0) ).
fof(c_0_337_338,axiom,
! [X12,X49,X50,X51,X19,X8,X3] :
( hBOOL(hAPP(hAPP(X49,hAPP(hAPP(X51,X8),X19)),X12))
| ~ hBOOL(hAPP(hAPP(X49,X19),X12))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
file('<stdin>',cls_lower__semilattice_Ole__infI2_0) ).
fof(c_0_338_339,axiom,
! [X17,X12,X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X3),X3),X9)),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X17),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X9))
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_fold1__below__iff_2) ).
fof(c_0_339_340,axiom,
! [X17,X12,X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X3),X3),X9)),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X17),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X9))
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_fold1__strict__below__iff_2) ).
fof(c_0_340_341,axiom,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_add__nonpos__neg_0) ).
fof(c_0_341_342,axiom,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_add__neg__nonpos_0) ).
fof(c_0_342_343,axiom,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_add__neg__neg_0) ).
fof(c_0_343_344,axiom,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_add__nonpos__nonpos_0) ).
fof(c_0_344_345,axiom,
! [X35,X7,X18] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Option_Othe(hAPP(c_Com_Obody,X18),tc_Com_Ocom)),X7),X35))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OBODY(X18)),X7),X35)) ),
file('<stdin>',cls_evalc__elim__cases_I6_J_0) ).
fof(c_0_345_346,axiom,
! [X12,X55,X42,X56,X21,X3] :
( hAPP(c_Map_Omap__add(X42,X55,X21,X3),X56) != hAPP(c_Option_Ooption_OSome(X3),X12)
| hAPP(X42,X56) = hAPP(c_Option_Ooption_OSome(X3),X12)
| hAPP(X55,X56) = hAPP(c_Option_Ooption_OSome(X3),X12) ),
file('<stdin>',cls_map__add__SomeD_1) ).
fof(c_0_346_347,axiom,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X23)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
file('<stdin>',cls_add__le__cancel__right_1) ).
fof(c_0_347_348,axiom,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X8)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
file('<stdin>',cls_add__le__cancel__left_1) ).
fof(c_0_348_349,axiom,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X23)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
file('<stdin>',cls_add__right__mono_0) ).
fof(c_0_349_350,axiom,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X8)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
file('<stdin>',cls_add__left__mono_0) ).
fof(c_0_350_351,axiom,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X23)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19)) ),
file('<stdin>',cls_add__strict__right__mono_0) ).
fof(c_0_351_352,axiom,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X23)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19)) ),
file('<stdin>',cls_add__less__cancel__right_1) ).
fof(c_0_352_353,axiom,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X8)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19)) ),
file('<stdin>',cls_add__strict__left__mono_0) ).
fof(c_0_353_354,axiom,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X8)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19)) ),
file('<stdin>',cls_add__less__cancel__left_1) ).
fof(c_0_354_355,axiom,
! [X12,X49,X50,X51,X19,X8,X3] :
( hBOOL(hAPP(hAPP(X49,X12),hAPP(hAPP(X51,X8),X19)))
| ~ hBOOL(hAPP(hAPP(X49,X12),X19))
| ~ hBOOL(hAPP(hAPP(X49,X12),X8))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
file('<stdin>',cls_lower__semilattice_Ole__infI_0) ).
fof(c_0_355_356,axiom,
! [X70,X14,X12,X49,X50,X51,X3] :
( hBOOL(hAPP(hAPP(X49,X12),hAPP(hAPP(X51,X14),X70)))
| ~ hBOOL(hAPP(hAPP(X49,X12),X70))
| ~ hBOOL(hAPP(hAPP(X49,X12),X14))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
file('<stdin>',cls_lower__semilattice_Ole__inf__iff_2) ).
fof(c_0_356_357,axiom,
! [X70,X14,X12,X49,X50,X51,X3] :
( hBOOL(hAPP(hAPP(X49,X12),hAPP(hAPP(X51,X14),X70)))
| ~ hBOOL(hAPP(hAPP(X49,X12),X70))
| ~ hBOOL(hAPP(hAPP(X49,X12),X14))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
file('<stdin>',cls_lower__semilattice_Oinf__greatest_0) ).
fof(c_0_357_358,axiom,
! [X12,X55,X42,X56,X21,X3] :
( hAPP(c_Map_Omap__add(X42,X55,X21,X3),X56) != hAPP(c_Option_Ooption_OSome(X3),X12)
| hAPP(X55,X56) = c_Option_Ooption_ONone(X3)
| hAPP(X55,X56) = hAPP(c_Option_Ooption_OSome(X3),X12) ),
file('<stdin>',cls_map__add__SomeD_0) ).
fof(c_0_358_359,axiom,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X8))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X8))) ),
file('<stdin>',cls_zero__less__mult__pos2_0) ).
fof(c_0_359_360,axiom,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X8))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19))) ),
file('<stdin>',cls_zero__less__mult__pos_0) ).
fof(c_0_360_361,axiom,
! [X12,X19,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X8),X19)),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X12)) ),
file('<stdin>',cls_min__max_Ole__supI_0) ).
fof(c_0_361_362,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X14),X70)),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X70),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12)) ),
file('<stdin>',cls_min__max_Osup__least_0) ).
fof(c_0_362_363,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14)),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X70)) ),
file('<stdin>',cls_min__max_Ole__sup__iff_2) ).
fof(c_0_363_364,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14)),X70))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X70))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X70)) ),
file('<stdin>',cls_max__less__iff__conj_2) ).
fof(c_0_364_365,axiom,
! [X12,X19,X8,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X8),X19)),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X12)) ),
file('<stdin>',cls_le__supI_0) ).
fof(c_0_365_366,axiom,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X14),X70)),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X70),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12)) ),
file('<stdin>',cls_sup__least_0) ).
fof(c_0_366_367,axiom,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14)),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X70)) ),
file('<stdin>',cls_le__sup__iff_2) ).
fof(c_0_367_368,axiom,
! [X15,X6,X16,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X6),X15),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,X15,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X6),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))),X3) ),
file('<stdin>',cls_hoare__derivs_Oinsert_0) ).
fof(c_0_368_369,axiom,
! [X8,X80,X13,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X3),X8),X13)),X80) = hAPP(hAPP(c_Set_Oinsert(X3),X8),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X13),X80))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X80)) ),
file('<stdin>',cls_Int__insert__left_0) ).
fof(c_0_369_370,axiom,
! [X81,X82,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(c_Finite__Set_Olinorder__class_OMax(X3),X82)),hAPP(c_Finite__Set_Olinorder__class_OMax(X3),X81)))
| ~ c_Finite__Set_Ofinite(X81,X3)
| X82 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X82),X81)) ),
file('<stdin>',cls_Max__mono_0) ).
fof(c_0_370_371,axiom,
! [X81,X82,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(c_Finite__Set_Olinorder__class_OMin(X3),X81)),hAPP(c_Finite__Set_Olinorder__class_OMin(X3),X82)))
| ~ c_Finite__Set_Ofinite(X81,X3)
| X82 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X82),X81)) ),
file('<stdin>',cls_Min__antimono_0) ).
fof(c_0_371_372,axiom,
! [X70,X14,X12,X49,X50,X51,X3] :
( hBOOL(hAPP(hAPP(X49,X12),X70))
| ~ hBOOL(hAPP(hAPP(X49,X12),hAPP(hAPP(X51,X14),X70)))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
file('<stdin>',cls_lower__semilattice_Ole__inf__iff_1) ).
fof(c_0_372_373,axiom,
! [X70,X14,X12,X49,X50,X51,X3] :
( hBOOL(hAPP(hAPP(X49,X12),X14))
| ~ hBOOL(hAPP(hAPP(X49,X12),hAPP(hAPP(X51,X14),X70)))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
file('<stdin>',cls_lower__semilattice_Ole__inf__iff_0) ).
fof(c_0_373_374,axiom,
! [X12,X49,X50,X51,X19,X8,X3] :
( hBOOL(hAPP(hAPP(X49,X12),X8))
| ~ hBOOL(hAPP(hAPP(X49,X12),hAPP(hAPP(X51,X8),X19)))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
file('<stdin>',cls_lower__semilattice_Ole__infE_0) ).
fof(c_0_374_375,axiom,
! [X12,X49,X50,X51,X19,X8,X3] :
( hBOOL(hAPP(hAPP(X49,X12),X19))
| ~ hBOOL(hAPP(hAPP(X49,X12),hAPP(hAPP(X51,X8),X19)))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
file('<stdin>',cls_lower__semilattice_Ole__infE_1) ).
fof(c_0_375_376,axiom,
! [X23,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X23),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X23),X13)) ),
file('<stdin>',cls_UnCI_0) ).
fof(c_0_376_377,axiom,
! [X23,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X23),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X23),X9)) ),
file('<stdin>',cls_UnCI_1) ).
fof(c_0_377_378,axiom,
! [X42,X43,X44,X21,X3] :
( hAPP(c_Map_Omap__add(X44,X43,X3,X21),X42) = hAPP(X44,X42)
| hBOOL(hAPP(hAPP(c_in(X3),X42),c_Map_Odom(X43,X3,X21))) ),
file('<stdin>',cls_map__add__dom__app__simps_I3_J_0) ).
fof(c_0_378_379,axiom,
! [X42,X43,X44,X21,X3] :
( hAPP(c_Map_Omap__add(X44,X43,X3,X21),X42) = hAPP(X43,X42)
| hBOOL(hAPP(hAPP(c_in(X3),X42),c_Map_Odom(X44,X3,X21))) ),
file('<stdin>',cls_map__add__dom__app__simps_I2_J_0) ).
fof(c_0_379_380,axiom,
! [X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X8)),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_not__square__less__zero_0) ).
fof(c_0_380_381,axiom,
! [X17,X12,X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X17))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X9))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X3),X3),X9)))
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_strict__below__fold1__iff_0) ).
fof(c_0_381_382,axiom,
! [X17,X12,X9,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X17))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X3),X3),X9)))
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_below__fold1__iff_0) ).
fof(c_0_382_383,axiom,
! [X55,X42,X56,X21,X3] :
( hAPP(c_Map_Omap__add(X42,X55,X21,X3),X56) != c_Option_Ooption_ONone(X3)
| hAPP(X55,X56) = c_Option_Ooption_ONone(X3) ),
file('<stdin>',cls_map__add__None_0) ).
fof(c_0_383_384,axiom,
! [X55,X42,X56,X21,X3] :
( hAPP(c_Map_Omap__add(X42,X55,X21,X3),X56) != c_Option_Ooption_ONone(X3)
| hAPP(X42,X56) = c_Option_Ooption_ONone(X3) ),
file('<stdin>',cls_map__add__None_1) ).
fof(c_0_384_385,axiom,
! [X19,X8,X3] :
( X19 = X8
| ~ hBOOL(hAPP(hAPP(c_in(X3),X19),hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))))) ),
file('<stdin>',cls_singletonE_0) ).
fof(c_0_385_386,axiom,
! [X24,X23,X19,X8,X3] :
( hAPP(hAPP(c_Set_Oinsert(X3),X8),hAPP(hAPP(c_Set_Oinsert(X3),X19),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X3),X23),hAPP(hAPP(c_Set_Oinsert(X3),X24),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))))
| X19 = X23
| X19 = X24 ),
file('<stdin>',cls_doubleton__eq__iff_3) ).
fof(c_0_386_387,axiom,
! [X24,X23,X19,X8,X3] :
( hAPP(hAPP(c_Set_Oinsert(X3),X8),hAPP(hAPP(c_Set_Oinsert(X3),X19),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X3),X23),hAPP(hAPP(c_Set_Oinsert(X3),X24),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))))
| X8 = X24
| X19 = X24 ),
file('<stdin>',cls_doubleton__eq__iff_2) ).
fof(c_0_387_388,axiom,
! [X24,X23,X19,X8,X3] :
( hAPP(hAPP(c_Set_Oinsert(X3),X8),hAPP(hAPP(c_Set_Oinsert(X3),X19),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X3),X23),hAPP(hAPP(c_Set_Oinsert(X3),X24),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))))
| X19 = X23
| X8 = X23 ),
file('<stdin>',cls_doubleton__eq__iff_1) ).
fof(c_0_388_389,axiom,
! [X24,X23,X19,X8,X3] :
( hAPP(hAPP(c_Set_Oinsert(X3),X8),hAPP(hAPP(c_Set_Oinsert(X3),X19),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X3),X23),hAPP(hAPP(c_Set_Oinsert(X3),X24),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))))
| X8 = X24
| X8 = X23 ),
file('<stdin>',cls_doubleton__eq__iff_0) ).
fof(c_0_389_390,axiom,
! [X57,X38,X21,X3] :
( ~ class_HOL_Oord(X21)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,X21)),X38),X57))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,X21)),X38),X57)) ),
file('<stdin>',cls_less__fun__def_0) ).
fof(c_0_390_391,axiom,
! [X23,X13,X9,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X3),X23),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X23),c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(X3,tc_bool)))) ),
file('<stdin>',cls_DiffE_1) ).
fof(c_0_391_392,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OlessThan(X12,X3)),c_SetInterval_Oord__class_OlessThan(X14,X3))) ),
file('<stdin>',cls_lessThan__subset__iff_0) ).
fof(c_0_392_393,axiom,
! [X13,X9,X3] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X3),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X3),X3),X9)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X3),X3),X13))
| X13 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X13,X3)
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_fold1__Un2_0) ).
fof(c_0_393_394,axiom,
! [X8,X9,X3] :
( hAPP(hAPP(c_Set_Oinsert(X3),X8),c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))) = X9
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X9)) ),
file('<stdin>',cls_insert__Diff_0) ).
fof(c_0_394_395,axiom,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),c_HOL_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19))) ),
file('<stdin>',cls_zero__le__mult__iff_0) ).
fof(c_0_395_396,axiom,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19))) ),
file('<stdin>',cls_zero__le__mult__iff_1) ).
fof(c_0_396_397,axiom,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),c_HOL_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19))) ),
file('<stdin>',cls_zero__le__mult__iff_2) ).
fof(c_0_397_398,axiom,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19))) ),
file('<stdin>',cls_zero__le__mult__iff_3) ).
fof(c_0_398_399,axiom,
! [X14,X12,X49,X50,X51,X3] :
( hBOOL(hAPP(hAPP(X49,hAPP(hAPP(X51,X12),X14)),X14))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
file('<stdin>',cls_lower__semilattice_Oinf__le2_0) ).
fof(c_0_399_400,axiom,
! [X14,X12,X49,X50,X51,X3] :
( hBOOL(hAPP(hAPP(X49,hAPP(hAPP(X51,X12),X14)),X12))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
file('<stdin>',cls_lower__semilattice_Oinf__le1_0) ).
fof(c_0_400_401,axiom,
! [X57,X38,X21,X3] :
( X38 = X57
| ~ c_Map_Omap__le(X57,X38,X3,X21)
| ~ c_Map_Omap__le(X38,X57,X3,X21) ),
file('<stdin>',cls_map__le__antisym_0) ).
fof(c_0_401_402,axiom,
! [X25,X26,X27,X28,X29,X30,X3] :
( c_Hoare__Mirabelle_Otriple_Otriple(X28,X30,X26,X3) != c_Hoare__Mirabelle_Otriple_Otriple(X27,X29,X25,X3)
| X26 = X25 ),
file('<stdin>',cls_triple_Oinject_2) ).
fof(c_0_402_403,axiom,
! [X25,X26,X27,X28,X29,X30,X3] :
( c_Hoare__Mirabelle_Otriple_Otriple(X28,X30,X26,X3) != c_Hoare__Mirabelle_Otriple_Otriple(X27,X29,X25,X3)
| X30 = X29 ),
file('<stdin>',cls_triple_Oinject_1) ).
fof(c_0_403_404,axiom,
! [X25,X26,X27,X28,X29,X30,X3] :
( c_Hoare__Mirabelle_Otriple_Otriple(X28,X30,X26,X3) != c_Hoare__Mirabelle_Otriple_Otriple(X27,X29,X25,X3)
| X28 = X27 ),
file('<stdin>',cls_triple_Oinject_0) ).
fof(c_0_404_405,axiom,
! [X12,X57,X38,X21,X3] :
( ~ class_HOL_Oord(X21)
| hBOOL(hAPP(hAPP(c_lessequals(X21),hAPP(X38,X12)),hAPP(X57,X12)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,X21)),X38),X57)) ),
file('<stdin>',cls_le__funD_0) ).
fof(c_0_405_406,axiom,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
file('<stdin>',cls_mult__pos__pos_0) ).
fof(c_0_406_407,axiom,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
file('<stdin>',cls_add__pos__pos_0) ).
fof(c_0_407_408,axiom,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
file('<stdin>',cls_add__nonneg__nonneg_0) ).
fof(c_0_408_409,axiom,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
file('<stdin>',cls_add__nonneg__pos_0) ).
fof(c_0_409_410,axiom,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
file('<stdin>',cls_add__pos__nonneg_0) ).
fof(c_0_410_411,axiom,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
file('<stdin>',cls_mult__nonneg__nonneg_0) ).
fof(c_0_411_412,axiom,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
file('<stdin>',cls_zero__le__mult__iff_4) ).
fof(c_0_412_413,axiom,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
file('<stdin>',cls_split__mult__pos__le_0) ).
fof(c_0_413_414,axiom,
! [X23,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X23),X9))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X23),c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(X3,tc_bool)))) ),
file('<stdin>',cls_DiffE_0) ).
fof(c_0_414_415,axiom,
! [X12,X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(c_Finite__Set_Olinorder__class_OMin(X3),X9) = X12
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(X9,X12,X3)),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_Min__eqI_0) ).
fof(c_0_415_416,axiom,
! [X12,X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(c_Finite__Set_Olinorder__class_OMax(X3),X9) = X12
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(X9,X12,X3)),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_Max__eqI_0) ).
fof(c_0_416_417,axiom,
! [X13,X9,X3] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),c_HOL_Ominus__class_Ominus(X13,X9,tc_fun(X3,tc_bool))) = X13
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
file('<stdin>',cls_Diff__partition_0) ).
fof(c_0_417_418,axiom,
! [X8,X13,X9,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X8),X13)) = hAPP(hAPP(c_Set_Oinsert(X3),X8),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X9)) ),
file('<stdin>',cls_Int__insert__right_0) ).
fof(c_0_418_419,axiom,
! [X8,X13,X9,X3] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X8),X13),tc_fun(X3,tc_bool)),X3) ),
file('<stdin>',cls_finite__Diff__insert_0) ).
fof(c_0_419_420,axiom,
! [X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),X13))
| X9 = X13
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
file('<stdin>',cls_psubset__eq_2) ).
fof(c_0_420_421,axiom,
! [X13,X9,X3] :
( X9 = X13
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),X13))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
file('<stdin>',cls_subset__iff__psubset__eq_0) ).
fof(c_0_421_422,axiom,
! [X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),X13)) ),
file('<stdin>',cls_psubset__eq_0) ).
fof(c_0_422_423,axiom,
! [X12,X24,X23,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X24)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X24)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X23)) ),
file('<stdin>',cls_class__ringb_Onoteq__reduce_1) ).
fof(c_0_423_424,axiom,
! [X70,X14,X12,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X14)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X70)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X70)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X14)) ),
file('<stdin>',cls_class__ringb_Oadd__mul__solve_1) ).
fof(c_0_424_425,axiom,
! [X24,X23,X19,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X23,X24,X3)) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X8),X23),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X19),X24),X3) ),
file('<stdin>',cls_Int__atLeastAtMost_0) ).
fof(c_0_425_426,axiom,
! [X6,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X6),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
file('<stdin>',cls_subset__iff_0) ).
fof(c_0_426_427,axiom,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X12),X13))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9)) ),
file('<stdin>',cls_set__rev__mp_0) ).
fof(c_0_427_428,axiom,
! [X23,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X23),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X23),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
file('<stdin>',cls_subsetD_0) ).
fof(c_0_428_429,axiom,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X12),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
file('<stdin>',cls_set__mp_0) ).
fof(c_0_429_430,axiom,
! [X23,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X23),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X23),X9))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),X13)) ),
file('<stdin>',cls_psubsetD_0) ).
fof(c_0_430_431,axiom,
! [X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(X9,X3)),c_Finite__Set_Ocard(X13,X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),X13))
| ~ c_Finite__Set_Ofinite(X13,X3) ),
file('<stdin>',cls_psubset__card__mono_0) ).
fof(c_0_431_432,axiom,
! [X83,X84,X86,X85,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X85),X86)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X84),X83)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X85),X84)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X86),X83)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I13_J_0) ).
fof(c_0_432_433,axiom,
! [X83,X84,X86,X85,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X85),X86)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X84),X83)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X85),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X86),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X84),X83))) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I14_J_0) ).
fof(c_0_433_434,axiom,
! [X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X24)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X24)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I20_J_0) ).
fof(c_0_434_435,axiom,
! [X37,X13,X9,X3] :
( hAPP(c_Finite__Set_Ofold1(X37,X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13)) = hAPP(hAPP(X37,hAPP(c_Finite__Set_Ofold1(X37,X3),X9)),hAPP(c_Finite__Set_Ofold1(X37,X3),X13))
| X13 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X13,X3)
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X37,X3) ),
file('<stdin>',cls_ab__semigroup__idem__mult_Ofold1__Un2_0) ).
fof(c_0_435_436,axiom,
! [X12,X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(c_Finite__Set_Olinorder__class_OMin(X3),X9) = X12
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(X9,X12,X3)))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_Min__eqI_1) ).
fof(c_0_436_437,axiom,
! [X12,X9,X3] :
( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3) = c_Finite__Set_Ocard(X9,X3)
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_card__Diff__singleton__if_1) ).
fof(c_0_437_438,axiom,
! [X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X8)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_double__add__less__zero__iff__single__less__zero_1) ).
fof(c_0_438_439,axiom,
! [X8,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X8)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_even__less__0__iff_1) ).
fof(c_0_439_440,axiom,
! [X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X8)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
fof(c_0_440_441,axiom,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ominus__class_Ominus(X8,X19,X3)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
file('<stdin>',cls_le__iff__diff__le__0_0) ).
fof(c_0_441_442,axiom,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ominus__class_Ominus(X8,X19,X3)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19)) ),
file('<stdin>',cls_less__iff__diff__less__0_0) ).
fof(c_0_442_443,axiom,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_mult__neg__neg_0) ).
fof(c_0_443_444,axiom,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_zero__le__mult__iff_5) ).
fof(c_0_444_445,axiom,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_mult__nonpos__nonpos_0) ).
fof(c_0_445_446,axiom,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),c_HOL_Ozero__class_Ozero(X3))) ),
file('<stdin>',cls_split__mult__pos__le_1) ).
fof(c_0_446_447,axiom,
! [X8,X9,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X3),X3),X9)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_fold1__belowI_0) ).
fof(c_0_447_448,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X70),X14))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X70),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X70),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14))) ),
file('<stdin>',cls_le__max__iff__disj_0) ).
fof(c_0_448_449,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),X14))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14))) ),
file('<stdin>',cls_less__max__iff__disj_0) ).
fof(c_0_449_450,axiom,
! [X70,X14,X12,X49,X50,X51,X3] :
( hAPP(hAPP(X51,hAPP(hAPP(X51,X12),X14)),X70) = hAPP(hAPP(X51,X12),hAPP(hAPP(X51,X14),X70))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
file('<stdin>',cls_lower__semilattice_Oinf__assoc_0) ).
fof(c_0_450_451,axiom,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X23)) ),
file('<stdin>',cls_add__increasing2_0) ).
fof(c_0_451_452,axiom,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X23))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
file('<stdin>',cls_add__increasing_0) ).
fof(c_0_452_453,axiom,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X23))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
file('<stdin>',cls_add__strict__increasing_0) ).
fof(c_0_453_454,axiom,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X23))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
file('<stdin>',cls_add__strict__increasing2_0) ).
fof(c_0_454_455,axiom,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13),X12))
| ~ hBOOL(hAPP(X13,X12))
| ~ hBOOL(hAPP(X9,X12)) ),
file('<stdin>',cls_inf1I_0) ).
fof(c_0_455_456,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X23))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
file('<stdin>',cls_pos__add__strict_0) ).
fof(c_0_456_457,axiom,
! [X12,X19,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X8),X19)),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X12)) ),
file('<stdin>',cls_min__max_Ole__infI1_0) ).
fof(c_0_457_458,axiom,
! [X12,X19,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X8),X19)),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X12)) ),
file('<stdin>',cls_min__max_Ole__infI2_0) ).
fof(c_0_458_459,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14)),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X70)) ),
file('<stdin>',cls_min__le__iff__disj_1) ).
fof(c_0_459_460,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14)),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X70)) ),
file('<stdin>',cls_min__le__iff__disj_2) ).
fof(c_0_460_461,axiom,
! [X12,X19,X8,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X8),X19)),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X12)) ),
file('<stdin>',cls_less__infI2_0) ).
fof(c_0_461_462,axiom,
! [X12,X19,X8,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X8),X19)),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X12)) ),
file('<stdin>',cls_less__infI1_0) ).
fof(c_0_462_463,axiom,
! [X12,X19,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X8),X19)),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X12)) ),
file('<stdin>',cls_min__max_Oless__infI1_0) ).
fof(c_0_463_464,axiom,
! [X12,X19,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X8),X19)),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X12)) ),
file('<stdin>',cls_min__max_Oless__infI2_0) ).
fof(c_0_464_465,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14)),X70))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X70)) ),
file('<stdin>',cls_min__less__iff__disj_1) ).
fof(c_0_465_466,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14)),X70))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X70)) ),
file('<stdin>',cls_min__less__iff__disj_2) ).
fof(c_0_466_467,axiom,
! [X12,X19,X8,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X8),X19)),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X12)) ),
file('<stdin>',cls_le__infI1_0) ).
fof(c_0_467_468,axiom,
! [X12,X19,X8,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X8),X19)),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X12)) ),
file('<stdin>',cls_le__infI2_0) ).
fof(c_0_468_469,axiom,
! [X12,X42,X9,X21,X3] :
( hAPP(c_Map_Orestrict__map(X42,X9,X3,X21),X12) = hAPP(X42,X12)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9)) ),
file('<stdin>',cls_restrict__in_0) ).
fof(c_0_469_470,axiom,
! [X23,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X23),c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(X3,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(X3),X23),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X23),X9)) ),
file('<stdin>',cls_DiffI_0) ).
fof(c_0_470_471,axiom,
! [X23,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X23),c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(X3,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(X3),X23),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X23),X9)) ),
file('<stdin>',cls_Diff__iff_2) ).
fof(c_0_471_472,axiom,
! [X15,X6,X16,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X6),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X6),X15),X3) ),
file('<stdin>',cls_derivs__insertD_0) ).
fof(c_0_472_473,axiom,
! [X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X8))) ),
file('<stdin>',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
fof(c_0_473_474,axiom,
! [X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X8))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X8))) ),
file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
fof(c_0_474_475,axiom,
! [X12,X19,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X8)) ),
file('<stdin>',cls_min__max_Ole__infI_0) ).
fof(c_0_475_476,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X14),X70)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
file('<stdin>',cls_min__max_Ole__inf__iff_2) ).
fof(c_0_476_477,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X14),X70)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
file('<stdin>',cls_min__max_Oinf__greatest_0) ).
fof(c_0_477_478,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),X14))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),X12)) ),
file('<stdin>',cls_min__less__iff__conj_2) ).
fof(c_0_478_479,axiom,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X14),X70)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
file('<stdin>',cls_inf__greatest_0) ).
fof(c_0_479_480,axiom,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X14),X70)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
file('<stdin>',cls_le__inf__iff_2) ).
fof(c_0_480_481,axiom,
! [X12,X19,X8,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X8)) ),
file('<stdin>',cls_le__infI_0) ).
fof(c_0_481_482,axiom,
! [X76,X35,X36,X77,X78] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X78,X77)),X36),X76))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X77),X35),X76))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X78),X36),X35)) ),
file('<stdin>',cls_evalc_OSemi_0) ).
fof(c_0_482_483,axiom,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13),X12))
| ~ hBOOL(hAPP(X13,X12)) ),
file('<stdin>',cls_sup1CI_0) ).
fof(c_0_483_484,axiom,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13),X12))
| ~ hBOOL(hAPP(X9,X12)) ),
file('<stdin>',cls_sup1CI_1) ).
fof(c_0_484_485,axiom,
! [X9,X3] :
( X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) ),
file('<stdin>',cls_subset__empty_0) ).
fof(c_0_485_486,axiom,
! [X8,X13,X9,X3] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X8),X13),tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(X3,tc_bool)),X3) ),
file('<stdin>',cls_finite__Diff__insert_1) ).
fof(c_0_486_487,axiom,
! [X70,X14,X12,X49,X50,X51,X3] :
( hAPP(hAPP(X51,X12),hAPP(hAPP(X51,X14),X70)) = hAPP(hAPP(X51,X14),hAPP(hAPP(X51,X12),X70))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
file('<stdin>',cls_lower__semilattice_Oinf__left__commute_0) ).
fof(c_0_487_488,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X14),X70)),X12) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X14),X12)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X70),X12)) ),
file('<stdin>',cls_min__max_Oinf__sup__distrib2_0) ).
fof(c_0_488_489,axiom,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Odistrib__lattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X14),X70)),X12) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X14),X12)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X70),X12)) ),
file('<stdin>',cls_inf__sup__distrib2_0) ).
fof(c_0_489_490,axiom,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add__join(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X8),X19)),X23) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X23)) ),
file('<stdin>',cls_add__sup__distrib__right_0) ).
fof(c_0_490_491,axiom,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X8),X19)),X23) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X23)) ),
file('<stdin>',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0) ).
fof(c_0_491_492,axiom,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X8),X19)),X23) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X23)) ),
file('<stdin>',cls_add__inf__distrib__right_0) ).
fof(c_0_492_493,axiom,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X8),X19)),X23) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X23)) ),
file('<stdin>',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0) ).
fof(c_0_493_494,axiom,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Odistrib__lattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X14),X70)),X12) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X14),X12)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X70),X12)) ),
file('<stdin>',cls_sup__inf__distrib2_0) ).
fof(c_0_494_495,axiom,
! [X70,X14,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14)),X70) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X70)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X14),X70)) ),
file('<stdin>',cls_min__add__distrib__left_0) ).
fof(c_0_495_496,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X14),X70)),X12) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X14),X12)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X70),X12)) ),
file('<stdin>',cls_min__max_Osup__inf__distrib2_0) ).
fof(c_0_496_497,axiom,
! [X70,X14,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14)),X70) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X70)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X14),X70)) ),
file('<stdin>',cls_max__add__distrib__left_0) ).
fof(c_0_497_498,axiom,
! [X42,X19,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X42)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X42)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),X42) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I1_J_0) ).
fof(c_0_498_499,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),X23) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I8_J_0) ).
fof(c_0_499_500,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),X23) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23)) ),
file('<stdin>',cls_comm__semiring__class_Odistrib_0) ).
fof(c_0_500_501,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OlessThan(X12,X3)),c_SetInterval_Oord__class_OlessThan(X14,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
file('<stdin>',cls_lessThan__subset__iff_1) ).
fof(c_0_501_502,axiom,
! [X12,X42,X9,X21,X3] :
( hAPP(c_Map_Orestrict__map(X42,X9,X3,X21),X12) = c_Option_Ooption_ONone(X21)
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9)) ),
file('<stdin>',cls_restrict__out_0) ).
fof(c_0_502_503,axiom,
! [X12,X55,X42,X56,X21,X3] :
( hAPP(X42,X56) != hAPP(c_Option_Ooption_OSome(X3),X12)
| hAPP(X55,X56) != c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X42,X55,X21,X3),X56) = hAPP(c_Option_Ooption_OSome(X3),X12) ),
file('<stdin>',cls_map__add__Some__iff_3) ).
fof(c_0_503_504,axiom,
! [X12,X13,X9,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_disjoint__iff__not__equal_0) ).
fof(c_0_504_505,axiom,
! [X12,X19,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X8),X19))) ),
file('<stdin>',cls_min__max_Ole__infE_0) ).
fof(c_0_505_506,axiom,
! [X12,X19,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X8),X19))) ),
file('<stdin>',cls_min__max_Ole__infE_1) ).
fof(c_0_506_507,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X14),X70))) ),
file('<stdin>',cls_min__max_Ole__inf__iff_0) ).
fof(c_0_507_508,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X14),X70))) ),
file('<stdin>',cls_min__max_Ole__inf__iff_1) ).
fof(c_0_508_509,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14))) ),
file('<stdin>',cls_min__less__iff__conj_0) ).
fof(c_0_509_510,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),X14))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14))) ),
file('<stdin>',cls_min__less__iff__conj_1) ).
fof(c_0_510_511,axiom,
! [X12,X19,X8,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X8),X19))) ),
file('<stdin>',cls_le__infE_0) ).
fof(c_0_511_512,axiom,
! [X12,X19,X8,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X8),X19))) ),
file('<stdin>',cls_le__infE_1) ).
fof(c_0_512_513,axiom,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X14),X70))) ),
file('<stdin>',cls_le__inf__iff_0) ).
fof(c_0_513_514,axiom,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X14),X70))) ),
file('<stdin>',cls_le__inf__iff_1) ).
fof(c_0_514_515,axiom,
! [X13,X9,X3] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13) = X13
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
file('<stdin>',cls_Un__absorb1_0) ).
fof(c_0_515_516,axiom,
! [X13,X9,X3] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13) = X9
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X13),X9)) ),
file('<stdin>',cls_Un__absorb2_0) ).
fof(c_0_516_517,axiom,
! [X13,X9,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13) = X9
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
file('<stdin>',cls_Int__absorb2_0) ).
fof(c_0_517_518,axiom,
! [X13,X9,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13) = X13
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X13),X9)) ),
file('<stdin>',cls_Int__absorb1_0) ).
fof(c_0_518_519,axiom,
! [X8,X80,X13,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X3),X8),X13)),X80) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X13),X80)
| hBOOL(hAPP(hAPP(c_in(X3),X8),X80)) ),
file('<stdin>',cls_Int__insert__left_1) ).
fof(c_0_519_520,axiom,
! [X19,X8,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| X8 = X19
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),hAPP(hAPP(c_Set_Oinsert(X3),X19),X9))) ),
file('<stdin>',cls_insertE_0) ).
fof(c_0_520_521,axiom,
! [X19,X8,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X3),X8),hAPP(hAPP(c_Set_Oinsert(X3),X19),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X8),X19) ),
file('<stdin>',cls_Inf__binary_0) ).
fof(c_0_521_522,axiom,
! [X19,X8,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X3),X8),hAPP(hAPP(c_Set_Oinsert(X3),X19),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X8),X19) ),
file('<stdin>',cls_Sup__binary_0) ).
fof(c_0_522_523,axiom,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X12)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X14),X14)) != c_HOL_Ozero__class_Ozero(X3)
| X14 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_sum__squares__eq__zero__iff_1) ).
fof(c_0_523_524,axiom,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X12)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X14),X14)) != c_HOL_Ozero__class_Ozero(X3)
| X12 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_sum__squares__eq__zero__iff_0) ).
fof(c_0_524_525,axiom,
! [X13,X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(c_Finite__Set_Olinorder__class_OMax(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),hAPP(c_Finite__Set_Olinorder__class_OMax(X3),X9)),hAPP(c_Finite__Set_Olinorder__class_OMax(X3),X13))
| X13 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X13,X3)
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_Max__Un_0) ).
fof(c_0_525_526,axiom,
! [X13,X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(c_Finite__Set_Olinorder__class_OMin(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),hAPP(c_Finite__Set_Olinorder__class_OMin(X3),X9)),hAPP(c_Finite__Set_Olinorder__class_OMin(X3),X13))
| X13 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X13,X3)
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_Min__Un_0) ).
fof(c_0_526_527,axiom,
! [X12,X55,X42,X56,X21,X3] :
( hAPP(X55,X56) != hAPP(c_Option_Ooption_OSome(X3),X12)
| hAPP(c_Map_Omap__add(X42,X55,X21,X3),X56) = hAPP(c_Option_Ooption_OSome(X3),X12) ),
file('<stdin>',cls_map__add__Some__iff_2) ).
fof(c_0_527_528,axiom,
! [X71,X55,X42,X56,X21,X3] :
( hAPP(X55,X56) != hAPP(c_Option_Ooption_OSome(X3),X71)
| hAPP(c_Map_Omap__add(X42,X55,X21,X3),X56) = hAPP(c_Option_Ooption_OSome(X3),X71) ),
file('<stdin>',cls_map__add__find__right_0) ).
fof(c_0_528_529,axiom,
! [X55,X42,X56,X21,X3] :
( hAPP(X42,X56) != c_Option_Ooption_ONone(X3)
| hAPP(X55,X56) != c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X42,X55,X21,X3),X56) = c_Option_Ooption_ONone(X3) ),
file('<stdin>',cls_map__add__None_2) ).
fof(c_0_529_530,axiom,
! [X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))))
| c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),X3) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) ),
file('<stdin>',cls_card__Suc__eq_5) ).
fof(c_0_530_531,axiom,
! [X14,X12,X49,X50,X51,X3] :
( hAPP(hAPP(X51,X12),X14) = X14
| ~ hBOOL(hAPP(hAPP(X49,X14),X12))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
file('<stdin>',cls_lower__semilattice_Oinf__absorb2_0) ).
fof(c_0_531_532,axiom,
! [X14,X12,X49,X50,X51,X3] :
( hAPP(hAPP(X51,X12),X14) = X12
| ~ hBOOL(hAPP(hAPP(X49,X12),X14))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
file('<stdin>',cls_lower__semilattice_Ole__iff__inf_0) ).
fof(c_0_532_533,axiom,
! [X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X8)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
file('<stdin>',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
fof(c_0_533_534,axiom,
! [X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X8)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
file('<stdin>',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
fof(c_0_534_535,axiom,
! [X14,X12,X49,X50,X51,X3] :
( hAPP(hAPP(X51,X12),hAPP(hAPP(X51,X12),X14)) = hAPP(hAPP(X51,X12),X14)
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
file('<stdin>',cls_lower__semilattice_Oinf__left__idem_0) ).
fof(c_0_535_536,axiom,
! [X14,X12,X49,X50,X51,X3] :
( hAPP(hAPP(X51,X12),X14) != X12
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3)
| hBOOL(hAPP(hAPP(X49,X12),X14)) ),
file('<stdin>',cls_lower__semilattice_Ole__iff__inf_1) ).
fof(c_0_536_537,axiom,
! [X70,X14,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14),X70,X3) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),c_HOL_Ominus__class_Ominus(X12,X70,X3)),c_HOL_Ominus__class_Ominus(X14,X70,X3)) ),
file('<stdin>',cls_min__diff__distrib__left_0) ).
fof(c_0_537_538,axiom,
! [X70,X14,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14),X70,X3) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),c_HOL_Ominus__class_Ominus(X12,X70,X3)),c_HOL_Ominus__class_Ominus(X14,X70,X3)) ),
file('<stdin>',cls_max__diff__distrib__left_0) ).
fof(c_0_538_539,axiom,
! [X12,X33,X18,X3] :
( hBOOL(hAPP(X33,X12))
| ~ hBOOL(hAPP(X18,X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X18),X33)) ),
file('<stdin>',cls_predicate1D_0) ).
fof(c_0_539_540,axiom,
! [X12,X33,X18,X3] :
( hBOOL(hAPP(X33,X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X18),X33))
| ~ hBOOL(hAPP(X18,X12)) ),
file('<stdin>',cls_rev__predicate1D_0) ).
fof(c_0_540_541,axiom,
! [X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3)))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3)) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_add__nonneg__eq__0__iff_2) ).
fof(c_0_541_542,axiom,
! [X42,X8,X21,X3] :
( hAPP(X42,X8) != c_Option_Ooption_ONone(X21)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),c_Map_Odom(X42,X3,X21))) ),
file('<stdin>',cls_domIff_0) ).
fof(c_0_542_543,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14)),X12)) ),
file('<stdin>',cls_min__max_Oinf__le1_0) ).
fof(c_0_543_544,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14)),X14)) ),
file('<stdin>',cls_min__max_Oinf__le2_0) ).
fof(c_0_544_545,axiom,
! [X14,X12,X3] :
( ~ class_Lattices_Olattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14)),X12)) ),
file('<stdin>',cls_inf__sup__ord_I1_J_0) ).
fof(c_0_545_546,axiom,
! [X14,X12,X3] :
( ~ class_Lattices_Olattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14)),X14)) ),
file('<stdin>',cls_inf__sup__ord_I2_J_0) ).
fof(c_0_546_547,axiom,
! [X14,X12,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14)),X14)) ),
file('<stdin>',cls_inf__le2_0) ).
fof(c_0_547_548,axiom,
! [X14,X12,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14)),X12)) ),
file('<stdin>',cls_inf__le1_0) ).
fof(c_0_548_549,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X14),X70)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X70)) ),
file('<stdin>',cls_min__max_Oinf__sup__distrib1_0) ).
fof(c_0_549_550,axiom,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Odistrib__lattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X14),X70)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X70)) ),
file('<stdin>',cls_inf__sup__distrib1_0) ).
fof(c_0_550_551,axiom,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add__join(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X19),X23)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)) ),
file('<stdin>',cls_add__sup__distrib__left_0) ).
fof(c_0_551_552,axiom,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X19),X23)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)) ),
file('<stdin>',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0) ).
fof(c_0_552_553,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),X23) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),X19) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(c_0_553_554,axiom,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X19),X23)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)) ),
file('<stdin>',cls_add__inf__distrib__left_0) ).
fof(c_0_554_555,axiom,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X19),X23)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)) ),
file('<stdin>',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0) ).
fof(c_0_555_556,axiom,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Odistrib__lattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X14),X70)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X70)) ),
file('<stdin>',cls_sup__inf__distrib1_0) ).
fof(c_0_556_557,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X14),X70)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X70)) ),
file('<stdin>',cls_min__max_Osup__inf__distrib1_0) ).
fof(c_0_557_558,axiom,
! [X84,X86,X85,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X85),X86)),X84) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X85),X84)),X86) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I16_J_0) ).
fof(c_0_558_559,axiom,
! [X70,X14,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X14),X70)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X14)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X70)) ),
file('<stdin>',cls_class__semiring_Omul__d_0) ).
fof(c_0_559_560,axiom,
! [X13,X9,X3] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13) != X13
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
file('<stdin>',cls_subset__Un__eq_1) ).
fof(c_0_560_561,axiom,
! [X14,X12,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X14) != c_HOL_Ozero__class_Ozero(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X14))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X12))
| X14 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_add__nonneg__eq__0__iff_1) ).
fof(c_0_561_562,axiom,
! [X14,X12,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X14) != c_HOL_Ozero__class_Ozero(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X14))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X12))
| X12 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_add__nonneg__eq__0__iff_0) ).
fof(c_0_562_563,axiom,
! [X38,X9,X3] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X38,X9,X3),c_ATP__Linkup_Osko__Finite__Set__Xfinite__nonempty__imp__fold1Set__1__1(X9,X38,X3)))
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_finite__nonempty__imp__fold1Set_0) ).
fof(c_0_563_564,axiom,
! [X12,X89,X24,X23,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X89),X23)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X89),X24))
| X23 = X24
| X89 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
fof(c_0_564_565,axiom,
! [X12,X38,X9,X21,X3] :
( hAPP(X38,X12) != c_Option_Ooption_ONone(X3)
| c_HOL_Ominus__class_Ominus(c_Map_Odom(X38,X21,X3),hAPP(hAPP(c_Set_Oinsert(X21),X12),X9),tc_fun(X21,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Map_Odom(X38,X21,X3),X9,tc_fun(X21,tc_bool)) ),
file('<stdin>',cls_dom__minus_0) ).
fof(c_0_565_566,axiom,
! [X8,X13,X9,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X8),X13)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13)
| hBOOL(hAPP(hAPP(c_in(X3),X8),X9)) ),
file('<stdin>',cls_Int__insert__right_1) ).
fof(c_0_566_567,axiom,
! [X12,X9,X3] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X3),X12),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)) = X9
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9)) ),
file('<stdin>',cls_Diff__insert__absorb_0) ).
fof(c_0_567_568,axiom,
! [X13,X9,X3] :
( c_Finite__Set_Ofinite(X9,X3)
| ~ c_Finite__Set_Ofinite(X13,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
file('<stdin>',cls_finite__subset_0) ).
fof(c_0_568_569,axiom,
! [X13,X9,X3] :
( c_Finite__Set_Ofinite(X9,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| ~ c_Finite__Set_Ofinite(X13,X3) ),
file('<stdin>',cls_rev__finite__subset_0) ).
fof(c_0_569_570,axiom,
! [X12,X13,X9,X3] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X3),X12),X9),X13,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X3),X12),c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(X3,tc_bool)))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X13)) ),
file('<stdin>',cls_insert__Diff__if_1) ).
fof(c_0_570_571,axiom,
! [X23,X9,X21,X3] :
( c_Set_Ovimage(c_COMBK(X23,X21,X3),X9,X3,X21) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X21),X23),X9)) ),
file('<stdin>',cls_vimage__const_1) ).
fof(c_0_571_572,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X70),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X70),X14)) ),
file('<stdin>',cls_le__max__iff__disj_2) ).
fof(c_0_572_573,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X70),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X70),X12)) ),
file('<stdin>',cls_le__max__iff__disj_1) ).
fof(c_0_573_574,axiom,
! [X12,X19,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X19)) ),
file('<stdin>',cls_min__max_Ole__supI2_0) ).
fof(c_0_574_575,axiom,
! [X12,X19,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X8)) ),
file('<stdin>',cls_min__max_Ole__supI1_0) ).
fof(c_0_575_576,axiom,
! [X12,X19,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X8)) ),
file('<stdin>',cls_min__max_Oless__supI1_0) ).
fof(c_0_576_577,axiom,
! [X12,X19,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X19)) ),
file('<stdin>',cls_min__max_Oless__supI2_0) ).
fof(c_0_577_578,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),X12)) ),
file('<stdin>',cls_less__max__iff__disj_1) ).
fof(c_0_578_579,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),X14)) ),
file('<stdin>',cls_less__max__iff__disj_2) ).
fof(c_0_579_580,axiom,
! [X12,X19,X8,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X19)) ),
file('<stdin>',cls_le__supI2_0) ).
fof(c_0_580_581,axiom,
! [X12,X19,X8,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X8)) ),
file('<stdin>',cls_le__supI1_0) ).
fof(c_0_581_582,axiom,
! [X12,X19,X8,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X8)) ),
file('<stdin>',cls_less__supI1_0) ).
fof(c_0_582_583,axiom,
! [X12,X19,X8,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X19)) ),
file('<stdin>',cls_less__supI2_0) ).
fof(c_0_583_584,axiom,
! [X16,X58,X3] :
( c_Finite__Set_Ofinite(X58,X3)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X58),X16),X3) ),
file('<stdin>',cls_finite__Un_0) ).
fof(c_0_584_585,axiom,
! [X16,X58,X3] :
( c_Finite__Set_Ofinite(X16,X3)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X58),X16),X3) ),
file('<stdin>',cls_finite__Un_1) ).
fof(c_0_585_586,axiom,
! [X12,X38,X9,X21,X3] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X21)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X21)
| hAPP(X38,X12) != c_HOL_Ozero__class_Ozero(X21)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Finite__Set_Ofinite(X9,X3)
| c_Finite__Set_Osetprod(X38,X9,X3,X21) = c_HOL_Ozero__class_Ozero(X21) ),
file('<stdin>',cls_setprod__zero__iff_2) ).
fof(c_0_586_587,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_sum__squares__eq__zero__iff_2) ).
fof(c_0_587_588,axiom,
! [X19,X8,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X8),hAPP(hAPP(c_Set_Oinsert(X3),X19),X9)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X9)) ),
file('<stdin>',cls_insert__iff_2) ).
fof(c_0_588_589,axiom,
! [X19,X8,X13,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X8),hAPP(hAPP(c_Set_Oinsert(X3),X19),X13)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X13)) ),
file('<stdin>',cls_insertCI_0) ).
fof(c_0_589_590,axiom,
! [X12,X38,X9,X21,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X21)
| hAPP(X38,X12) != c_HOL_Ozero__class_Ozero(X21)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Finite__Set_Ofinite(X9,X3)
| c_Finite__Set_Osetprod(X38,X9,X3,X21) = c_HOL_Ozero__class_Ozero(X21) ),
file('<stdin>',cls_setprod__zero_0) ).
fof(c_0_590_591,axiom,
! [X12,X9,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X3),X3),hAPP(hAPP(c_Set_Oinsert(X3),X12),X9)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X3),X3),X9))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Finite__Set_Ofinite(X9,X3)
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_comm__monoid__add_Ofold1__insert_0) ).
fof(c_0_591_592,axiom,
! [X12,X9,X3] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X3),X3),hAPP(hAPP(c_Set_Oinsert(X3),X12),X9)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X3),X3),X9))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Finite__Set_Ofinite(X9,X3)
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_fold1__insert_0) ).
fof(c_0_592_593,axiom,
! [X14,X12,X49,X50,X51,X3] :
( hAPP(hAPP(X51,X12),X14) = hAPP(hAPP(X51,X14),X12)
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
file('<stdin>',cls_lower__semilattice_Oinf__commute_0) ).
fof(c_0_593_594,axiom,
! [X12,X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(c_Finite__Set_Olinorder__class_OMin(X3),X9)),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_Min__le_0) ).
fof(c_0_594_595,axiom,
! [X68,X14,X69,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X12,X14,X3) != c_HOL_Ominus__class_Ominus(X69,X68,X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X68),X69))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12)) ),
file('<stdin>',cls_le__eqI_0) ).
fof(c_0_595_596,axiom,
! [X68,X14,X69,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X12,X14,X3) != c_HOL_Ominus__class_Ominus(X69,X68,X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X68),X69)) ),
file('<stdin>',cls_le__eqI_1) ).
fof(c_0_596_597,axiom,
! [X68,X14,X69,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X12,X14,X3) != c_HOL_Ominus__class_Ominus(X69,X68,X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X69),X68))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14)) ),
file('<stdin>',cls_less__eqI_0) ).
fof(c_0_597_598,axiom,
! [X68,X14,X69,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X12,X14,X3) != c_HOL_Ominus__class_Ominus(X69,X68,X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X69),X68)) ),
file('<stdin>',cls_less__eqI_1) ).
fof(c_0_598_599,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Opreorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X70))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X70))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14)) ),
file('<stdin>',cls_order__less__trans_0) ).
fof(c_0_599_600,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),X14))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X12)) ),
file('<stdin>',cls_xt1_I10_J_0) ).
fof(c_0_600_601,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X70),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X70),X14))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12)) ),
file('<stdin>',cls_xt1_I6_J_0) ).
fof(c_0_601_602,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X70),X14))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X12)) ),
file('<stdin>',cls_xt1_I7_J_0) ).
fof(c_0_602_603,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),X14))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12)) ),
file('<stdin>',cls_xt1_I8_J_0) ).
fof(c_0_603_604,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Opreorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
file('<stdin>',cls_order__trans_0) ).
fof(c_0_604_605,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Opreorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X70))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
file('<stdin>',cls_order__le__less__trans_0) ).
fof(c_0_605_606,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Opreorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X70))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14)) ),
file('<stdin>',cls_order__less__le__trans_0) ).
fof(c_0_606_607,axiom,
! [X12,X37,X9,X3] :
( hAPP(c_Finite__Set_Ofold1(X37,X3),hAPP(hAPP(c_Set_Oinsert(X3),X12),X9)) = hAPP(hAPP(X37,X12),hAPP(c_Finite__Set_Ofold1(X37,X3),X9))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Finite__Set_Ofinite(X9,X3)
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__mult(X37,X3) ),
file('<stdin>',cls_ab__semigroup__mult_Ofold1__insert_0) ).
fof(c_0_607_608,axiom,
! [X12,X49,X50,X51,X3] :
( hAPP(hAPP(X51,X12),X12) = X12
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
file('<stdin>',cls_lower__semilattice_Oinf__idem_0) ).
fof(c_0_608_609,axiom,
! [X57,X38,X21] :
( ~ class_Lattices_Olattice(X21)
| hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,X21)),X38),X57),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X21),hAPP(X38,v_x)),hAPP(X57,v_x)) ),
file('<stdin>',cls_inf__fun__eq_0) ).
fof(c_0_609_610,axiom,
! [X57,X38,X21] :
( ~ class_Lattices_Olattice(X21)
| hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,X21)),X38),X57),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X21),hAPP(X38,v_x)),hAPP(X57,v_x)) ),
file('<stdin>',cls_sup__fun__eq_0) ).
fof(c_0_610_611,axiom,
! [X12,X13,X9,X3] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X3),X12),X9),X13,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X13)) ),
file('<stdin>',cls_insert__Diff1_0) ).
fof(c_0_611_612,axiom,
! [X56,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X3),X56),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),c_SetInterval_Oord__class_OlessThan(X56,X3),tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X3),X56),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) ),
file('<stdin>',cls_single__Diff__lessThan_0) ).
fof(c_0_612_613,axiom,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X8),X19)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X8),X19)) ),
file('<stdin>',cls_add__eq__inf__sup_0) ).
fof(c_0_613_614,axiom,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Olattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14)),X70) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X14),X70)) ),
file('<stdin>',cls_inf__sup__aci_I2_J_0) ).
fof(c_0_614_615,axiom,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14)),X70) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X14),X70)) ),
file('<stdin>',cls_inf__assoc_0) ).
fof(c_0_615_616,axiom,
! [X70,X14,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X14),X70)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X14)),X70) ),
file('<stdin>',cls_class__semiring_Oadd__a_0) ).
fof(c_0_616_617,axiom,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),X23) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X23)) ),
file('<stdin>',cls_comm__monoid__add_Omult__assoc_0) ).
fof(c_0_617_618,axiom,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Oab__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),X23) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X23)) ),
file('<stdin>',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(c_0_618_619,axiom,
! [X24,X23,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X24)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),X24) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I25_J_0) ).
fof(c_0_619_620,axiom,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),X23) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X23)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I21_J_0) ).
fof(c_0_620_621,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14)),X70) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X14),X70)) ),
file('<stdin>',cls_min__max_Oinf__assoc_0) ).
fof(c_0_621_622,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14)),X70) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X14),X70)) ),
file('<stdin>',cls_min__max_Osup__assoc_0) ).
fof(c_0_622_623,axiom,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)),X23) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23)) ),
file('<stdin>',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
fof(c_0_623_624,axiom,
! [X84,X86,X85,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X85),X86)),X84) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X85),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X86),X84)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I17_J_0) ).
fof(c_0_624_625,axiom,
! [X83,X84,X85,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X85),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X84),X83)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X85),X84)),X83) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I18_J_0) ).
fof(c_0_625_626,axiom,
! [X70,X14,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X14),X70)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X14)),X70) ),
file('<stdin>',cls_class__semiring_Omul__a_0) ).
fof(c_0_626_627,axiom,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Olattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14)),X70) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X14),X70)) ),
file('<stdin>',cls_inf__sup__aci_I6_J_0) ).
fof(c_0_627_628,axiom,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14)),X70) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X14),X70)) ),
file('<stdin>',cls_sup__assoc_0) ).
fof(c_0_628_629,axiom,
! [X56,X91,X92] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X92)),X56))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X91),X56))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X92),X91)) ),
file('<stdin>',cls_less__trans__Suc_0) ).
fof(c_0_629_630,axiom,
! [X49,X50,X51,X3] :
( c_OrderedGroup_Oab__semigroup__idem__mult(X51,X3)
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
file('<stdin>',cls_lower__semilattice_Oab__semigroup__idem__mult__inf_0) ).
fof(c_0_630_631,axiom,
! [X14,X12,X9,X3] :
( hBOOL(hAPP(X9,X12))
| X14 = X12
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X14),X9),X12)) ),
file('<stdin>',cls_insert__code_0) ).
fof(c_0_631_632,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Opreorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
file('<stdin>',cls_less__le__not__le_2) ).
fof(c_0_632_633,axiom,
! [X12,X9,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_Complete__Lattice_OInf__class_OInf(X9,X3)),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9)) ),
file('<stdin>',cls_Inf__lower_0) ).
fof(c_0_633_634,axiom,
! [X70,X14,X12,X22,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X14),X70)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X14),X22)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X70) = X22 ),
file('<stdin>',cls_add__cancel__21_0) ).
fof(c_0_634_635,axiom,
! [X12,X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(c_Finite__Set_Olinorder__class_OMax(X3),X9)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_Max__ge_0) ).
fof(c_0_635_636,axiom,
! [X12,X13,X9,X3] :
( hAPP(hAPP(c_Set_Oinsert(X3),X12),X9) != hAPP(hAPP(c_Set_Oinsert(X3),X12),X13)
| hBOOL(hAPP(hAPP(c_in(X3),X12),X13))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| X9 = X13 ),
file('<stdin>',cls_insert__ident_0) ).
fof(c_0_636_637,axiom,
! [X12,X18,X3] :
( ~ hBOOL(hAPP(X18,X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) ),
file('<stdin>',cls_bex__empty_0) ).
fof(c_0_637_638,axiom,
! [X15,X6,X16,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,X15,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X6),X15),X3) ),
file('<stdin>',cls_derivs__insertD_1) ).
fof(c_0_638_639,axiom,
! [X9,X21,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_Finite__Set_Osetsum(c_COMBK(c_HOL_Ozero__class_Ozero(X3),X3,X21),X9,X21,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_setsum__0_0) ).
fof(c_0_639_640,axiom,
! [X42,X19,X8,X21,X3] :
( hAPP(X42,X8) != hAPP(c_Option_Ooption_OSome(X3),X19)
| hBOOL(hAPP(hAPP(c_in(X21),X8),c_Map_Odom(X42,X21,X3))) ),
file('<stdin>',cls_domI_0) ).
fof(c_0_640_641,axiom,
! [X12,X9,X3] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X3),X3),hAPP(hAPP(c_Set_Oinsert(X3),X12),X9)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X3),X3),X9))
| ~ c_Finite__Set_Ofinite(X9,X3)
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_fold1__insert__idem_0) ).
fof(c_0_641_642,axiom,
! [X56,X92,X3] :
( ~ class_HOL_Oord(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X92),X56))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X92),c_SetInterval_Oord__class_OlessThan(X56,X3))) ),
file('<stdin>',cls_lessThan__iff_0) ).
fof(c_0_642_643,axiom,
! [X12,X18,X3] :
( hBOOL(hAPP(X18,X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) ),
file('<stdin>',cls_ball__empty_0) ).
fof(c_0_643_644,axiom,
! [X13,X9,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(X3,tc_bool)) = X9 ),
file('<stdin>',cls_Diff__triv_0) ).
fof(c_0_644_645,axiom,
! [X16,X58,X3] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X58),X16),X3)
| ~ c_Finite__Set_Ofinite(X16,X3)
| ~ c_Finite__Set_Ofinite(X58,X3) ),
file('<stdin>',cls_finite__Un_2) ).
fof(c_0_645_646,axiom,
! [X16,X58,X3] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X58),X16),X3)
| ~ c_Finite__Set_Ofinite(X16,X3)
| ~ c_Finite__Set_Ofinite(X58,X3) ),
file('<stdin>',cls_finite__UnI_0) ).
fof(c_0_646_647,axiom,
! [X14,X12,X49,X50,X3] :
( ~ hBOOL(hAPP(hAPP(X50,X12),X14))
| ~ hBOOL(hAPP(hAPP(X50,X14),X12))
| ~ c_Orderings_Olinorder(X49,X50,X3) ),
file('<stdin>',cls_linorder_Onot__less__iff__gr__or__eq_1) ).
fof(c_0_647_648,axiom,
! [X14,X12,X49,X50,X3] :
( ~ hBOOL(hAPP(hAPP(X50,X12),X14))
| ~ hBOOL(hAPP(hAPP(X49,X14),X12))
| ~ c_Orderings_Olinorder(X49,X50,X3) ),
file('<stdin>',cls_linorder_OleD_0) ).
fof(c_0_648_649,axiom,
! [X14,X12,X49,X50,X3] :
( ~ hBOOL(hAPP(hAPP(X49,X12),X14))
| ~ hBOOL(hAPP(hAPP(X50,X14),X12))
| ~ c_Orderings_Olinorder(X49,X50,X3) ),
file('<stdin>',cls_linorder_Onot__le_1) ).
fof(c_0_649_650,axiom,
! [X12,X49,X50,X3] :
( ~ hBOOL(hAPP(hAPP(X49,X12),X12))
| ~ c_Orderings_Olinorder(X49,X50,X3)
| ~ hBOOL(hAPP(hAPP(X50,X12),X12)) ),
file('<stdin>',cls_linorder_Oantisym__conv2_1) ).
fof(c_0_650_651,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Oorder(X3)
| X12 = X14
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
file('<stdin>',cls_order__eq__iff_2) ).
fof(c_0_651_652,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Oorder(X3)
| X12 = X14
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
file('<stdin>',cls_order__antisym_0) ).
fof(c_0_652_653,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Oorder(X3)
| X12 = X14
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12)) ),
file('<stdin>',cls_order__antisym__conv_0) ).
fof(c_0_653_654,axiom,
! [X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X12)) ),
file('<stdin>',cls_linorder__antisym__conv2_1) ).
fof(c_0_654_655,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12)) ),
file('<stdin>',cls_linorder__not__less_1) ).
fof(c_0_655_656,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X12)) ),
file('<stdin>',cls_linorder__not__le_1) ).
fof(c_0_656_657,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14)) ),
file('<stdin>',cls_less__le__not__le_1) ).
fof(c_0_657_658,axiom,
! [X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X8))) ),
file('<stdin>',cls_zero__le__square_0) ).
fof(c_0_658_659,axiom,
! [X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X8)) ),
file('<stdin>',cls_xt1_I9_J_0) ).
fof(c_0_659_660,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X12)) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_1) ).
fof(c_0_660_661,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14)) ),
file('<stdin>',cls_order__less__asym_0) ).
fof(c_0_661_662,axiom,
! [X19,X8,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X8))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19)) ),
file('<stdin>',cls_order__less__asym_H_0) ).
fof(c_0_662_663,axiom,
! [X42,X8,X21,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X8),c_Map_Odom(X42,X3,X21)))
| hAPP(X42,X8) = c_Option_Ooption_ONone(X21) ),
file('<stdin>',cls_domIff_1) ).
fof(c_0_663_664,axiom,
! [X22,X6,X7,X23] :
( X22 = X6
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X23),X7),X22))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X23),X7),X6)) ),
file('<stdin>',cls_com__det_0) ).
fof(c_0_664_665,axiom,
! [X22,X88,X3] :
( ~ class_Orderings_Oorder(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OlessThan(X88,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X88,X22,X3)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_ivl__disj__int_I4_J_0) ).
fof(c_0_665_666,axiom,
! [X37,X23,X19,X8,X3] :
( hAPP(hAPP(X37,hAPP(hAPP(X37,X8),X19)),X23) = hAPP(hAPP(X37,X8),hAPP(hAPP(X37,X19),X23))
| ~ c_OrderedGroup_Oab__semigroup__mult(X37,X3) ),
file('<stdin>',cls_ab__semigroup__mult_Omult__ac_I1_J_0) ).
fof(c_0_666_667,axiom,
! [X12,X37,X9,X3] :
( hAPP(c_Finite__Set_Ofold1(X37,X3),hAPP(hAPP(c_Set_Oinsert(X3),X12),X9)) = hAPP(hAPP(X37,X12),hAPP(c_Finite__Set_Ofold1(X37,X3),X9))
| ~ c_Finite__Set_Ofinite(X9,X3)
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X37,X3) ),
file('<stdin>',cls_ab__semigroup__idem__mult_Ofold1__insert__idem_0) ).
fof(c_0_667_668,axiom,
! [X56,X92,X3] :
( ~ class_HOL_Oord(X3)
| hBOOL(hAPP(hAPP(c_in(X3),X92),c_SetInterval_Oord__class_OlessThan(X56,X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X92),X56)) ),
file('<stdin>',cls_lessThan__iff_1) ).
fof(c_0_668_669,axiom,
! [X12,X9,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),c_Complete__Lattice_OSup__class_OSup(X9,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9)) ),
file('<stdin>',cls_Sup__upper_0) ).
fof(c_0_669_670,axiom,
! [X49,X50,X38,X8,X21,X3] :
( ~ c_Orderings_Olinorder(X49,X50,X3)
| hAPP(c_Finite__Set_Ofold1(X38,X21),hAPP(hAPP(c_Set_Oinsert(X21),X8),c_Orderings_Obot__class_Obot(tc_fun(X21,tc_bool)))) = X8 ),
file('<stdin>',cls_linorder_OMax__singleton_0) ).
fof(c_0_670_671,axiom,
! [X19,X8,X3] :
( hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) != hAPP(hAPP(c_Set_Oinsert(X3),X19),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))
| X8 = X19 ),
file('<stdin>',cls_singleton__inject_0) ).
fof(c_0_671_672,axiom,
! [X16,X58,X3] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X58),X16),X3)
| ~ c_Finite__Set_Ofinite(X16,X3) ),
file('<stdin>',cls_finite__Int_1) ).
fof(c_0_672_673,axiom,
! [X16,X58,X3] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X58),X16),X3)
| ~ c_Finite__Set_Ofinite(X58,X3) ),
file('<stdin>',cls_finite__Int_0) ).
fof(c_0_673_674,axiom,
! [X70,X14,X12,X38,X21,X3] :
( hAPP(hAPP(X38,X12),hAPP(hAPP(X38,X14),X70)) = hAPP(hAPP(X38,X14),hAPP(hAPP(X38,X12),X70))
| ~ c_Finite__Set_Ofun__left__comm(X38,X3,X21) ),
file('<stdin>',cls_fun__left__comm_Ofun__left__comm_0) ).
fof(c_0_674_675,axiom,
! [X12,X9,X3] :
( c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(X3),X12),X9),X3) = c_Finite__Set_Ocard(X9,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_card__insert__if_0) ).
fof(c_0_675_676,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X14),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14))) ),
file('<stdin>',cls_le__maxI2_0) ).
fof(c_0_676_677,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14))) ),
file('<stdin>',cls_le__maxI1_0) ).
fof(c_0_677_678,axiom,
! [X14,X12,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14))) ),
file('<stdin>',cls_sup__ge1_0) ).
fof(c_0_678_679,axiom,
! [X14,X12,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X14),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14))) ),
file('<stdin>',cls_sup__ge2_0) ).
fof(c_0_679_680,axiom,
! [X14,X12,X3] :
( ~ class_Lattices_Olattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X14),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14))) ),
file('<stdin>',cls_inf__sup__ord_I4_J_0) ).
fof(c_0_680_681,axiom,
! [X14,X12,X3] :
( ~ class_Lattices_Olattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14))) ),
file('<stdin>',cls_inf__sup__ord_I3_J_0) ).
fof(c_0_681_682,axiom,
! [X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_in(X3),hAPP(c_Finite__Set_Olinorder__class_OMax(X3),X9)),X9))
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_Max__in_0) ).
fof(c_0_682_683,axiom,
! [X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_in(X3),hAPP(c_Finite__Set_Olinorder__class_OMin(X3),X9)),X9))
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_Min__in_0) ).
fof(c_0_683_684,axiom,
! [X55,X42] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X42),X55))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X55),c_Suc(X42))) ),
file('<stdin>',cls_not__less__eq_1) ).
fof(c_0_684_685,axiom,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Olattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X14),X70)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X14),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X70)) ),
file('<stdin>',cls_inf__sup__aci_I3_J_0) ).
fof(c_0_685_686,axiom,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X14),X70)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X14),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X70)) ),
file('<stdin>',cls_inf__left__commute_0) ).
fof(c_0_686_687,axiom,
! [X70,X14,X12,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X14),X70)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X70)) ),
file('<stdin>',cls_add__cancel__21_1) ).
fof(c_0_687_688,axiom,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X23)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)) ),
file('<stdin>',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(c_0_688_689,axiom,
! [X24,X23,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X24)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X24)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(c_0_689_690,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X14),X70)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X14),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X70)) ),
file('<stdin>',cls_min__max_Oinf__left__commute_0) ).
fof(c_0_690_691,axiom,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X14),X70)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X14),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X70)) ),
file('<stdin>',cls_min__max_Osup__left__commute_0) ).
fof(c_0_691_692,axiom,
! [X83,X84,X85,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X85),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X84),X83)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X84),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X85),X83)) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I19_J_0) ).
fof(c_0_692_693,axiom,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Olattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X14),X70)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X14),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X70)) ),
file('<stdin>',cls_inf__sup__aci_I7_J_0) ).
fof(c_0_693_694,axiom,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X14),X70)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X14),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X70)) ),
file('<stdin>',cls_sup__left__commute_0) ).
fof(c_0_694_695,axiom,
! [X38,X21,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_Finite__Set_Osetsum(X38,c_Orderings_Obot__class_Obot(tc_fun(X21,tc_bool)),X21,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_setsum__empty_0) ).
fof(c_0_695_696,axiom,
! [X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
file('<stdin>',cls_atLeastatMost__empty__iff2_0) ).
fof(c_0_696_697,axiom,
! [X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
file('<stdin>',cls_atLeastatMost__empty__iff_0) ).
fof(c_0_697_698,axiom,
! [X55,X42] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X42),X55))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X42)),c_Suc(X55))) ),
file('<stdin>',cls_Suc__less__eq_0) ).
fof(c_0_698_699,axiom,
! [X14,X12,X49,X50,X3] :
( X12 = X14
| hBOOL(hAPP(hAPP(X50,X12),X14))
| ~ hBOOL(hAPP(hAPP(X49,X12),X14))
| ~ c_Orderings_Olinorder(X49,X50,X3) ),
file('<stdin>',cls_linorder_Oantisym__conv2_0) ).
fof(c_0_699_700,axiom,
! [X14,X12,X49,X50,X3] :
( X12 = X14
| ~ hBOOL(hAPP(hAPP(X49,X12),X14))
| hBOOL(hAPP(hAPP(X50,X12),X14))
| ~ c_Orderings_Olinorder(X49,X50,X3) ),
file('<stdin>',cls_linorder_Oantisym__conv1_0) ).
fof(c_0_700_701,axiom,
! [X13,X9,X3] :
( c_Finite__Set_Ofinite(X9,X3)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X13,X3) ),
file('<stdin>',cls_finite__Diff2_0) ).
fof(c_0_701_702,axiom,
! [X13,X9,X3] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X13 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__empty_1) ).
fof(c_0_702_703,axiom,
! [X13,X9,X3] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__empty_0) ).
fof(c_0_703_704,axiom,
! [X8,X9,X3] :
( ~ class_Lattices_Olattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X8),hAPP(c_Finite__Set_Olattice__class_OInf__fin(X3),X9)) = X8
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_sup__Inf__absorb_0) ).
fof(c_0_704_705,axiom,
! [X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X8))
| X8 = X19
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X8)) ),
file('<stdin>',cls_xt1_I11_J_0) ).
fof(c_0_705_706,axiom,
! [X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X8))
| X8 = X19 ),
file('<stdin>',cls_xt1_I12_J_0) ).
fof(c_0_706_707,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Oorder(X3)
| X12 = X14
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
file('<stdin>',cls_order__le__less_0) ).
fof(c_0_707_708,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14))
| X12 = X14
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
file('<stdin>',cls_order__less__le_2) ).
fof(c_0_708_709,axiom,
! [X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| X8 = X19
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
file('<stdin>',cls_order__le__neq__trans_0) ).
fof(c_0_709_710,axiom,
! [X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19))
| X8 = X19 ),
file('<stdin>',cls_order__neq__le__trans_0) ).
fof(c_0_710_711,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| X12 = X14
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14)) ),
file('<stdin>',cls_linorder__antisym__conv1_0) ).
fof(c_0_711_712,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| X12 = X14
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
file('<stdin>',cls_linorder__antisym__conv2_0) ).
fof(c_0_712_713,axiom,
! [X14,X12,X9,X3] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X14),X9),X12))
| ~ hBOOL(hAPP(X9,X12)) ),
file('<stdin>',cls_insert__code_2) ).
fof(c_0_713_714,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14)) ),
file('<stdin>',cls_order__le__less_1) ).
fof(c_0_714_715,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Opreorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14)) ),
file('<stdin>',cls_order__less__imp__le_0) ).
fof(c_0_715_716,axiom,
! [X55,X42] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X42),X55))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X42)),X55)) ),
file('<stdin>',cls_Suc__lessD_0) ).
fof(c_0_716_717,axiom,
! [X12,X55] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X12)),c_Suc(X55)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X12),X55)) ),
file('<stdin>',cls_less__Suc__eq__0__disj_3) ).
fof(c_0_717_718,axiom,
! [X55,X42] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X42)),c_Suc(X55)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X42),X55)) ),
file('<stdin>',cls_Suc__mono_0) ).
fof(c_0_718_719,axiom,
! [X12,X9,X3] :
( c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(X3),X12),X9),X3) = c_Suc(c_Finite__Set_Ocard(X9,X3))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_card__insert__if_1) ).
fof(c_0_719_720,axiom,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ominus__class_Ominus(X8,X19,X3)),X19) = X8 ),
file('<stdin>',cls_diff__add__cancel_0) ).
fof(c_0_720_721,axiom,
! [X55,X42,X18] :
( hBOOL(hAPP(hAPP(X18,X55),X42))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X55),X42))
| X42 = X55
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X42),X55)) ),
file('<stdin>',cls_nat__less__cases_0) ).
fof(c_0_721_722,axiom,
! [X38,X9,X21,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_Finite__Set_Osetsum(X38,X9,X21,X3) = c_HOL_Ozero__class_Ozero(X3)
| c_Finite__Set_Ofinite(X9,X21) ),
file('<stdin>',cls_setsum__def_1) ).
fof(c_0_722_723,axiom,
! [X38,X9,X21,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X21)
| c_Finite__Set_Osetsum(X38,X9,X3,X21) = c_HOL_Ozero__class_Ozero(X21)
| c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_setsum__infinite_0) ).
fof(c_0_723_724,axiom,
! [X55,X42] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X42)),X55))
| c_Suc(X42) = X55
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X42),X55)) ),
file('<stdin>',cls_Suc__lessI_0) ).
fof(c_0_724_725,axiom,
! [X13,X9,X21] :
( ~ class_HOL_Ominus(X21)
| hAPP(c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(t_a,X21)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(X9,v_x),hAPP(X13,v_x),X21) ),
file('<stdin>',cls_fun__diff__def_0) ).
fof(c_0_725_726,axiom,
! [X12,X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(c_Finite__Set_Olinorder__class_OMin(X3),hAPP(hAPP(c_Set_Oinsert(X3),X12),X9)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),hAPP(c_Finite__Set_Olinorder__class_OMin(X3),X9))
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_Min__insert_0) ).
fof(c_0_726_727,axiom,
! [X12,X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(c_Finite__Set_Olinorder__class_OMax(X3),hAPP(hAPP(c_Set_Oinsert(X3),X12),X9)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),hAPP(c_Finite__Set_Olinorder__class_OMax(X3),X9))
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_Max__insert_0) ).
fof(c_0_727_728,axiom,
! [X79,X12,X3] :
( X79 = hAPP(c_Option_Ooption_OSome(X3),X12)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),c_Option_Oset(X79,X3))) ),
file('<stdin>',cls_elem__set_0) ).
fof(c_0_728_729,axiom,
! [X14,X12,X38,X21,X3] :
( hAPP(X38,X12) != hAPP(c_Option_Ooption_OSome(X3),X14)
| hAPP(hAPP(c_Set_Oinsert(X21),X12),c_Map_Odom(X38,X21,X3)) = c_Map_Odom(X38,X21,X3) ),
file('<stdin>',cls_insert__dom_0) ).
fof(c_0_729_730,axiom,
! [X55,X42] :
( X42 = X55
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X42),X55))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X42),c_Suc(X55))) ),
file('<stdin>',cls_less__SucE_0) ).
fof(c_0_730_731,axiom,
! [X55,X42] :
( X42 = X55
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X55),c_Suc(X42)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X55),X42)) ),
file('<stdin>',cls_less__antisym_0) ).
fof(c_0_731_732,axiom,
! [X55,X42] :
( X55 = X42
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X55),c_Suc(X42)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X55),X42)) ),
file('<stdin>',cls_not__less__less__Suc__eq_0) ).
fof(c_0_732_733,axiom,
! [X37,X23,X19,X8,X3] :
( hAPP(hAPP(X37,X8),hAPP(hAPP(X37,X19),X23)) = hAPP(hAPP(X37,X19),hAPP(hAPP(X37,X8),X23))
| ~ c_OrderedGroup_Oab__semigroup__mult(X37,X3) ),
file('<stdin>',cls_ab__semigroup__mult_Omult__left__commute_0) ).
fof(c_0_733_734,axiom,
! [X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X8)) ),
file('<stdin>',cls_atLeastatMost__empty_0) ).
fof(c_0_734_735,axiom,
! [X55,X42] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X42),c_Suc(X55)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X42),X55)) ),
file('<stdin>',cls_less__SucI_0) ).
fof(c_0_735_736,axiom,
! [X17,X12,X37,X21,X3] :
( hAPP(hAPP(c_Set_Oinsert(X21),X12),X17) != c_Orderings_Obot__class_Obot(tc_fun(X21,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X21),X12),X17))
| ~ c_OrderedGroup_Oab__semigroup__mult(X37,X3) ),
file('<stdin>',cls_ab__semigroup__mult_Ononempty__iff_2) ).
fof(c_0_736_737,axiom,
! [X14,X12,X49,X50,X3] :
( X12 = X14
| hBOOL(hAPP(hAPP(X50,X14),X12))
| hBOOL(hAPP(hAPP(X50,X12),X14))
| ~ c_Orderings_Olinorder(X49,X50,X3) ),
file('<stdin>',cls_linorder_Onot__less__iff__gr__or__eq_0) ).
fof(c_0_737_738,axiom,
! [X14,X12,X49,X50,X3] :
( hBOOL(hAPP(hAPP(X50,X14),X12))
| hBOOL(hAPP(hAPP(X50,X12),X14))
| X12 = X14
| ~ c_Orderings_Olinorder(X49,X50,X3) ),
file('<stdin>',cls_linorder_OneqE_0) ).
fof(c_0_738_739,axiom,
! [X14,X12,X49,X50,X3] :
( hBOOL(hAPP(hAPP(X50,X14),X12))
| X12 = X14
| hBOOL(hAPP(hAPP(X50,X12),X14))
| ~ c_Orderings_Olinorder(X49,X50,X3) ),
file('<stdin>',cls_linorder_Oless__linear_0) ).
fof(c_0_739_740,axiom,
! [X14,X12,X49,X50,X3] :
( X12 = X14
| hBOOL(hAPP(hAPP(X50,X12),X14))
| hBOOL(hAPP(hAPP(X50,X14),X12))
| ~ c_Orderings_Olinorder(X49,X50,X3) ),
file('<stdin>',cls_linorder_Oantisym__conv3_0) ).
fof(c_0_740_741,axiom,
! [X14,X12,X49,X50,X3] :
( hBOOL(hAPP(hAPP(X49,X14),X12))
| hBOOL(hAPP(hAPP(X50,X12),X14))
| ~ c_Orderings_Olinorder(X49,X50,X3) ),
file('<stdin>',cls_linorder_OleI_0) ).
fof(c_0_741_742,axiom,
! [X14,X12,X49,X50,X3] :
( hBOOL(hAPP(hAPP(X49,X14),X12))
| hBOOL(hAPP(hAPP(X49,X12),X14))
| ~ c_Orderings_Olinorder(X49,X50,X3) ),
file('<stdin>',cls_linorder_Olinear_0) ).
fof(c_0_742_743,axiom,
! [X14,X12,X49,X50,X3] :
( hBOOL(hAPP(hAPP(X50,X14),X12))
| hBOOL(hAPP(hAPP(X49,X12),X14))
| ~ c_Orderings_Olinorder(X49,X50,X3) ),
file('<stdin>',cls_linorder_Onot__le_0) ).
fof(c_0_743_744,axiom,
! [X14,X12,X49,X50,X3] :
( hBOOL(hAPP(hAPP(X50,X12),X14))
| hBOOL(hAPP(hAPP(X49,X14),X12))
| ~ c_Orderings_Olinorder(X49,X50,X3) ),
file('<stdin>',cls_linorder_Onot__leE_0) ).
fof(c_0_744_745,axiom,
! [X12,X49,X50,X3] :
( hBOOL(hAPP(hAPP(X50,X12),X12))
| ~ c_Orderings_Olinorder(X49,X50,X3)
| hBOOL(hAPP(hAPP(X49,X12),X12)) ),
file('<stdin>',cls_linorder_Oantisym__conv1_1) ).
fof(c_0_745_746,axiom,
! [X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(c_Finite__Set_Olinorder__class_OMin(X3),hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) = X8 ),
file('<stdin>',cls_Min__singleton_0) ).
fof(c_0_746_747,axiom,
! [X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(c_Finite__Set_Olinorder__class_OMax(X3),hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) = X8 ),
file('<stdin>',cls_Max__singleton_0) ).
fof(c_0_747_748,axiom,
! [X17,X12,X3] :
( hAPP(hAPP(c_Set_Oinsert(X3),X12),X17) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X17)) ),
file('<stdin>',cls_comm__monoid__add_Ononempty__iff_2) ).
fof(c_0_748_749,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14) = X14
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
file('<stdin>',cls_min__max_Ole__iff__sup_0) ).
fof(c_0_749_750,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14) = X12
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12)) ),
file('<stdin>',cls_min__max_Osup__absorb1_0) ).
fof(c_0_750_751,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14) = X12
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
file('<stdin>',cls_min__max_Ole__iff__inf_0) ).
fof(c_0_751_752,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14) = X14
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12)) ),
file('<stdin>',cls_min__max_Oinf__absorb2_0) ).
fof(c_0_752_753,axiom,
! [X14,X12,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14) = X12
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12)) ),
file('<stdin>',cls_sup__absorb1_0) ).
fof(c_0_753_754,axiom,
! [X14,X12,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14) = X14
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
file('<stdin>',cls_le__iff__sup_0) ).
fof(c_0_754_755,axiom,
! [X14,X12,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14) = X12
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
file('<stdin>',cls_le__iff__inf_0) ).
fof(c_0_755_756,axiom,
! [X14,X12,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14) = X14
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12)) ),
file('<stdin>',cls_inf__absorb2_0) ).
fof(c_0_756_757,axiom,
! [X8,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),X3) = X8 ),
file('<stdin>',cls_Sup__singleton_0) ).
fof(c_0_757_758,axiom,
! [X8,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),X3) = X8 ),
file('<stdin>',cls_Inf__singleton_0) ).
fof(c_0_758_759,axiom,
! [X15,X31,X16,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,X15,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,X31,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X31,X15,X3) ),
file('<stdin>',cls_cut_0) ).
fof(c_0_759_760,axiom,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14))
| X12 = X14 ),
file('<stdin>',cls_linorder__neqE__ordered__idom_0) ).
fof(c_0_760_761,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| X12 = X14
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14)) ),
file('<stdin>',cls_not__less__iff__gr__or__eq_0) ).
fof(c_0_761_762,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14))
| X12 = X14 ),
file('<stdin>',cls_linorder__neqE_0) ).
fof(c_0_762_763,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X12))
| X12 = X14
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14)) ),
file('<stdin>',cls_linorder__less__linear_0) ).
fof(c_0_763_764,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| X12 = X14
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X12)) ),
file('<stdin>',cls_linorder__antisym__conv3_0) ).
fof(c_0_764_765,axiom,
! [X8,X9,X3] :
( hAPP(hAPP(c_Set_Oinsert(X3),X8),X9) = X9
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X9)) ),
file('<stdin>',cls_insert__absorb_0) ).
fof(c_0_765_766,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12)) ),
file('<stdin>',cls_not__leE_0) ).
fof(c_0_766_767,axiom,
! [X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X12))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X12)) ),
file('<stdin>',cls_linorder__antisym__conv1_1) ).
fof(c_0_767_768,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14)) ),
file('<stdin>',cls_linorder__not__less_0) ).
fof(c_0_768_769,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X12))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
file('<stdin>',cls_linorder__not__le_0) ).
fof(c_0_769_770,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
file('<stdin>',cls_linorder__linear_0) ).
fof(c_0_770_771,axiom,
! [X12,X49,X50,X3] :
( ~ hBOOL(hAPP(hAPP(X50,X12),X12))
| ~ c_Orderings_Olinorder(X49,X50,X3) ),
file('<stdin>',cls_linorder_Oneq__iff_1) ).
fof(c_0_771_772,axiom,
! [X12,X49,X50,X3] :
( ~ c_Orderings_Olinorder(X49,X50,X3)
| ~ hBOOL(hAPP(hAPP(X50,X12),X12)) ),
file('<stdin>',cls_linorder_Onot__less__iff__gr__or__eq_2) ).
fof(c_0_772_773,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14) ),
file('<stdin>',cls_min__max_Oinf__left__idem_0) ).
fof(c_0_773_774,axiom,
! [X14,X12,X3] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X14)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X14) ),
file('<stdin>',cls_mult__left__idem_0) ).
fof(c_0_774_775,axiom,
! [X14,X12,X3] :
( ~ class_Lattices_Olattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14) ),
file('<stdin>',cls_inf__sup__aci_I4_J_0) ).
fof(c_0_775_776,axiom,
! [X14,X12,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14) ),
file('<stdin>',cls_inf__left__idem_0) ).
fof(c_0_776_777,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14) ),
file('<stdin>',cls_min__max_Osup__left__idem_0) ).
fof(c_0_777_778,axiom,
! [X14,X12,X3] :
( ~ class_Lattices_Olattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14) ),
file('<stdin>',cls_inf__sup__aci_I8_J_0) ).
fof(c_0_778_779,axiom,
! [X14,X12,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14) ),
file('<stdin>',cls_sup__left__idem_0) ).
fof(c_0_779_780,axiom,
! [X13,X9,X3] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_Finite__Set_Ofinite(X13,X3) ),
file('<stdin>',cls_finite__Diff2_1) ).
fof(c_0_780_781,axiom,
! [X8,X9,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X3),X8),X9),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X8),c_Complete__Lattice_OSup__class_OSup(X9,X3)) ),
file('<stdin>',cls_Sup__insert_0) ).
fof(c_0_781_782,axiom,
! [X8,X9,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X3),X8),X9),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X8),c_Complete__Lattice_OInf__class_OInf(X9,X3)) ),
file('<stdin>',cls_Inf__insert_0) ).
fof(c_0_782_783,axiom,
! [X12] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X12),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X12),c_Suc(X12))) ),
file('<stdin>',cls_not__less__less__Suc__eq_1) ).
fof(c_0_783_784,axiom,
! [X55,X42] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X55),c_Suc(X42)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X42),X55)) ),
file('<stdin>',cls_not__less__eq_0) ).
fof(c_0_784_785,axiom,
! [X12,X20,X3] :
( hBOOL(hAPP(X20,X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X20)) ),
file('<stdin>',cls_mem__def_0) ).
fof(c_0_785_786,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14) != X14
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
file('<stdin>',cls_min__max_Ole__iff__sup_1) ).
fof(c_0_786_787,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14) != X12
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
file('<stdin>',cls_min__max_Ole__iff__inf_1) ).
fof(c_0_787_788,axiom,
! [X14,X12,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14) != X14
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
file('<stdin>',cls_le__iff__sup_1) ).
fof(c_0_788_789,axiom,
! [X14,X12,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14) != X12
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
file('<stdin>',cls_le__iff__inf_1) ).
fof(c_0_789_790,axiom,
! [X8,X9,X3] :
( c_Finite__Set_Ofinite(X9,X3)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X3),X8),X9),X3) ),
file('<stdin>',cls_finite__insert_0) ).
fof(c_0_790_791,axiom,
! [X38,X21,X3] :
( c_Map_Odom(X38,X3,X21) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X38 = c_COMBK(c_Option_Ooption_ONone(X21),tc_Option_Ooption(X21),X3) ),
file('<stdin>',cls_dom__eq__empty__conv_0) ).
fof(c_0_791_792,axiom,
! [X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
file('<stdin>',cls_atLeastatMost__empty__iff2_1) ).
fof(c_0_792_793,axiom,
! [X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
file('<stdin>',cls_atLeastatMost__empty__iff_1) ).
fof(c_0_793_794,axiom,
! [X55,X42] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X55),X42))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X42),X55))
| X42 = X55 ),
file('<stdin>',cls_nat__neq__iff_0) ).
fof(c_0_794_795,axiom,
! [X14,X12] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X14),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X12),X14))
| X12 = X14 ),
file('<stdin>',cls_linorder__neqE__nat_0) ).
fof(c_0_795_796,axiom,
! [X13,X9,X3] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_finite__Diff_0) ).
fof(c_0_796_797,axiom,
! [X70,X14,X12,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X14) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X70)
| X14 = X70 ),
file('<stdin>',cls_class__ringb_Oadd__cancel_0) ).
fof(c_0_797_798,axiom,
! [X68,X69,X12,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X12,X12,X3) != c_HOL_Ominus__class_Ominus(X69,X68,X3)
| X69 = X68 ),
file('<stdin>',cls_eq__eqI_0) ).
fof(c_0_798_799,axiom,
! [X14,X17,X12,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X17,X14,X3) != c_HOL_Ominus__class_Ominus(X12,X12,X3)
| X17 = X14 ),
file('<stdin>',cls_eq__eqI_1) ).
fof(c_0_799_800,axiom,
! [X14,X12,X37,X3] :
( hAPP(hAPP(X37,X12),hAPP(hAPP(X37,X12),X14)) = hAPP(hAPP(X37,X12),X14)
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X37,X3) ),
file('<stdin>',cls_ab__semigroup__idem__mult_Omult__left__idem_0) ).
fof(c_0_800_801,axiom,
! [X12,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X12)) ),
file('<stdin>',cls_order__less__le_1) ).
fof(c_0_801_802,axiom,
! [X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X12)) ),
file('<stdin>',cls_linorder__neq__iff_1) ).
fof(c_0_802_803,axiom,
! [X12,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X12)) ),
file('<stdin>',cls_order__less__irrefl_0) ).
fof(c_0_803_804,axiom,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)
| X19 = X23 ),
file('<stdin>',cls_add__imp__eq_0) ).
fof(c_0_804_805,axiom,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)
| X19 = X23 ),
file('<stdin>',cls_add__left__cancel_0) ).
fof(c_0_805_806,axiom,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X8) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X8)
| X19 = X23 ),
file('<stdin>',cls_add__right__cancel_0) ).
fof(c_0_806_807,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_807_808,axiom,
! [X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X8,X8,X3) = hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) ),
file('<stdin>',cls_atLeastAtMost__singleton_0) ).
fof(c_0_808_809,axiom,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19),X19,X3) = X8 ),
file('<stdin>',cls_add__diff__cancel_0) ).
fof(c_0_809_810,axiom,
! [X14,X12,X3] :
( ~ class_Lattices_Olattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14)) = X12 ),
file('<stdin>',cls_sup__inf__absorb_0) ).
fof(c_0_810_811,axiom,
! [X14,X12,X3] :
( ~ class_Lattices_Olattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14)) = X12 ),
file('<stdin>',cls_inf__sup__absorb_0) ).
fof(c_0_811_812,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14)) = X12 ),
file('<stdin>',cls_min__max_Oinf__sup__absorb_0) ).
fof(c_0_812_813,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14)) = X12 ),
file('<stdin>',cls_min__max_Osup__inf__absorb_0) ).
fof(c_0_813_814,axiom,
! [X12,X20,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X12),X20))
| ~ hBOOL(hAPP(X20,X12)) ),
file('<stdin>',cls_mem__def_1) ).
fof(c_0_814_815,axiom,
! [X6,X7] :
( X6 = X7
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X7),X6)) ),
file('<stdin>',cls_evalc__elim__cases_I1_J_0) ).
fof(c_0_815_816,axiom,
! [X15,X16,X3] :
( c_Hoare__Mirabelle_Ohoare__valids(X16,X15,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,X15,X3) ),
file('<stdin>',cls_hoare__sound_0) ).
fof(c_0_816_817,axiom,
! [X8,X9,X3] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X3),X8),X9),X3)
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_finite__insert_1) ).
fof(c_0_817_818,axiom,
! [X12,X3] :
( ~ class_Orderings_Obot(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_Orderings_Obot__class_Obot(X3)),X12)) ),
file('<stdin>',cls_bot__least_0) ).
fof(c_0_818_819,axiom,
! [X12,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X12)) ),
file('<stdin>',cls_order__eq__iff_0) ).
fof(c_0_819_820,axiom,
! [X12,X3] :
( ~ class_Orderings_Opreorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X12)) ),
file('<stdin>',cls_order__eq__refl_0) ).
fof(c_0_820_821,axiom,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X14) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X14),X12) ),
file('<stdin>',cls_class__semiring_Oadd__c_0) ).
fof(c_0_821_822,axiom,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X8) ),
file('<stdin>',cls_comm__monoid__add_Omult__commute_0) ).
fof(c_0_822_823,axiom,
! [X23,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X8) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(c_0_823_824,axiom,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X14) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X14),X12) ),
file('<stdin>',cls_class__semiring_Omul__c_0) ).
fof(c_0_824_825,axiom,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X8) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I7_J_0) ).
fof(c_0_825_826,axiom,
! [X14,X12,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X14),X12) ),
file('<stdin>',cls_inf__commute_0) ).
fof(c_0_826_827,axiom,
! [X14,X12,X3] :
( ~ class_Lattices_Olattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X14),X12) ),
file('<stdin>',cls_inf__sup__aci_I1_J_0) ).
fof(c_0_827_828,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X14),X12) ),
file('<stdin>',cls_min__max_Oinf__commute_0) ).
fof(c_0_828_829,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X14),X12) ),
file('<stdin>',cls_min__max_Osup__commute_0) ).
fof(c_0_829_830,axiom,
! [X14,X12,X3] :
( ~ class_Lattices_Olattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X14),X12) ),
file('<stdin>',cls_inf__sup__aci_I5_J_0) ).
fof(c_0_830_831,axiom,
! [X14,X12,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X14),X12) ),
file('<stdin>',cls_sup__commute_0) ).
fof(c_0_831_832,axiom,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X12,X14,X3) != c_HOL_Ozero__class_Ozero(X3)
| X12 = X14 ),
file('<stdin>',cls_class__ringb_Osubr0__iff_0) ).
fof(c_0_832_833,axiom,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19) != c_HOL_Ozero__class_Ozero(X3)
| X19 = c_HOL_Ozero__class_Ozero(X3)
| X8 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult__eq__0__iff_0) ).
fof(c_0_833_834,axiom,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19) != c_HOL_Ozero__class_Ozero(X3)
| X19 = c_HOL_Ozero__class_Ozero(X3)
| X8 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_no__zero__divisors_0) ).
fof(c_0_834_835,axiom,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19) != c_HOL_Ozero__class_Ozero(X3)
| X8 = c_HOL_Ozero__class_Ozero(X3)
| X19 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_no__zero__divirors__neq0_0) ).
fof(c_0_835_836,axiom,
! [X12,X8,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X12 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X8)
| X8 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_class__ringb_Oadd__r0__iff_0) ).
fof(c_0_836_837,axiom,
! [X37,X19,X8,X3] :
( hAPP(hAPP(X37,X8),X19) = hAPP(hAPP(X37,X19),X8)
| ~ c_OrderedGroup_Oab__semigroup__mult(X37,X3) ),
file('<stdin>',cls_ab__semigroup__mult_Omult__commute_0) ).
fof(c_0_837_838,axiom,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X8,X19,X3) != c_HOL_Ozero__class_Ozero(X3)
| X8 = X19 ),
file('<stdin>',cls_right__minus__eq_0) ).
fof(c_0_838_839,axiom,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X8,X19,X3) != c_HOL_Ozero__class_Ozero(X3)
| X8 = X19 ),
file('<stdin>',cls_eq__iff__diff__eq__0_1) ).
fof(c_0_839_840,axiom,
! [X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X8) != c_HOL_Ozero__class_Ozero(X3)
| X8 = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_double__eq__0__iff_0) ).
fof(c_0_840_841,axiom,
! [X13,X9,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X9),X13) != c_Orderings_Obot__class_Obot(X3)
| X13 = c_Orderings_Obot__class_Obot(X3) ),
file('<stdin>',cls_sup__eq__bot__eq2_0) ).
fof(c_0_841_842,axiom,
! [X13,X9,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X9),X13) != c_Orderings_Obot__class_Obot(X3)
| X9 = c_Orderings_Obot__class_Obot(X3) ),
file('<stdin>',cls_sup__eq__bot__eq1_0) ).
fof(c_0_842_843,axiom,
! [X9,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| hAPP(c_Finite__Set_Olattice__class_OInf__fin(X3),X9) = c_Complete__Lattice_OInf__class_OInf(X9,X3)
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_Inf__fin__Inf_0) ).
fof(c_0_843_844,axiom,
! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3)) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_double__eq__0__iff_1) ).
fof(c_0_844_845,axiom,
! [X37,X3] :
( c_Finite__Set_Ofun__left__comm(X37,X3,X3)
| ~ c_OrderedGroup_Oab__semigroup__mult(X37,X3) ),
file('<stdin>',cls_ab__semigroup__mult_Ofun__left__comm_0) ).
fof(c_0_845_846,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_846_847,axiom,
! [X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X8) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I9_J_0) ).
fof(c_0_847_848,axiom,
! [X19,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X19) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult__eq__0__iff_1) ).
fof(c_0_848_849,axiom,
! [X8,X3] :
( ~ class_Ring__and__Field_Omult__zero(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X8) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult__zero__left_0) ).
fof(c_0_849_850,axiom,
! [X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X12) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_class__semiring_Omul__0_0) ).
fof(c_0_850_851,axiom,
! [X12,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),c_Orderings_Obot__class_Obot(X3)),X12) = c_Orderings_Obot__class_Obot(X3) ),
file('<stdin>',cls_inf__bot__left_0) ).
fof(c_0_851_852,axiom,
! [X21] :
( ~ class_Orderings_Obot(X21)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X21)),v_x) = c_Orderings_Obot__class_Obot(X21) ),
file('<stdin>',cls_bot__fun__eq_0) ).
fof(c_0_852_853,axiom,
! [X12,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X12 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),c_HOL_Ozero__class_Ozero(X3)) ),
file('<stdin>',cls_class__ringb_Oadd__r0__iff_1) ).
fof(c_0_853_854,axiom,
! [X12,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X12,X12,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_class__ringb_Osubr0__iff_1) ).
fof(c_0_854_855,axiom,
! [X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X12) = X12 ),
file('<stdin>',cls_class__semiring_Oadd__0_0) ).
fof(c_0_855_856,axiom,
! [X8,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X8) = X8 ),
file('<stdin>',cls_comm__monoid__add_Omult__1_0) ).
fof(c_0_856_857,axiom,
! [X8,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X8) = X8 ),
file('<stdin>',cls_add__0__left_0) ).
fof(c_0_857_858,axiom,
! [X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X8) = X8 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(c_0_858_859,axiom,
! [X12,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),c_Orderings_Obot__class_Obot(X3)),X12) = X12 ),
file('<stdin>',cls_sup__bot__left_0) ).
fof(c_0_859_860,axiom,
! [X79,X3] :
( c_Option_Oset(X79,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X79 = c_Option_Ooption_ONone(X3) ),
file('<stdin>',cls_set__empty__eq_0) ).
fof(c_0_860_861,axiom,
! [X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),c_HOL_Ozero__class_Ozero(X3)) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(c_0_861_862,axiom,
! [X8,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),c_HOL_Ozero__class_Ozero(X3)) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult__eq__0__iff_2) ).
fof(c_0_862_863,axiom,
! [X8,X3] :
( ~ class_Ring__and__Field_Omult__zero(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),c_HOL_Ozero__class_Ozero(X3)) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_mult__zero__right_0) ).
fof(c_0_863_864,axiom,
! [X12,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),c_Orderings_Obot__class_Obot(X3)) = c_Orderings_Obot__class_Obot(X3) ),
file('<stdin>',cls_inf__bot__right_0) ).
fof(c_0_864_865,axiom,
! [X8,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X8,c_HOL_Ozero__class_Ozero(X3),X3) = X8 ),
file('<stdin>',cls_diff__0__right_0) ).
fof(c_0_865_866,axiom,
! [X3] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
| c_Finite__Set_Ofun__left__comm(c_HOL_Otimes__class_Otimes(X3),X3,X3) ),
file('<stdin>',cls_fun__left__comm_0) ).
fof(c_0_866_867,axiom,
! [X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_Finite__Set_Ofun__left__comm(c_HOL_Oplus__class_Oplus(X3),X3,X3) ),
file('<stdin>',cls_comm__monoid__add_Ofun__left__comm_0) ).
fof(c_0_867_868,axiom,
! [X8,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),c_HOL_Ozero__class_Ozero(X3)) = X8 ),
file('<stdin>',cls_comm__monoid__add_Omult__1__right_0) ).
fof(c_0_868_869,axiom,
! [X8,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),c_HOL_Ozero__class_Ozero(X3)) = X8 ),
file('<stdin>',cls_monoid__add__class_Oadd__0__right_0) ).
fof(c_0_869_870,axiom,
! [X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),c_HOL_Ozero__class_Ozero(X3)) = X8 ),
file('<stdin>',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(c_0_870_871,axiom,
! [X12,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),c_Orderings_Obot__class_Obot(X3)) = X12 ),
file('<stdin>',cls_sup__bot__right_0) ).
fof(c_0_871_872,axiom,
! [X8,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X8,X8,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_diff__self_0) ).
fof(c_0_872_873,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X12,X12,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_right__minus__eq_1) ).
fof(c_0_873_874,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X12,X12,X3) = c_HOL_Ozero__class_Ozero(X3) ),
file('<stdin>',cls_eq__iff__diff__eq__0_0) ).
fof(c_0_874_875,axiom,
! [X59,X8,X3] :
( hAPP(c_Option_Ooption_OSome(X3),X8) != hAPP(c_Option_Ooption_OSome(X3),X59)
| X8 = X59 ),
file('<stdin>',cls_option_Oinject_0) ).
fof(c_0_875_876,axiom,
! [X12,X37,X3] :
( hAPP(hAPP(X37,X12),X12) = X12
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X37,X3) ),
file('<stdin>',cls_ab__semigroup__idem__mult_Omult__idem_0) ).
fof(c_0_876_877,axiom,
! [X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X12) = X12 ),
file('<stdin>',cls_min__max_Oinf__idem_0) ).
fof(c_0_877_878,axiom,
! [X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X12) = X12 ),
file('<stdin>',cls_min__max_Osup__idem_0) ).
fof(c_0_878_879,axiom,
! [X12,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X12) = X12 ),
file('<stdin>',cls_inf__idem_0) ).
fof(c_0_879_880,axiom,
! [X12,X3] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X12) = X12 ),
file('<stdin>',cls_mult__idem_0) ).
fof(c_0_880_881,axiom,
! [X12,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X12) = X12 ),
file('<stdin>',cls_sup__idem_0) ).
fof(c_0_881_882,axiom,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_SetInterval_Oord__class_OlessThan(X12,X3) != c_SetInterval_Oord__class_OlessThan(X14,X3)
| X12 = X14 ),
file('<stdin>',cls_lessThan__eq__iff_0) ).
fof(c_0_882_883,axiom,
! [X64,X65,X66,X67] :
( c_Com_Ocom_OSemi(X67,X65) != c_Com_Ocom_OSemi(X66,X64)
| X65 = X64 ),
file('<stdin>',cls_com_Osimps_I3_J_1) ).
fof(c_0_883_884,axiom,
! [X64,X65,X66,X67] :
( c_Com_Ocom_OSemi(X67,X65) != c_Com_Ocom_OSemi(X66,X64)
| X67 = X66 ),
file('<stdin>',cls_com_Osimps_I3_J_0) ).
fof(c_0_884_885,axiom,
! [X5,X4] :
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X5,X4))
| ~ class_Finite__Set_Ofinite_Ofinite(X4)
| ~ class_Finite__Set_Ofinite_Ofinite(X5) ),
file('<stdin>',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
fof(c_0_885_886,axiom,
! [X5,X4] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X5,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ),
file('<stdin>',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
fof(c_0_886_887,axiom,
! [X5,X4] :
( class_Lattices_Oupper__semilattice(tc_fun(X5,X4))
| ~ class_Lattices_Olattice(X4) ),
file('<stdin>',clsarity_fun__Lattices_Oupper__semilattice) ).
fof(c_0_887_888,axiom,
! [X5,X4] :
( class_Lattices_Olower__semilattice(tc_fun(X5,X4))
| ~ class_Lattices_Olattice(X4) ),
file('<stdin>',clsarity_fun__Lattices_Olower__semilattice) ).
fof(c_0_888_889,axiom,
! [X5,X4] :
( class_Lattices_Odistrib__lattice(tc_fun(X5,X4))
| ~ class_Lattices_Odistrib__lattice(X4) ),
file('<stdin>',clsarity_fun__Lattices_Odistrib__lattice) ).
fof(c_0_889_890,axiom,
! [X5,X4] :
( class_Lattices_Obounded__lattice(tc_fun(X5,X4))
| ~ class_Lattices_Obounded__lattice(X4) ),
file('<stdin>',clsarity_fun__Lattices_Obounded__lattice) ).
fof(c_0_890_891,axiom,
! [X5,X4] :
( class_Orderings_Opreorder(tc_fun(X5,X4))
| ~ class_Orderings_Opreorder(X4) ),
file('<stdin>',clsarity_fun__Orderings_Opreorder) ).
fof(c_0_891_892,axiom,
! [X5,X4] :
( class_Lattices_Olattice(tc_fun(X5,X4))
| ~ class_Lattices_Olattice(X4) ),
file('<stdin>',clsarity_fun__Lattices_Olattice) ).
fof(c_0_892_893,axiom,
! [X5,X4] :
( class_Orderings_Oorder(tc_fun(X5,X4))
| ~ class_Orderings_Oorder(X4) ),
file('<stdin>',clsarity_fun__Orderings_Oorder) ).
fof(c_0_893_894,axiom,
! [X5,X4] :
( class_Orderings_Obot(tc_fun(X5,X4))
| ~ class_Orderings_Obot(X4) ),
file('<stdin>',clsarity_fun__Orderings_Obot) ).
fof(c_0_894_895,axiom,
! [X5,X4] :
( class_HOL_Ominus(tc_fun(X5,X4))
| ~ class_HOL_Ominus(X4) ),
file('<stdin>',clsarity_fun__HOL_Ominus) ).
fof(c_0_895_896,axiom,
! [X5,X4] :
( class_HOL_Oord(tc_fun(X5,X4))
| ~ class_HOL_Oord(X4) ),
file('<stdin>',clsarity_fun__HOL_Oord) ).
fof(c_0_896_897,axiom,
! [X3] :
( ~ class_Lattices_Olattice(X3)
| c_Finite__Set_Olattice__class_OInf__fin(X3) = c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X3),X3) ),
file('<stdin>',cls_Inf__fin__def__raw_0) ).
fof(c_0_897_898,axiom,
! [X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Finite__Set_Olinorder__class_OMax(X3) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(X3),X3) ),
file('<stdin>',cls_Max__def__raw_0) ).
fof(c_0_898_899,axiom,
! [X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Finite__Set_Olinorder__class_OMin(X3) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X3),X3) ),
file('<stdin>',cls_linorder__class_OMin__def__raw_0) ).
fof(c_0_899_900,axiom,
! [X3] :
( ~ class_Orderings_Olinorder(X3)
| c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omin(X3),X3) ),
file('<stdin>',cls_ab__semigroup__idem__mult__min_0) ).
fof(c_0_900_901,axiom,
! [X3] :
( ~ class_Orderings_Olinorder(X3)
| c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omax(X3),X3) ),
file('<stdin>',cls_ab__semigroup__idem__mult__max_0) ).
fof(c_0_901_902,axiom,
! [X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Oupper__semilattice__class_Osup(X3),X3) ),
file('<stdin>',cls_ab__semigroup__idem__mult__sup_0) ).
fof(c_0_902_903,axiom,
! [X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Olower__semilattice__class_Oinf(X3),X3) ),
file('<stdin>',cls_ab__semigroup__idem__mult__inf_0) ).
fof(c_0_903_904,axiom,
! [X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X3) = c_Orderings_Oord__class_Omax(X3) ),
file('<stdin>',cls_sup__max_0) ).
fof(c_0_904_905,axiom,
! [X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X3) = c_Orderings_Oord__class_Omin(X3) ),
file('<stdin>',cls_inf__min_0) ).
fof(c_0_905_906,axiom,
! [X9,X3] :
( ~ class_Finite__Set_Ofinite_Ofinite(X3)
| c_Finite__Set_Ofinite(X9,X3) ),
file('<stdin>',cls_finite_0) ).
fof(c_0_906_907,axiom,
! [X4] :
( class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(X4))
| ~ class_Finite__Set_Ofinite_Ofinite(X4) ),
file('<stdin>',clsarity_Option__Ooption__Finite__Set_Ofinite_Ofinite) ).
fof(c_0_907_908,axiom,
! [X14,X12] :
( c_Suc(X12) != c_Suc(X14)
| X12 = X14 ),
file('<stdin>',cls_Suc__inject_0) ).
fof(c_0_908_909,axiom,
! [X96,X97] :
( c_Suc(X97) != c_Suc(X96)
| X97 = X96 ),
file('<stdin>',cls_nat_Oinject_0) ).
fof(c_0_909_910,axiom,
! [X10,X11] :
( c_Com_Ocom_OBODY(X11) != c_Com_Ocom_OBODY(X10)
| X11 = X10 ),
file('<stdin>',cls_com_Osimps_I6_J_0) ).
fof(c_0_910_911,plain,
! [X47,X48,X49,X50,X51,X52,X53,X54,X3] :
( c_Complete__Lattice_Ocomplete__lattice(X53,X54,c_COMBC(X49,X3,X3,tc_bool),c_COMBC(X50,X3,X3,tc_bool),X48,X51,X47,X52,X3)
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_911_912,plain,
! [X47,X48,X49,X50,X51,X52,X53,X54,X13,X9,X3] :
( hAPP(hAPP(X48,X13),hAPP(X53,X9)) = c_Finite__Set_Ofold(X48,X13,X9,X3,X3)
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_912_913,plain,
! [X47,X48,X49,X50,X51,X52,X53,X54,X13,X9,X3] :
( hAPP(hAPP(X51,X13),hAPP(X54,X9)) = c_Finite__Set_Ofold(X51,X13,X9,X3,X3)
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_913_914,plain,
! [X47,X48,X49,X50,X51,X52,X53,X54,X9,X3] :
( hAPP(X53,X9) = c_Finite__Set_Ofold(X48,X52,X9,X3,X3)
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_914_915,plain,
! [X47,X48,X49,X50,X51,X52,X53,X54,X9,X3] :
( hAPP(X54,X9) = c_Finite__Set_Ofold(X51,X47,X9,X3,X3)
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_915_916,plain,
! [X47,X48,X49,X50,X51,X52,X19,X8,X53,X54,X3] :
( hAPP(X54,hAPP(hAPP(c_Set_Oinsert(X3),X8),hAPP(hAPP(c_Set_Oinsert(X3),X19),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))))) = hAPP(hAPP(X51,X8),X19)
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_916_917,plain,
! [X47,X48,X49,X50,X51,X52,X19,X8,X53,X54,X3] :
( hAPP(X53,hAPP(hAPP(c_Set_Oinsert(X3),X8),hAPP(hAPP(c_Set_Oinsert(X3),X19),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))))) = hAPP(hAPP(X48,X8),X19)
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_917_918,plain,
! [X12,X47,X48,X49,X50,X51,X52,X53,X54,X9,X3] :
( hBOOL(hAPP(hAPP(X49,hAPP(X54,X9)),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_918_919,plain,
! [X12,X47,X48,X49,X50,X51,X52,X53,X54,X9,X3] :
( hBOOL(hAPP(hAPP(X49,X12),hAPP(X53,X9)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_919_920,plain,
! [X47,X48,X49,X50,X51,X52,X8,X53,X54,X3] :
( hAPP(X54,hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) = X8
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_920_921,plain,
! [X47,X48,X49,X50,X51,X52,X8,X53,X54,X3] :
( hAPP(X53,hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) = X8
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_921_922,plain,
! [X47,X48,X49,X50,X51,X52,X8,X53,X54,X9,X3] :
( hAPP(X54,hAPP(hAPP(c_Set_Oinsert(X3),X8),X9)) = hAPP(hAPP(X51,X8),hAPP(X54,X9))
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_922_923,plain,
! [X47,X48,X49,X50,X51,X52,X8,X53,X54,X9,X3] :
( hAPP(X53,hAPP(hAPP(c_Set_Oinsert(X3),X8),X9)) = hAPP(hAPP(X48,X8),hAPP(X53,X9))
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_923_924,plain,
! [X47,X48,X49,X50,X51,X52,X53,X54,X9,X3] :
( c_Finite__Set_Olattice_OSup__fin(X48,X9,X3) = hAPP(X53,X9)
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_924_925,plain,
! [X47,X48,X49,X50,X51,X52,X53,X54,X9,X3] :
( c_Finite__Set_Olattice_OInf__fin(X51,X9,X3) = hAPP(X54,X9)
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_925_926,plain,
! [X47,X48,X49,X50,X51,X52,X53,X54,X3] :
( hAPP(X53,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) = X52
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_926_927,plain,
! [X47,X48,X49,X50,X51,X52,X53,X54,X3] :
( hAPP(X54,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) = X47
| ~ c_Complete__Lattice_Ocomplete__lattice(X54,X53,X49,X50,X51,X48,X52,X47,X3) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_927_928,plain,
! [X23,X33,X18,X16] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X16,X18,X33,X23)),tc_fun(tc_Com_Ostate,tc_bool),t_a),X23,c_COMBK(hAPP(X33,v_sko__Hoare__Mirabelle__Xescape__1(X16,X18,X33,X23)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_928_929,plain,
! [X57,X13,X9,X21,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X21)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X21),X57,c_HOL_Ozero__class_Ozero(X21),X9,X21,X3)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X21),X57,c_HOL_Ozero__class_Ozero(X21),X13,X21,X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X21),X57,c_HOL_Ozero__class_Ozero(X21),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13),X21,X3)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X21),X57,c_HOL_Ozero__class_Ozero(X21),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13),X21,X3))
| ~ c_Finite__Set_Ofinite(X13,X3)
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_929_930,plain,
! [X17,X12,X23,X33,X18,X16] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X33,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X16,X18,X33,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X16,X18,X33,X23,X12,X17)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X12,X23,X17,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_930_931,plain,
! [X17,X12,X23,X33,X18,X16] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X33,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X16,X18,X33,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X16,X18,X33,X23,X12,X17)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X12,X23,X17,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_931_932,plain,
! [X57,X13,X9,X21,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X21)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X13,X3)
| ~ c_Finite__Set_Ofinite(X9,X3)
| c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X21),X57,c_HOL_Ozero__class_Ozero(X21),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13),X21,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X21),X57,c_HOL_Ozero__class_Ozero(X21),X9,X21,X3)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X21),X57,c_HOL_Ozero__class_Ozero(X21),X13,X21,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_932_933,plain,
! [X17,X12,X23,X41,X33,X18,X16] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X17,X41),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X16,X18,X33,X23,X12,X17)))
| ~ hBOOL(hAPP(hAPP(X12,X41),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X16,X18,X33,X23)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X12,X23,X17,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_933_934,plain,
! [X17,X12,X23,X41,X33,X18,X16] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X17,X41),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X16,X18,X33,X23,X12,X17)))
| ~ hBOOL(hAPP(hAPP(X12,X41),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X16,X18,X33,X23)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X12,X23,X17,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_934_935,plain,
! [X70,X57,X8,X9,X21,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X21)
| c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X21),X57,X70,hAPP(hAPP(c_Set_Oinsert(X3),X8),X9),X21,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),hAPP(X57,X8)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X21),X57,X70,X9,X21,X3))
| hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_935_936,plain,
! [X70,X57,X8,X9,X21,X3] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X21)
| c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(X21),X57,X70,hAPP(hAPP(c_Set_Oinsert(X3),X8),X9),X21,X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X21),hAPP(X57,X8)),c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(X21),X57,X70,X9,X21,X3))
| hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_936_937,plain,
! [X70,X37,X57,X8,X9,X21,X3] :
( c_Finite__Set_Ofold__image(X37,X57,X70,hAPP(hAPP(c_Set_Oinsert(X21),X8),X9),X3,X21) = hAPP(hAPP(X37,hAPP(X57,X8)),c_Finite__Set_Ofold__image(X37,X57,X70,X9,X3,X21))
| hBOOL(hAPP(hAPP(c_in(X21),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X21)
| ~ c_OrderedGroup_Oab__semigroup__mult(X37,X3) ),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_937_938,plain,
! [X12,X19,X8,X9,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X3),X8,hAPP(hAPP(c_Set_Oinsert(X3),X19),c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))),X3,X3),X12))
| hBOOL(hAPP(hAPP(c_in(X3),X19),X9))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X3),X19,X9,X3,X3),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_938_939,plain,
! [X12,X19,X8,X9,X3] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X3),X8,hAPP(hAPP(c_Set_Oinsert(X3),X19),c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))),X3,X3),X12))
| hBOOL(hAPP(hAPP(c_in(X3),X19),X9))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X3),X19,X9,X3,X3),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_939_940,plain,
! [X12,X37,X19,X8,X9,X3] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X37,X8,hAPP(hAPP(c_Set_Oinsert(X3),X19),c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))),X3,X3),X12))
| hBOOL(hAPP(hAPP(c_in(X3),X19),X9))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X37,X19,X9,X3,X3),X12))
| ~ c_OrderedGroup_Oab__semigroup__mult(X37,X3) ),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_940_941,plain,
! [X90,X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X90)),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X90)),X24)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X8,X19,X3)),X90)),X23)),X24)) ),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_941_942,plain,
! [X90,X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X90)),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X90)),X24)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X8,X19,X3)),X90)),X23)),X24)) ),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_942_943,plain,
! [X70,X14,X12,X38,X9,X21,X3] :
( c_Nitpick_Ofold__graph_H(X38,X70,X9,hAPP(hAPP(X38,X12),X14),X3,X21)
| ~ c_Nitpick_Ofold__graph_H(X38,X70,c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X14,X3,X21)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_943_944,plain,
! [X70,X14,X12,X38,X9,X21,X3] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X38,X70,X9,X3,X21),hAPP(hAPP(X38,X12),X14)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X38,X70,c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3,X21),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_944_945,plain,
! [X70,X14,X12,X38,X9,X21,X3] :
( X14 = X12
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X38,X70,X9,X3,X21),X14))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X38,X70,X9,X3,X21),X12))
| ~ c_Finite__Set_Ofun__left__comm(X38,X3,X21) ),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_945_946,plain,
! [X14,X12,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X3),X14),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3)),c_Finite__Set_Ocard(X9,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X14),X9))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_946_947,plain,
! [X90,X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X8,X19,X3)),X90)),X23)),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X90)),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X90)),X24))) ),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_947_948,plain,
! [X90,X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X8,X19,X3)),X90)),X23)),X24))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X90)),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X90)),X24))) ),
inference(fof_simplification,[status(thm)],[c_0_37]) ).
fof(c_0_948_949,plain,
! [X70,X14,X19,X9,X3] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X3),X70,hAPP(hAPP(c_Set_Oinsert(X3),X19),X9),X3,X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X70),X14)))
| hBOOL(hAPP(hAPP(c_in(X3),X19),X9))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X3),X19,X9,X3,X3),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_949_950,plain,
! [X70,X14,X19,X9,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X3),X70,hAPP(hAPP(c_Set_Oinsert(X3),X19),X9),X3,X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X70),X14)))
| hBOOL(hAPP(hAPP(c_in(X3),X19),X9))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X3),X19,X9,X3,X3),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_950_951,plain,
! [X70,X17,X12,X38,X9,X87,X3] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X38,X70,X9,X87,X3),X17))
| hBOOL(hAPP(hAPP(c_in(X87),X12),X9))
| ~ c_Finite__Set_Ofun__left__comm(X38,X87,X3)
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X38,X70,hAPP(hAPP(c_Set_Oinsert(X87),X12),X9),X87,X3),hAPP(hAPP(X38,X12),X17))) ),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_951_952,plain,
! [X70,X14,X37,X19,X9,X3] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X37,X70,hAPP(hAPP(c_Set_Oinsert(X3),X19),X9),X3,X3),hAPP(hAPP(X37,X70),X14)))
| hBOOL(hAPP(hAPP(c_in(X3),X19),X9))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X37,X19,X9,X3,X3),X14))
| ~ c_OrderedGroup_Oab__semigroup__mult(X37,X3) ),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_952_953,plain,
! [X70,X14,X12,X38,X9,X21,X3] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X38,X70,hAPP(hAPP(c_Set_Oinsert(X3),X12),X9),X3,X21),hAPP(hAPP(X38,X12),X14)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X38,X70,X9,X3,X21),X14))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_953_954,plain,
! [X20,X34,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X34),X20))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X34)),hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X20))) ),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_954_955,plain,
! [X23,X39,X33,X40,X18,X16] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X33,v_sko__Hoare__Mirabelle__Xconseq12__1(X18,X40,X33,X39)),v_sko__Hoare__Mirabelle__Xconseq12__3(X18,X40,X33,X39)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X40,X23,X39,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_955_956,plain,
! [X49,X50,X51,X19,X8,X9,X3] :
( hBOOL(hAPP(hAPP(X49,c_Finite__Set_Ofold(X51,X19,X9,X3,X3)),hAPP(hAPP(X51,X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_956_957,plain,
! [X90,X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X90)),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X90)),X24)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X19,X8,X3)),X90)),X24))) ),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_957_958,plain,
! [X90,X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X90)),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X90)),X24)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X19,X8,X3)),X90)),X24))) ),
inference(fof_simplification,[status(thm)],[c_0_47]) ).
fof(c_0_958_959,plain,
! [X32,X33,X18,X16,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),c_Hoare__Mirabelle_Otriple_Otriple(X18,c_Com_Ocom_OBODY(X32),X33,X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),c_Hoare__Mirabelle_Otriple_Otriple(X18,c_Com_Ocom_OBODY(X32),X33,X3)),X16),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),c_Hoare__Mirabelle_Otriple_Otriple(X18,c_Option_Othe(hAPP(c_Com_Obody,X32),tc_Com_Ocom),X33,X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))),X3) ),
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_959_960,plain,
! [X19,X8,X9,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X3),X19,X9,X3,X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_960_961,plain,
! [X24,X23,X34,X33,X18,X16,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),c_Hoare__Mirabelle_Otriple_Otriple(X18,c_Com_Ocom_OSemi(X23,X24),X34,X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),c_Hoare__Mirabelle_Otriple_Otriple(X33,X24,X34,X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))),X3) ),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_961_962,plain,
! [X90,X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X19,X8,X3)),X90)),X24)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X90)),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X90)),X24))) ),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_962_963,plain,
! [X90,X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X19,X8,X3)),X90)),X24)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X90)),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X90)),X24))) ),
inference(fof_simplification,[status(thm)],[c_0_52]) ).
fof(c_0_963_964,plain,
! [X70,X14,X38,X9,X21,X3] :
( c_Finite__Set_Ofold(X38,X70,X9,X3,X21) = X14
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X38,X70,X9,X3,X21),X14))
| ~ c_Finite__Set_Ofun__left__comm(X38,X3,X21) ),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_964_965,plain,
! [X23,X39,X33,X40,X18,X16] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X18,v_sko__Hoare__Mirabelle__Xconseq12__1(X18,X40,X33,X39)),v_sko__Hoare__Mirabelle__Xconseq12__2(X18,X40,X33,X39)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X40,X23,X39,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_965_966,plain,
! [X23,X41,X39,X33,X40,X18,X16] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X39,X41),v_sko__Hoare__Mirabelle__Xconseq12__3(X18,X40,X33,X39)))
| ~ hBOOL(hAPP(hAPP(X40,X41),v_sko__Hoare__Mirabelle__Xconseq12__2(X18,X40,X33,X39)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X40,X23,X39,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_966_967,plain,
! [X12,X38,X8,X9,X3] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X38,hAPP(hAPP(c_Set_Oinsert(X3),X8),X9),X3),X12))
| hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X38,X8,X9,X3,X3),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_967_968,plain,
! [X70,X12,X38,X21,X3] :
( X12 = X70
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X38,X70,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X21),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_57]) ).
fof(c_0_968_969,plain,
! [X93,X94,X8,X18] :
( ~ hBOOL(hAPP(X18,c_Option_Ooption_Ooption__case(X94,X93,hAPP(c_Option_Ooption_OSome(t_b),X8),t_a,t_b)))
| hBOOL(hAPP(X18,hAPP(X93,X8))) ),
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_969_970,plain,
! [X17,X93,X94,X18] :
( ~ hBOOL(hAPP(X18,c_Option_Ooption_Ooption__case(X94,X93,hAPP(c_Option_Ooption_OSome(t_b),X17),t_a,t_b)))
| hBOOL(hAPP(X18,hAPP(X93,X17))) ),
inference(fof_simplification,[status(thm)],[c_0_59]) ).
fof(c_0_970_971,plain,
! [X93,X94,X18] :
( ~ hBOOL(hAPP(X18,c_Option_Ooption_Ooption__case(X94,X93,c_Option_Ooption_ONone(t_b),t_a,t_b)))
| hBOOL(hAPP(X18,X94)) ),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_971_972,plain,
! [X70,X12,X38,X9,X21,X3] :
( c_Finite__Set_Ofinite(X9,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X38,X70,X9,X3,X21),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_972_973,plain,
! [X20,X34,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X34)),hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X20)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X34),X20)) ),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_973_974,axiom,
! [X42,X24,X23,X19,X8,X21,X3] :
( c_Fun_Ofun__upd(c_Fun_Ofun__upd(X42,X8,X19,X3,X21),X23,X24,X3,X21) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X42,X23,X24,X3,X21),X8,X19,X3,X21)
| X8 = X23 ),
c_0_63 ).
fof(c_0_974_975,plain,
! [X32,X33,X18,X16,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),c_Hoare__Mirabelle_Otriple_Otriple(X18,c_Com_Ocom_OBODY(X32),X33,X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),c_Hoare__Mirabelle_Otriple_Otriple(X18,c_Option_Othe(hAPP(c_Com_Obody,X32),tc_Com_Ocom),X33,X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))),X3) ),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_975_976,plain,
! [X23,X33,X18] :
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,tc_Com_Ostate)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,tc_Com_Ostate)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(X23)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))),tc_Com_Ostate) ),
inference(fof_simplification,[status(thm)],[c_0_65]) ).
fof(c_0_976_977,plain,
! [X38,X9,X21,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_Finite__Set_Osetsum(X38,X9,X21,X3) = c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X3),X38,c_HOL_Ozero__class_Ozero(X3),X9,X3,X21)
| ~ c_Finite__Set_Ofinite(X9,X21) ),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_977_978,plain,
! [X23,X33,X40,X18,X16] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X40,v_sko__Hoare__Mirabelle__Xconseq1__1(X18,X40)),v_sko__Hoare__Mirabelle__Xconseq1__2(X18,X40)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X40,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_978_979,plain,
! [X23,X39,X33,X18,X16] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X33,v_sko__Hoare__Mirabelle__Xconseq2__1(X33,X39)),v_sko__Hoare__Mirabelle__Xconseq2__2(X33,X39)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X39,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_68]) ).
fof(c_0_979_980,plain,
! [X23,X39,X33,X18,X16] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X39,v_sko__Hoare__Mirabelle__Xconseq2__1(X33,X39)),v_sko__Hoare__Mirabelle__Xconseq2__2(X33,X39)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X39,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_69]) ).
fof(c_0_980,plain,
! [X23,X33,X40,X18,X16] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X18,v_sko__Hoare__Mirabelle__Xconseq1__1(X18,X40)),v_sko__Hoare__Mirabelle__Xconseq1__2(X18,X40)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X40,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_70]) ).
fof(c_0_981,plain,
! [X14,X12,X42,X72,X21,X3] :
( c_Map_Orestrict__map(c_Fun_Ofun__upd(X42,X12,X14,X3,tc_Option_Ooption(X21)),X72,X3,X21) = c_Fun_Ofun__upd(c_Map_Orestrict__map(X42,c_HOL_Ominus__class_Ominus(X72,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3,X21),X12,X14,X3,tc_Option_Ooption(X21))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X72)) ),
inference(fof_simplification,[status(thm)],[c_0_71]) ).
fof(c_0_982,plain,
! [X14,X12,X61,X62,X21,X3] :
( c_Map_Omap__le(c_Fun_Ofun__upd(X62,X12,c_Option_Ooption_ONone(X21),X3,tc_Option_Ooption(X21)),c_Fun_Ofun__upd(X61,X12,hAPP(c_Option_Ooption_OSome(X21),X14),X3,tc_Option_Ooption(X21)),X3,X21)
| ~ c_Map_Omap__le(X62,X61,X3,X21) ),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_983,plain,
! [X19,X8,X9,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X8),X19)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X3),X19,X9,X3,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_73]) ).
fof(c_0_984,plain,
! [X57,X38,X19,X8,X21,X3] :
( c_Map_Omap__le(c_Fun_Ofun__upd(X38,X8,X19,X3,tc_Option_Ooption(X21)),c_Fun_Ofun__upd(X57,X8,X19,X3,tc_Option_Ooption(X21)),X3,X21)
| ~ c_Map_Omap__le(X38,X57,X3,X21) ),
inference(fof_simplification,[status(thm)],[c_0_74]) ).
fof(c_0_985,plain,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))),X13))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_75]) ).
fof(c_0_986,axiom,
! [X23,X33,X18,X16] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X18,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X16,X18,X33,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X16,X18,X33,X23))) ),
c_0_76 ).
fof(c_0_987,axiom,
! [X23,X33,X18,X16] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X18,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X16,X18,X33,X23)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X16,X18,X33,X23))) ),
c_0_77 ).
fof(c_0_988,axiom,
! [X23,X33,X18,X16] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X18,X23,X33,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X18,v_sko__Hoare__Mirabelle__Xescape__1(X16,X18,X33,X23)),v_sko__Hoare__Mirabelle__Xescape__2(X16,X18,X33,X23))) ),
c_0_78 ).
fof(c_0_989,plain,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))),X13))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_79]) ).
fof(c_0_990,plain,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))),X13))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_80]) ).
fof(c_0_991,plain,
! [X70,X12,X38,X9,X21,X3] :
( c_Finite__Set_Ofold(X38,X70,X9,X3,X21) = hAPP(hAPP(X38,X12),c_Finite__Set_Ofold(X38,X70,c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3,X21))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_Finite__Set_Ofun__left__comm(X38,X3,X21) ),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_992,plain,
! [X70,X12,X38,X9,X21,X3] :
( c_Finite__Set_Ofold(X38,X70,hAPP(hAPP(c_Set_Oinsert(X3),X12),X9),X3,X21) = hAPP(hAPP(X38,X12),c_Finite__Set_Ofold(X38,X70,c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3,X21))
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_Finite__Set_Ofun__left__comm(X38,X3,X21) ),
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_993,plain,
! [X12,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3)),c_Finite__Set_Ocard(X9,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_994,plain,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_995,plain,
! [X57,X13,X9,X21,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X21)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),c_Finite__Set_Osetsum(X57,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13),X3,X21)),c_Finite__Set_Osetsum(X57,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13),X3,X21)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),c_Finite__Set_Osetsum(X57,X9,X3,X21)),c_Finite__Set_Osetsum(X57,X13,X3,X21))
| ~ c_Finite__Set_Ofinite(X13,X3)
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_996,plain,
! [X57,X13,X9,X21,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X21)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X21),c_Finite__Set_Osetprod(X57,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13),X3,X21)),c_Finite__Set_Osetprod(X57,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13),X3,X21)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X21),c_Finite__Set_Osetprod(X57,X9,X3,X21)),c_Finite__Set_Osetprod(X57,X13,X3,X21))
| ~ c_Finite__Set_Ofinite(X13,X3)
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_86]) ).
fof(c_0_997,axiom,
! [X73,X42,X74,X75,X21,X3] :
( c_Map_Omap__add(c_Fun_Ofun__upd(X75,X42,hAPP(c_Option_Ooption_OSome(X21),X73),X3,tc_Option_Ooption(X21)),X74,X3,X21) = c_Fun_Ofun__upd(c_Map_Omap__add(X75,X74,X3,X21),X42,hAPP(c_Option_Ooption_OSome(X21),X73),X3,tc_Option_Ooption(X21))
| hBOOL(hAPP(hAPP(c_in(X3),X42),c_Map_Odom(X74,X3,X21))) ),
c_0_87 ).
fof(c_0_998,plain,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))),X13))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_88]) ).
fof(c_0_999,plain,
! [X38,X13,X9,X21,X3] :
( ~ class_OrderedGroup_Oab__group__add(X21)
| c_Finite__Set_Osetsum(X38,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13),X3,X21) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),c_Finite__Set_Osetsum(X38,X9,X3,X21)),c_Finite__Set_Osetsum(X38,X13,X3,X21)),c_Finite__Set_Osetsum(X38,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13),X3,X21),X21)
| ~ c_Finite__Set_Ofinite(X13,X3)
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_1000,plain,
! [X37,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),hAPP(c_Finite__Set_Ofold1(X37,X3),X9)),X9))
| ~ hBOOL(hAPP(hAPP(c_in(X3),hAPP(hAPP(X37,c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1(X37,X3)),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2(X37,X3))),hAPP(hAPP(c_Set_Oinsert(X3),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1(X37,X3)),hAPP(hAPP(c_Set_Oinsert(X3),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2(X37,X3)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))))))
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_OrderedGroup_Oab__semigroup__mult(X37,X3) ),
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_1001,plain,
! [X14,X12,X42,X72,X21,X3] :
( c_Fun_Ofun__upd(c_Map_Orestrict__map(X42,X72,X3,X21),X12,X14,X3,tc_Option_Ooption(X21)) = c_Fun_Ofun__upd(c_Map_Orestrict__map(X42,c_HOL_Ominus__class_Ominus(X72,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3,X21),X12,X14,X3,tc_Option_Ooption(X21))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X72)) ),
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_1002,plain,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| X12 = c_HOL_Ozero__class_Ozero(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X12)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X14),X14))),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_1003,plain,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| X14 = c_HOL_Ozero__class_Ozero(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X12)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X14),X14))),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_1004,plain,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X12)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X14),X14))),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_94]) ).
fof(c_0_1005,plain,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_95]) ).
fof(c_0_1006,plain,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_96]) ).
fof(c_0_1007,plain,
! [X49,X50,X51,X19,X8,X9,X3] :
( c_Finite__Set_Ofold(X51,X19,hAPP(hAPP(c_Set_Oinsert(X3),X8),X9),X3,X3) = hAPP(hAPP(X51,X8),c_Finite__Set_Ofold(X51,X19,X9,X3,X3))
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
inference(fof_simplification,[status(thm)],[c_0_97]) ).
fof(c_0_1008,axiom,
! [X14,X12,X42,X19,X8,X21,X3] :
( hAPP(c_Fun_Ofun__upd(X42,X8,hAPP(c_Option_Ooption_OSome(X3),X19),X21,tc_Option_Ooption(X3)),X12) != hAPP(c_Option_Ooption_OSome(X3),X14)
| hAPP(X42,X12) = hAPP(c_Option_Ooption_OSome(X3),X14)
| X19 = X14 ),
c_0_98 ).
fof(c_0_1009,axiom,
! [X14,X12,X42,X19,X8,X21,X3] :
( hAPP(c_Fun_Ofun__upd(X42,X8,hAPP(c_Option_Ooption_OSome(X3),X19),X21,tc_Option_Ooption(X3)),X12) != hAPP(c_Option_Ooption_OSome(X3),X14)
| hAPP(X42,X12) = hAPP(c_Option_Ooption_OSome(X3),X14)
| X12 = X8 ),
c_0_99 ).
fof(c_0_1010,axiom,
! [X14,X12,X42,X19,X87,X3] :
( X19 = X14
| hAPP(c_Fun_Ofun__upd(X42,X12,hAPP(c_Option_Ooption_OSome(X87),X19),X3,tc_Option_Ooption(X87)),X12) != hAPP(c_Option_Ooption_OSome(X87),X14) ),
c_0_100 ).
fof(c_0_1011,plain,
! [X70,X12,X38,X9,X21,X3] :
( c_Finite__Set_Ofold(X38,X70,hAPP(hAPP(c_Set_Oinsert(X3),X12),X9),X3,X21) = hAPP(hAPP(X38,X12),c_Finite__Set_Ofold(X38,X70,X9,X3,X21))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_Finite__Set_Ofun__left__comm(X38,X3,X21) ),
inference(fof_simplification,[status(thm)],[c_0_101]) ).
fof(c_0_1012,axiom,
! [X14,X12,X55,X42,X8,X21,X3] :
( c_Fun_Ofun__upd(X42,X8,hAPP(c_Option_Ooption_OSome(X21),X12),X3,tc_Option_Ooption(X21)) != c_Fun_Ofun__upd(X55,X8,hAPP(c_Option_Ooption_OSome(X21),X14),X3,tc_Option_Ooption(X21))
| X12 = X14 ),
c_0_102 ).
fof(c_0_1013,plain,
! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3)))),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_1014,plain,
! [X70,X12,X38,X9,X21,X3] :
( hAPP(hAPP(X38,X12),c_Finite__Set_Ofold(X38,X70,X9,X3,X21)) = c_Finite__Set_Ofold(X38,hAPP(hAPP(X38,X12),X70),X9,X3,X21)
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_Finite__Set_Ofun__left__comm(X38,X3,X21) ),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_1015,plain,
! [X19,X8,X9,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X3),X19,hAPP(hAPP(c_Set_Oinsert(X3),X8),X9),X3,X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X8),c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X3),X19,X9,X3,X3))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_1016,plain,
! [X19,X8,X9,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X3),X19,hAPP(hAPP(c_Set_Oinsert(X3),X8),X9),X3,X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X8),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X3),X19,X9,X3,X3))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_1017,plain,
! [X38,X13,X9,X21,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X21,tc_bool)),c_Set_Ovimage(X38,X9,X21,X3)),c_Set_Ovimage(X38,X13,X21,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_107]) ).
fof(c_0_1018,plain,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X13))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13))) ),
inference(fof_simplification,[status(thm)],[c_0_108]) ).
fof(c_0_1019,plain,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Olattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X70))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X14),X70)))) ),
inference(fof_simplification,[status(thm)],[c_0_109]) ).
fof(c_0_1020,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X70))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X14),X70)))) ),
inference(fof_simplification,[status(thm)],[c_0_110]) ).
fof(c_0_1021,plain,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13))) ),
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_1022,plain,
! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))))) ),
inference(fof_simplification,[status(thm)],[c_0_112]) ).
fof(c_0_1023,plain,
! [X38,X19,X8,X21,X3] :
( hAPP(X38,X8) = X19
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),c_Set_Ovimage(X38,hAPP(hAPP(c_Set_Oinsert(X21),X19),c_Orderings_Obot__class_Obot(tc_fun(X21,tc_bool))),X3,X21))) ),
inference(fof_simplification,[status(thm)],[c_0_113]) ).
fof(c_0_1024,axiom,
! [X14,X12,X42,X72,X21,X3] :
( c_Map_Orestrict__map(c_Fun_Ofun__upd(X42,X12,X14,X3,tc_Option_Ooption(X21)),X72,X3,X21) = c_Map_Orestrict__map(X42,X72,X3,X21)
| hBOOL(hAPP(hAPP(c_in(X3),X12),X72)) ),
c_0_114 ).
fof(c_0_1025,plain,
! [X72,X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X80),X72)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X13),X72))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X80)) ),
inference(fof_simplification,[status(thm)],[c_0_115]) ).
fof(c_0_1026,plain,
! [X72,X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X80),X72)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X13),X72))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X80)) ),
inference(fof_simplification,[status(thm)],[c_0_116]) ).
fof(c_0_1027,plain,
! [X70,X12,X38,X9,X21,X3] :
( c_Finite__Set_Ofold(X38,X70,hAPP(hAPP(c_Set_Oinsert(X3),X12),X9),X3,X21) = c_Finite__Set_Ofold(X38,hAPP(hAPP(X38,X12),X70),X9,X3,X21)
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_Finite__Set_Ofun__left__comm(X38,X3,X21) ),
inference(fof_simplification,[status(thm)],[c_0_117]) ).
fof(c_0_1028,plain,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Olattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X14),X70))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X70)))) ),
inference(fof_simplification,[status(thm)],[c_0_118]) ).
fof(c_0_1029,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X14),X70))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X70)))) ),
inference(fof_simplification,[status(thm)],[c_0_119]) ).
fof(c_0_1030,plain,
! [X90,X24,X19,X8,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X90)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X19,X8,X3)),X90)),X24)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X90)),X24) ),
inference(fof_simplification,[status(thm)],[c_0_120]) ).
fof(c_0_1031,plain,
! [X90,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X90)),X23) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X90)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X8,X19,X3)),X90)),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_121]) ).
fof(c_0_1032,plain,
! [X12,X42,X72,X21,X3] :
( c_Fun_Ofun__upd(c_Map_Orestrict__map(X42,X72,X3,X21),X12,c_Option_Ooption_ONone(X21),X3,tc_Option_Ooption(X21)) = c_Map_Orestrict__map(X42,c_HOL_Ominus__class_Ominus(X72,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3,X21)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X72)) ),
inference(fof_simplification,[status(thm)],[c_0_122]) ).
fof(c_0_1033,plain,
! [X63,X57,X38,X21,X3] :
( c_Map_Omap__le(c_Map_Omap__add(X38,X57,X3,X21),X63,X3,X21)
| ~ c_Map_Omap__le(X38,c_Map_Omap__add(X38,X57,X3,X21),X3,X21)
| ~ c_Map_Omap__le(X57,X63,X3,X21)
| ~ c_Map_Omap__le(X38,X63,X3,X21) ),
inference(fof_simplification,[status(thm)],[c_0_123]) ).
fof(c_0_1034,axiom,
! [X14,X12,X38,X21,X3] :
( c_Map_Odom(c_Fun_Ofun__upd(X38,X12,X14,X3,tc_Option_Ooption(X21)),X3,X21) = hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Map_Odom(X38,X3,X21))
| X14 = c_Option_Ooption_ONone(X21) ),
c_0_124 ).
fof(c_0_1035,axiom,
! [X14,X12,X42,X19,X8,X21,X3] :
( hAPP(X42,X12) != hAPP(c_Option_Ooption_OSome(X3),X14)
| X12 = X8
| hAPP(c_Fun_Ofun__upd(X42,X8,hAPP(c_Option_Ooption_OSome(X3),X19),X21,tc_Option_Ooption(X3)),X12) = hAPP(c_Option_Ooption_OSome(X3),X14) ),
c_0_125 ).
fof(c_0_1036,axiom,
! [X45,X46,X21,X3] :
( c_Map_Omap__le(X46,X45,X3,X21)
| hBOOL(hAPP(hAPP(c_in(X3),c_Map_Osko__Map__Xmap__le__def__1__1(X46,X45,X3,X21)),c_Map_Odom(X46,X3,X21))) ),
c_0_126 ).
fof(c_0_1037,plain,
! [X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X80))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13)),X80)) ),
inference(fof_simplification,[status(thm)],[c_0_127]) ).
fof(c_0_1038,plain,
! [X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X13),X80))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13)),X80)) ),
inference(fof_simplification,[status(thm)],[c_0_128]) ).
fof(c_0_1039,axiom,
! [X70,X14,X12,X38,X21,X3] :
( hAPP(c_Fun_Ofun__upd(X38,X12,X14,X21,X3),X70) = hAPP(X38,X70)
| X70 = X12 ),
c_0_129 ).
fof(c_0_1040,axiom,
! [X70,X14,X12,X38,X21,X3] :
( hAPP(c_Fun_Ofun__upd(X38,X12,X14,X3,X21),X70) = hAPP(X38,X70)
| X70 = X12 ),
c_0_130 ).
fof(c_0_1041,plain,
! [X57,X13,X9,X21,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X21)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X13,X3)
| ~ c_Finite__Set_Ofinite(X9,X3)
| c_Finite__Set_Osetsum(X57,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13),X3,X21) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),c_Finite__Set_Osetsum(X57,X9,X3,X21)),c_Finite__Set_Osetsum(X57,X13,X3,X21)) ),
inference(fof_simplification,[status(thm)],[c_0_131]) ).
fof(c_0_1042,plain,
! [X57,X13,X9,X21,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X21)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X13,X3)
| ~ c_Finite__Set_Ofinite(X9,X3)
| c_Finite__Set_Osetprod(X57,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13),X3,X21) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X21),c_Finite__Set_Osetprod(X57,X9,X3,X21)),c_Finite__Set_Osetprod(X57,X13,X3,X21)) ),
inference(fof_simplification,[status(thm)],[c_0_132]) ).
fof(c_0_1043,plain,
! [X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13)),X80))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X13),X80))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X80)) ),
inference(fof_simplification,[status(thm)],[c_0_133]) ).
fof(c_0_1044,plain,
! [X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13)),X80))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X13),X80))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X80)) ),
inference(fof_simplification,[status(thm)],[c_0_134]) ).
fof(c_0_1045,plain,
! [X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X13),X80)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(X3,tc_bool))),X80)) ),
inference(fof_simplification,[status(thm)],[c_0_135]) ).
fof(c_0_1046,plain,
! [X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(X3,tc_bool))),X80))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X13),X80))) ),
inference(fof_simplification,[status(thm)],[c_0_136]) ).
fof(c_0_1047,plain,
! [X38,X8,X9,X21,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X21)
| c_Finite__Set_Osetsum(X38,X9,X3,X21) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),hAPP(X38,X8)),c_Finite__Set_Osetsum(X38,c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3,X21))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_137]) ).
fof(c_0_1048,plain,
! [X72,X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(X3,tc_bool))),c_HOL_Ominus__class_Ominus(X80,X72,tc_fun(X3,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X72),X13))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X80)) ),
inference(fof_simplification,[status(thm)],[c_0_138]) ).
fof(c_0_1049,axiom,
! [X80,X13,X9,X3] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13)),X80) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X13),X80))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X80),X9)) ),
c_0_139 ).
fof(c_0_1050,axiom,
! [X12,X42,X72,X21,X3] :
( c_Fun_Ofun__upd(c_Map_Orestrict__map(X42,X72,X3,X21),X12,c_Option_Ooption_ONone(X21),X3,tc_Option_Ooption(X21)) = c_Map_Orestrict__map(X42,X72,X3,X21)
| hBOOL(hAPP(hAPP(c_in(X3),X12),X72)) ),
c_0_140 ).
fof(c_0_1051,plain,
! [X38,X8,X9,X21,X3] :
( hBOOL(hAPP(hAPP(c_in(X21),hAPP(X38,X8)),X9))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),c_Set_Ovimage(X38,X9,X3,X21))) ),
inference(fof_simplification,[status(thm)],[c_0_141]) ).
fof(c_0_1052,plain,
! [X38,X8,X13,X21,X3] :
( hBOOL(hAPP(hAPP(c_in(X21),hAPP(X38,X8)),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),c_Set_Ovimage(X38,X13,X3,X21))) ),
inference(fof_simplification,[status(thm)],[c_0_142]) ).
fof(c_0_1053,plain,
! [X90,X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X90)),X23) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X90)),X24)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X8,X19,X3)),X90)),X23) = X24 ),
inference(fof_simplification,[status(thm)],[c_0_143]) ).
fof(c_0_1054,plain,
! [X90,X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X90)),X23) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X90)),X24)
| X23 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ominus__class_Ominus(X19,X8,X3)),X90)),X24) ),
inference(fof_simplification,[status(thm)],[c_0_144]) ).
fof(c_0_1055,plain,
! [X38,X13,X9,X21,X3] :
( ~ class_OrderedGroup_Oab__group__add(X21)
| c_Finite__Set_Osetsum(X38,c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(X3,tc_bool)),X3,X21) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X38,X9,X3,X21),c_Finite__Set_Osetsum(X38,X13,X3,X21),X21)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X13),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_145]) ).
fof(c_0_1056,axiom,
! [X14,X12,X38,X21,X3] :
( c_Fun_Ofun__upd(X38,X12,X14,X3,X21) != X38
| hAPP(X38,X12) = X14 ),
c_0_146 ).
fof(c_0_1057,plain,
! [X24,X23,X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X24))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X23,X24,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_147]) ).
fof(c_0_1058,plain,
! [X90,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Osemiring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X90)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X90)),X23)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),X90)),X23) ),
inference(fof_simplification,[status(thm)],[c_0_148]) ).
fof(c_0_1059,axiom,
! [X45,X46,X21,X3] :
( hAPP(X46,c_Map_Osko__Map__Xmap__le__def__1__1(X46,X45,X3,X21)) != hAPP(X45,c_Map_Osko__Map__Xmap__le__def__1__1(X46,X45,X3,X21))
| c_Map_Omap__le(X46,X45,X3,X21) ),
c_0_149 ).
fof(c_0_1060,plain,
! [X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X80),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X80),X13))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X80),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_150]) ).
fof(c_0_1061,plain,
! [X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X80),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X80),X13))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X80),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_151]) ).
fof(c_0_1062,axiom,
! [X20,X34,X3] :
( hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X34) != hAPP(c_COMBC(c_in(X3),X3,tc_fun(X3,tc_bool),tc_bool),X20)
| X34 = X20 ),
c_0_152 ).
fof(c_0_1063,plain,
! [X24,X23,X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X23),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X23,X24,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_153]) ).
fof(c_0_1064,plain,
! [X24,X23,X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X23,X24,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_154]) ).
fof(c_0_1065,plain,
! [X24,X23,X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X23),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X23,X24,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_155]) ).
fof(c_0_1066,plain,
! [X24,X23,X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X23,X24,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_156]) ).
fof(c_0_1067,plain,
! [X38,X19,X8,X3] :
( X8 = X19
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X38,hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),X3),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_157]) ).
fof(c_0_1068,plain,
! [X12,X38,X9,X21,X3] :
( hBOOL(hAPP(X9,hAPP(X38,X12)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X38,X9,X3,X21),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_158]) ).
fof(c_0_1069,plain,
! [X57,X38,X21,X3] :
( c_Map_Omap__add(X38,X57,X3,X21) = c_Map_Omap__add(X57,X38,X3,X21)
| ~ c_Map_Omap__le(X38,c_Map_Omap__add(X38,X57,X3,X21),X3,X21) ),
inference(fof_simplification,[status(thm)],[c_0_159]) ).
fof(c_0_1070,plain,
! [X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X80),X13))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X80),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13))) ),
inference(fof_simplification,[status(thm)],[c_0_160]) ).
fof(c_0_1071,plain,
! [X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X80),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X80),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13))) ),
inference(fof_simplification,[status(thm)],[c_0_161]) ).
fof(c_0_1072,plain,
! [X24,X23,X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X23,X24,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X23),X24))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X23),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_162]) ).
fof(c_0_1073,plain,
! [X24,X23,X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X23,X24,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X23),X24))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X23),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_163]) ).
fof(c_0_1074,plain,
! [X80,X13,X9,X3] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13)),X80) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X13),X80))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X80),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_164]) ).
fof(c_0_1075,plain,
! [X38,X8,X9,X21,X3] :
( ~ class_Ring__and__Field_Oring(X21)
| c_Finite__Set_Osetsum(X38,c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3,X21) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X38,X9,X3,X21),hAPP(X38,X8),X21)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_165]) ).
fof(c_0_1076,plain,
! [X38,X8,X9,X21,X3] :
( ~ class_OrderedGroup_Oab__group__add(X21)
| c_Finite__Set_Osetsum(X38,c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3,X21) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X38,X9,X3,X21),hAPP(X38,X8),X21)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_166]) ).
fof(c_0_1077,plain,
! [X24,X23,X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X23),X24))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X23,X24,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_167]) ).
fof(c_0_1078,plain,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X12)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X14),X14))))
| X12 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_168]) ).
fof(c_0_1079,plain,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X12)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X14),X14))))
| X14 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_169]) ).
fof(c_0_1080,plain,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X12)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X14),X14)))) ),
inference(fof_simplification,[status(thm)],[c_0_170]) ).
fof(c_0_1081,axiom,
! [X57,X38,X21,X3] :
( c_Map_Omap__add(X38,X57,X3,X21) != c_Map_Omap__add(X57,X38,X3,X21)
| c_Map_Omap__le(X38,c_Map_Omap__add(X38,X57,X3,X21),X3,X21) ),
c_0_171 ).
fof(c_0_1082,plain,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_172]) ).
fof(c_0_1083,plain,
! [X8,X9,X3] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X3),X3),hAPP(hAPP(c_Set_Oinsert(X3),X8),X9)) = c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(X3),X8,X9,X3,X3)
| hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_173]) ).
fof(c_0_1084,plain,
! [X8,X9,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X3),X3),hAPP(hAPP(c_Set_Oinsert(X3),X8),X9)) = c_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(X3),X8,X9,X3,X3)
| hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_174]) ).
fof(c_0_1085,plain,
! [X37,X8,X9,X3] :
( hAPP(c_Finite__Set_Ofold1(X37,X3),hAPP(hAPP(c_Set_Oinsert(X3),X8),X9)) = c_Finite__Set_Ofold(X37,X8,X9,X3,X3)
| hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_OrderedGroup_Oab__semigroup__mult(X37,X3) ),
inference(fof_simplification,[status(thm)],[c_0_175]) ).
fof(c_0_1086,plain,
! [X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X24)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),X24))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_176]) ).
fof(c_0_1087,plain,
! [X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X24)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X23),X24))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_177]) ).
fof(c_0_1088,plain,
! [X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X24)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X8))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_178]) ).
fof(c_0_1089,plain,
! [X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X24)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),X24))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_179]) ).
fof(c_0_1090,plain,
! [X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__semiring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X24)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X23),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_180]) ).
fof(c_0_1091,plain,
! [X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__semiring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X24)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X23),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_181]) ).
fof(c_0_1092,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19))) ),
inference(fof_simplification,[status(thm)],[c_0_182]) ).
fof(c_0_1093,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23))) ),
inference(fof_simplification,[status(thm)],[c_0_183]) ).
fof(c_0_1094,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19))) ),
inference(fof_simplification,[status(thm)],[c_0_184]) ).
fof(c_0_1095,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23))) ),
inference(fof_simplification,[status(thm)],[c_0_185]) ).
fof(c_0_1096,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_186]) ).
fof(c_0_1097,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19))) ),
inference(fof_simplification,[status(thm)],[c_0_187]) ).
fof(c_0_1098,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23))) ),
inference(fof_simplification,[status(thm)],[c_0_188]) ).
fof(c_0_1099,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_189]) ).
fof(c_0_1100,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_190]) ).
fof(c_0_1101,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X8))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_191]) ).
fof(c_0_1102,plain,
! [X38,X8,X13,X21,X3] :
( hBOOL(hAPP(hAPP(c_in(X21),X8),c_Set_Ovimage(X38,X13,X21,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),hAPP(X38,X8)),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_192]) ).
fof(c_0_1103,plain,
! [X38,X8,X9,X21,X3] :
( hBOOL(hAPP(hAPP(c_in(X21),X8),c_Set_Ovimage(X38,X9,X21,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),hAPP(X38,X8)),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_193]) ).
fof(c_0_1104,plain,
! [X38,X8,X13,X21,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X8),c_Set_Ovimage(X38,X13,X3,X21)))
| ~ hBOOL(hAPP(hAPP(c_in(X21),hAPP(X38,X8)),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_194]) ).
fof(c_0_1105,plain,
! [X63,X57,X38,X21,X3] :
( c_Map_Omap__le(X57,X63,X3,X21)
| ~ c_Map_Omap__le(c_Map_Omap__add(X38,X57,X3,X21),X63,X3,X21) ),
inference(fof_simplification,[status(thm)],[c_0_195]) ).
fof(c_0_1106,plain,
! [X13,X9,X3] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13) = c_Finite__Set_Ofold(c_Set_Oinsert(X3),X13,X9,X3,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_196]) ).
fof(c_0_1107,plain,
! [X8,X9,X3] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X3),X3),hAPP(hAPP(c_Set_Oinsert(X3),X8),X9)) = c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(X3),X8,X9,X3,X3)
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_197]) ).
fof(c_0_1108,plain,
! [X37,X8,X9,X3] :
( hAPP(c_Finite__Set_Ofold1(X37,X3),hAPP(hAPP(c_Set_Oinsert(X3),X8),X9)) = c_Finite__Set_Ofold(X37,X8,X9,X3,X3)
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X37,X3) ),
inference(fof_simplification,[status(thm)],[c_0_198]) ).
fof(c_0_1109,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),c_HOL_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19))) ),
inference(fof_simplification,[status(thm)],[c_0_199]) ).
fof(c_0_1110,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),c_HOL_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23))) ),
inference(fof_simplification,[status(thm)],[c_0_200]) ).
fof(c_0_1111,plain,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X3),X12),X9)),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_201]) ).
fof(c_0_1112,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X8))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23))) ),
inference(fof_simplification,[status(thm)],[c_0_202]) ).
fof(c_0_1113,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X8))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19))) ),
inference(fof_simplification,[status(thm)],[c_0_203]) ).
fof(c_0_1114,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),c_HOL_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23))) ),
inference(fof_simplification,[status(thm)],[c_0_204]) ).
fof(c_0_1115,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),c_HOL_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19))) ),
inference(fof_simplification,[status(thm)],[c_0_205]) ).
fof(c_0_1116,plain,
! [X12,X9,X3] :
( c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3)) = c_Finite__Set_Ocard(X9,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_206]) ).
fof(c_0_1117,plain,
! [X8,X72,X80,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X3),X8),X80)),hAPP(hAPP(c_Set_Oinsert(X3),X8),X72)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X80),X72)) ),
inference(fof_simplification,[status(thm)],[c_0_207]) ).
fof(c_0_1118,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X8))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19))) ),
inference(fof_simplification,[status(thm)],[c_0_208]) ).
fof(c_0_1119,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X8))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23))) ),
inference(fof_simplification,[status(thm)],[c_0_209]) ).
fof(c_0_1120,plain,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X3),X12),X9)),X13))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_210]) ).
fof(c_0_1121,plain,
! [X57,X38,X21,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Map_Odom(X38,X3,X21)),c_Map_Odom(X57,X3,X21)))
| ~ c_Map_Omap__le(X38,X57,X3,X21) ),
inference(fof_simplification,[status(thm)],[c_0_211]) ).
fof(c_0_1122,plain,
! [X13,X9,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X13),c_Complete__Lattice_OInf__class_OInf(X9,X3)) = c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X3),X13,X9,X3,X3)
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_212]) ).
fof(c_0_1123,plain,
! [X13,X9,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X13),c_Complete__Lattice_OSup__class_OSup(X9,X3)) = c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X3),X13,X9,X3,X3)
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_213]) ).
fof(c_0_1124,axiom,
! [X12,X6,X56,X21,X3] :
( hAPP(X6,X56) != hAPP(c_Option_Ooption_OSome(X3),X12)
| c_Fun_Ofun__upd(X6,X56,hAPP(c_Option_Ooption_OSome(X3),X12),X21,tc_Option_Ooption(X3)) = X6 ),
c_0_214 ).
fof(c_0_1125,plain,
! [X12,X9,X3] :
( c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(X3),X12),X9),X3) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_215]) ).
fof(c_0_1126,plain,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X13))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13))) ),
inference(fof_simplification,[status(thm)],[c_0_216]) ).
fof(c_0_1127,plain,
! [X23,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X23),X13))
| hBOOL(hAPP(hAPP(c_in(X3),X23),X9))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X23),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13))) ),
inference(fof_simplification,[status(thm)],[c_0_217]) ).
fof(c_0_1128,plain,
! [X24,X23,X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X23,X24,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X23),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_218]) ).
fof(c_0_1129,axiom,
! [X61,X62,X21,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),c_Map_Odom(X62,X3,X21)),c_Map_Odom(X61,X3,X21)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_Map_Omap__add(X62,X61,X3,X21) = c_Map_Omap__add(X61,X62,X3,X21) ),
c_0_219 ).
fof(c_0_1130,plain,
! [X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Lattices_Olower__semilattice(c_COMBC(c_lessequals(X3),X3,X3,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(X3),X3,X3,tc_bool),c_Orderings_Oord__class_Omax(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_220]) ).
fof(c_0_1131,plain,
! [X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Olower__semilattice(c_COMBC(c_lessequals(X3),X3,X3,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(X3),X3,X3,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_221]) ).
fof(c_0_1132,plain,
! [X9,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OSup__class_OSup(X9,X3) = c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X3),c_Orderings_Obot__class_Obot(X3),X9,X3,X3)
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_222]) ).
fof(c_0_1133,plain,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X23))) ),
inference(fof_simplification,[status(thm)],[c_0_223]) ).
fof(c_0_1134,plain,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X8)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X19))) ),
inference(fof_simplification,[status(thm)],[c_0_224]) ).
fof(c_0_1135,plain,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X23))) ),
inference(fof_simplification,[status(thm)],[c_0_225]) ).
fof(c_0_1136,plain,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X8)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X19))) ),
inference(fof_simplification,[status(thm)],[c_0_226]) ).
fof(c_0_1137,plain,
! [X12,X9,X3] :
( X9 = hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))))) ),
inference(fof_simplification,[status(thm)],[c_0_227]) ).
fof(c_0_1138,plain,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X13))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13))) ),
inference(fof_simplification,[status(thm)],[c_0_228]) ).
fof(c_0_1139,plain,
! [X13,X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X3),X3),X13)),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X3),X3),X9)))
| ~ c_Finite__Set_Ofinite(X13,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_229]) ).
fof(c_0_1140,plain,
! [X38,X8,X9,X21,X3] :
( ~ class_Ring__and__Field_Ofield(X21)
| c_Finite__Set_Osetprod(X38,c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3,X21) = c_Finite__Set_Osetprod(X38,X9,X3,X21)
| hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| hAPP(X38,X8) = c_HOL_Ozero__class_Ozero(X21)
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_230]) ).
fof(c_0_1141,plain,
! [X24,X23,X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X23,X24,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X23),X24))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_231]) ).
fof(c_0_1142,plain,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X12),X13))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X3),X12),X9)),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_232]) ).
fof(c_0_1143,plain,
! [X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),X80))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X13),X80))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_233]) ).
fof(c_0_1144,plain,
! [X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X80))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X13),X80))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_234]) ).
fof(c_0_1145,plain,
! [X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),X80))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X13),X80))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_235]) ).
fof(c_0_1146,plain,
! [X80,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),X80))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X13),X80))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_236]) ).
fof(c_0_1147,plain,
! [X38,X8,X9,X21,X3] :
( ~ class_OrderedGroup_Oab__group__add(X21)
| c_Finite__Set_Osetsum(X38,c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3,X21) = c_Finite__Set_Osetsum(X38,X9,X3,X21)
| hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_237]) ).
fof(c_0_1148,plain,
! [X35,X36,X32] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OBODY(X32)),X36),X35))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Option_Othe(hAPP(c_Com_Obody,X32),tc_Com_Ocom)),X36),X35)) ),
inference(fof_simplification,[status(thm)],[c_0_238]) ).
fof(c_0_1149,plain,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13)))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_239]) ).
fof(c_0_1150,plain,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13))) ),
inference(fof_simplification,[status(thm)],[c_0_240]) ).
fof(c_0_1151,plain,
! [X23,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X23),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X23),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13))) ),
inference(fof_simplification,[status(thm)],[c_0_241]) ).
fof(c_0_1152,plain,
! [X23,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X23),X9))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X23),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13))) ),
inference(fof_simplification,[status(thm)],[c_0_242]) ).
fof(c_0_1153,plain,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_243]) ).
fof(c_0_1154,axiom,
! [X38,X8,X9,X3] :
( c_Finite__Set_Osetsum(X38,c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3,tc_nat) = c_Finite__Set_Osetsum(X38,X9,X3,tc_nat)
| hBOOL(hAPP(hAPP(c_in(X3),X8),X9)) ),
c_0_244 ).
fof(c_0_1155,plain,
! [X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),X13))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(X9,X3)),c_Finite__Set_Ocard(X13,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| ~ c_Finite__Set_Ofinite(X13,X3) ),
inference(fof_simplification,[status(thm)],[c_0_245]) ).
fof(c_0_1156,plain,
! [X70,X14,X12,X95,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X95),X14)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X70)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X95),X70)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X14))
| X14 = X70
| X95 = X12 ),
inference(fof_simplification,[status(thm)],[c_0_246]) ).
fof(c_0_1157,plain,
! [X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X24)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X24)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23))
| X23 = X24
| X8 = X19 ),
inference(fof_simplification,[status(thm)],[c_0_247]) ).
fof(c_0_1158,plain,
! [X12,X38,X9,X21,X3] :
( hBOOL(hAPP(c_Set_Ovimage(X38,X9,X3,X21),X12))
| ~ hBOOL(hAPP(X9,hAPP(X38,X12))) ),
inference(fof_simplification,[status(thm)],[c_0_248]) ).
fof(c_0_1159,plain,
! [X80,X13,X9,X3] :
( c_HOL_Ominus__class_Ominus(X13,c_HOL_Ominus__class_Ominus(X80,X9,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = X9
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X13),X80))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_249]) ).
fof(c_0_1160,plain,
! [X57,X38,X21,X3] :
( ~ class_HOL_Oord(X21)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,X21)),X38),X57))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,X21)),X57),X38))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,X21)),X38),X57)) ),
inference(fof_simplification,[status(thm)],[c_0_250]) ).
fof(c_0_1161,plain,
! [X49,X50,X3] :
( c_Orderings_Olinorder(c_COMBC(X49,X3,X3,tc_bool),c_COMBC(X50,X3,X3,tc_bool),X3)
| ~ c_Orderings_Olinorder(X49,X50,X3) ),
inference(fof_simplification,[status(thm)],[c_0_251]) ).
fof(c_0_1162,plain,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X13))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_252]) ).
fof(c_0_1163,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_253]) ).
fof(c_0_1164,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Omult__mono(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_254]) ).
fof(c_0_1165,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Omult__mono(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_255]) ).
fof(c_0_1166,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Omult__mono1(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_256]) ).
fof(c_0_1167,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_257]) ).
fof(c_0_1168,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_258]) ).
fof(c_0_1169,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_259]) ).
fof(c_0_1170,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_260]) ).
fof(c_0_1171,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_261]) ).
fof(c_0_1172,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X23))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_262]) ).
fof(c_0_1173,plain,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_263]) ).
fof(c_0_1174,plain,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_264]) ).
fof(c_0_1175,plain,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),c_HOL_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_265]) ).
fof(c_0_1176,plain,
! [X38,X8,X58,X21,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X21)
| c_Finite__Set_Osetsum(X38,hAPP(hAPP(c_Set_Oinsert(X3),X8),X58),X3,X21) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X21),hAPP(X38,X8)),c_Finite__Set_Osetsum(X38,X58,X3,X21))
| hBOOL(hAPP(hAPP(c_in(X3),X8),X58))
| ~ c_Finite__Set_Ofinite(X58,X3) ),
inference(fof_simplification,[status(thm)],[c_0_266]) ).
fof(c_0_1177,plain,
! [X38,X8,X9,X21,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X21)
| c_Finite__Set_Osetprod(X38,hAPP(hAPP(c_Set_Oinsert(X3),X8),X9),X3,X21) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X21),hAPP(X38,X8)),c_Finite__Set_Osetprod(X38,X9,X3,X21))
| hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_267]) ).
fof(c_0_1178,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X8))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_268]) ).
fof(c_0_1179,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X23),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_269]) ).
fof(c_0_1180,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X23),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_270]) ).
fof(c_0_1181,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X8))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_271]) ).
fof(c_0_1182,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_272]) ).
fof(c_0_1183,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X8)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X8))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_273]) ).
fof(c_0_1184,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_274]) ).
fof(c_0_1185,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X8))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_275]) ).
fof(c_0_1186,plain,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),c_HOL_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_276]) ).
fof(c_0_1187,plain,
! [X13,X9,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X13 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X13,X3)
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X3),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X3),X3),X9)),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X3),X3),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_277]) ).
fof(c_0_1188,plain,
! [X13,X9,X3] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X13 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X13,X3)
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X3),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X3),X3),X9)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X3),X3),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_278]) ).
fof(c_0_1189,plain,
! [X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Orderings_Olinorder(c_COMBC(c_lessequals(X3),X3,X3,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(X3),X3,X3,tc_bool),X3) ),
inference(fof_simplification,[status(thm)],[c_0_279]) ).
fof(c_0_1190,plain,
! [X17,X12,X49,X50,X51,X9,X3] :
( hBOOL(hAPP(hAPP(X49,X12),X17))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X9))
| ~ hBOOL(hAPP(hAPP(X49,X12),hAPP(c_Finite__Set_Ofold1(X51,X3),X9)))
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
inference(fof_simplification,[status(thm)],[c_0_280]) ).
fof(c_0_1191,plain,
! [X24,X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X24)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X23),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_281]) ).
fof(c_0_1192,plain,
! [X24,X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X24)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),X24))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_282]) ).
fof(c_0_1193,plain,
! [X24,X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X24)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X23),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_283]) ).
fof(c_0_1194,plain,
! [X24,X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X24)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X23),X24))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_284]) ).
fof(c_0_1195,plain,
! [X12,X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(c_Finite__Set_Olinorder__class_OMax(X3),X9) = X12
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(X9,X12,X3)),X12))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_285]) ).
fof(c_0_1196,plain,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_286]) ).
fof(c_0_1197,plain,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),X13)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_287]) ).
fof(c_0_1198,plain,
! [X24,X23,X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X23,X24,X3)))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_288]) ).
fof(c_0_1199,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X70))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14)),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_289]) ).
fof(c_0_1200,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X70))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X70))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14)),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_290]) ).
fof(c_0_1201,plain,
! [X42,X8,X21,X3] :
( hAPP(X42,X8) = hAPP(c_Option_Ooption_OSome(X21),c_Map_Osko__Map__XdomD__1__1(X8,X42,X3,X21))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),c_Map_Odom(X42,X3,X21))) ),
inference(fof_simplification,[status(thm)],[c_0_291]) ).
fof(c_0_1202,plain,
! [X60,X61,X62,X21,X3] :
( c_Map_Omap__le(X62,X60,X3,X21)
| ~ c_Map_Omap__le(X61,X60,X3,X21)
| ~ c_Map_Omap__le(X62,X61,X3,X21) ),
inference(fof_simplification,[status(thm)],[c_0_292]) ).
fof(c_0_1203,plain,
! [X42,X43,X44,X21,X3] :
( hAPP(c_Map_Omap__add(X44,X43,X3,X21),X42) = hAPP(X43,X42)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X42),c_Map_Odom(X43,X3,X21))) ),
inference(fof_simplification,[status(thm)],[c_0_293]) ).
fof(c_0_1204,plain,
! [X23,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X23),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X23),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X23),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_294]) ).
fof(c_0_1205,plain,
! [X23,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X23),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X23),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X23),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_295]) ).
fof(c_0_1206,plain,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(X13,X12))
| hBOOL(hAPP(X9,X12))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_296]) ).
fof(c_0_1207,plain,
! [X57,X38,X21,X3] :
( ~ class_HOL_Oord(X21)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,X21)),X57),X38))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,X21)),X38),X57)) ),
inference(fof_simplification,[status(thm)],[c_0_297]) ).
fof(c_0_1208,plain,
! [X37,X13,X9,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X13 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X13,X3)
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_OrderedGroup_Oab__semigroup__mult(X37,X3)
| hAPP(c_Finite__Set_Ofold1(X37,X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13)) = hAPP(hAPP(X37,hAPP(c_Finite__Set_Ofold1(X37,X3),X9)),hAPP(c_Finite__Set_Ofold1(X37,X3),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_298]) ).
fof(c_0_1209,plain,
! [X24,X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X24)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X23),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X23))) ),
inference(fof_simplification,[status(thm)],[c_0_299]) ).
fof(c_0_1210,plain,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(X13,X12))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_300]) ).
fof(c_0_1211,plain,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(X9,X12))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_301]) ).
fof(c_0_1212,plain,
! [X49,X50,X51,X8,X9,X3] :
( hBOOL(hAPP(hAPP(X49,hAPP(c_Finite__Set_Ofold1(X51,X3),X9)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
inference(fof_simplification,[status(thm)],[c_0_302]) ).
fof(c_0_1213,plain,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ominus__class_Ominus(X8,X19,X3)),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_303]) ).
fof(c_0_1214,plain,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ominus__class_Ominus(X8,X19,X3)),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_304]) ).
fof(c_0_1215,plain,
! [X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X8)),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_305]) ).
fof(c_0_1216,plain,
! [X8,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X8)),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_306]) ).
fof(c_0_1217,plain,
! [X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X8)),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_307]) ).
fof(c_0_1218,plain,
! [X19,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X19),X13)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_308]) ).
fof(c_0_1219,plain,
! [X83,X84,X86,X85,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X85),X86)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X84),X83)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X84),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X85),X86)),X83)) ),
inference(fof_simplification,[status(thm)],[c_0_309]) ).
fof(c_0_1220,plain,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X8)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_310]) ).
fof(c_0_1221,plain,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_311]) ).
fof(c_0_1222,plain,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_312]) ).
fof(c_0_1223,plain,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_313]) ).
fof(c_0_1224,plain,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_314]) ).
fof(c_0_1225,plain,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_315]) ).
fof(c_0_1226,plain,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_316]) ).
fof(c_0_1227,plain,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_317]) ).
fof(c_0_1228,plain,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_318]) ).
fof(c_0_1229,plain,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X8)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_319]) ).
fof(c_0_1230,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14)),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_320]) ).
fof(c_0_1231,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14)),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_321]) ).
fof(c_0_1232,plain,
! [X12,X19,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X8),X19)),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_322]) ).
fof(c_0_1233,plain,
! [X12,X19,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X8),X19)),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_323]) ).
fof(c_0_1234,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X70))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14)),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_324]) ).
fof(c_0_1235,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X70))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14)),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_325]) ).
fof(c_0_1236,plain,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14)),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_326]) ).
fof(c_0_1237,plain,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14)),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_327]) ).
fof(c_0_1238,plain,
! [X12,X19,X8,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X8),X19)),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_328]) ).
fof(c_0_1239,plain,
! [X12,X19,X8,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X8),X19)),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_329]) ).
fof(c_0_1240,plain,
! [X12,X45,X46,X21,X3] :
( hAPP(X46,X12) = hAPP(X45,X12)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),c_Map_Odom(X46,X3,X21)))
| ~ c_Map_Omap__le(X46,X45,X3,X21) ),
inference(fof_simplification,[status(thm)],[c_0_330]) ).
fof(c_0_1241,plain,
! [X14,X12,X3] :
( X14 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),X3)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_331]) ).
fof(c_0_1242,plain,
! [X13,X9,X3] :
( X9 = X13
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X13),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_332]) ).
fof(c_0_1243,plain,
! [X13,X9,X3] :
( X9 = X13
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X13),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_333]) ).
fof(c_0_1244,plain,
! [X12,X49,X50,X51,X19,X8,X3] :
( hBOOL(hAPP(hAPP(X50,hAPP(hAPP(X51,X8),X19)),X12))
| ~ hBOOL(hAPP(hAPP(X50,X19),X12))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
inference(fof_simplification,[status(thm)],[c_0_334]) ).
fof(c_0_1245,plain,
! [X12,X49,X50,X51,X19,X8,X3] :
( hBOOL(hAPP(hAPP(X50,hAPP(hAPP(X51,X8),X19)),X12))
| ~ hBOOL(hAPP(hAPP(X50,X8),X12))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
inference(fof_simplification,[status(thm)],[c_0_335]) ).
fof(c_0_1246,plain,
! [X12,X49,X50,X51,X19,X8,X3] :
( hBOOL(hAPP(hAPP(X49,hAPP(hAPP(X51,X8),X19)),X12))
| ~ hBOOL(hAPP(hAPP(X49,X8),X12))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
inference(fof_simplification,[status(thm)],[c_0_336]) ).
fof(c_0_1247,plain,
! [X12,X49,X50,X51,X19,X8,X3] :
( hBOOL(hAPP(hAPP(X49,hAPP(hAPP(X51,X8),X19)),X12))
| ~ hBOOL(hAPP(hAPP(X49,X19),X12))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
inference(fof_simplification,[status(thm)],[c_0_337]) ).
fof(c_0_1248,plain,
! [X17,X12,X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X3),X3),X9)),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X17),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X9))
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_338]) ).
fof(c_0_1249,plain,
! [X17,X12,X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X3),X3),X9)),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X17),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X9))
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_339]) ).
fof(c_0_1250,plain,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_340]) ).
fof(c_0_1251,plain,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_341]) ).
fof(c_0_1252,plain,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_342]) ).
fof(c_0_1253,plain,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_343]) ).
fof(c_0_1254,plain,
! [X35,X7,X18] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Option_Othe(hAPP(c_Com_Obody,X18),tc_Com_Ocom)),X7),X35))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OBODY(X18)),X7),X35)) ),
inference(fof_simplification,[status(thm)],[c_0_344]) ).
fof(c_0_1255,axiom,
! [X12,X55,X42,X56,X21,X3] :
( hAPP(c_Map_Omap__add(X42,X55,X21,X3),X56) != hAPP(c_Option_Ooption_OSome(X3),X12)
| hAPP(X42,X56) = hAPP(c_Option_Ooption_OSome(X3),X12)
| hAPP(X55,X56) = hAPP(c_Option_Ooption_OSome(X3),X12) ),
c_0_345 ).
fof(c_0_1256,plain,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X23)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_346]) ).
fof(c_0_1257,plain,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X8)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_347]) ).
fof(c_0_1258,plain,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X23)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_348]) ).
fof(c_0_1259,plain,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X8)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_349]) ).
fof(c_0_1260,plain,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X23)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_350]) ).
fof(c_0_1261,plain,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X23)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_351]) ).
fof(c_0_1262,plain,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X8)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_352]) ).
fof(c_0_1263,plain,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X8)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_353]) ).
fof(c_0_1264,plain,
! [X12,X49,X50,X51,X19,X8,X3] :
( hBOOL(hAPP(hAPP(X49,X12),hAPP(hAPP(X51,X8),X19)))
| ~ hBOOL(hAPP(hAPP(X49,X12),X19))
| ~ hBOOL(hAPP(hAPP(X49,X12),X8))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
inference(fof_simplification,[status(thm)],[c_0_354]) ).
fof(c_0_1265,plain,
! [X70,X14,X12,X49,X50,X51,X3] :
( hBOOL(hAPP(hAPP(X49,X12),hAPP(hAPP(X51,X14),X70)))
| ~ hBOOL(hAPP(hAPP(X49,X12),X70))
| ~ hBOOL(hAPP(hAPP(X49,X12),X14))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
inference(fof_simplification,[status(thm)],[c_0_355]) ).
fof(c_0_1266,plain,
! [X70,X14,X12,X49,X50,X51,X3] :
( hBOOL(hAPP(hAPP(X49,X12),hAPP(hAPP(X51,X14),X70)))
| ~ hBOOL(hAPP(hAPP(X49,X12),X70))
| ~ hBOOL(hAPP(hAPP(X49,X12),X14))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
inference(fof_simplification,[status(thm)],[c_0_356]) ).
fof(c_0_1267,axiom,
! [X12,X55,X42,X56,X21,X3] :
( hAPP(c_Map_Omap__add(X42,X55,X21,X3),X56) != hAPP(c_Option_Ooption_OSome(X3),X12)
| hAPP(X55,X56) = c_Option_Ooption_ONone(X3)
| hAPP(X55,X56) = hAPP(c_Option_Ooption_OSome(X3),X12) ),
c_0_357 ).
fof(c_0_1268,plain,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X8))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X8))) ),
inference(fof_simplification,[status(thm)],[c_0_358]) ).
fof(c_0_1269,plain,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X8))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19))) ),
inference(fof_simplification,[status(thm)],[c_0_359]) ).
fof(c_0_1270,plain,
! [X12,X19,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X8),X19)),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_360]) ).
fof(c_0_1271,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X14),X70)),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X70),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_361]) ).
fof(c_0_1272,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14)),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_362]) ).
fof(c_0_1273,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14)),X70))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X70))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_363]) ).
fof(c_0_1274,plain,
! [X12,X19,X8,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X8),X19)),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_364]) ).
fof(c_0_1275,plain,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X14),X70)),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X70),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_365]) ).
fof(c_0_1276,plain,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14)),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_366]) ).
fof(c_0_1277,plain,
! [X15,X6,X16,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X6),X15),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,X15,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X6),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))),X3) ),
inference(fof_simplification,[status(thm)],[c_0_367]) ).
fof(c_0_1278,plain,
! [X8,X80,X13,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X3),X8),X13)),X80) = hAPP(hAPP(c_Set_Oinsert(X3),X8),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X13),X80))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X80)) ),
inference(fof_simplification,[status(thm)],[c_0_368]) ).
fof(c_0_1279,plain,
! [X81,X82,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(c_Finite__Set_Olinorder__class_OMax(X3),X82)),hAPP(c_Finite__Set_Olinorder__class_OMax(X3),X81)))
| ~ c_Finite__Set_Ofinite(X81,X3)
| X82 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X82),X81)) ),
inference(fof_simplification,[status(thm)],[c_0_369]) ).
fof(c_0_1280,plain,
! [X81,X82,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(c_Finite__Set_Olinorder__class_OMin(X3),X81)),hAPP(c_Finite__Set_Olinorder__class_OMin(X3),X82)))
| ~ c_Finite__Set_Ofinite(X81,X3)
| X82 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X82),X81)) ),
inference(fof_simplification,[status(thm)],[c_0_370]) ).
fof(c_0_1281,plain,
! [X70,X14,X12,X49,X50,X51,X3] :
( hBOOL(hAPP(hAPP(X49,X12),X70))
| ~ hBOOL(hAPP(hAPP(X49,X12),hAPP(hAPP(X51,X14),X70)))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
inference(fof_simplification,[status(thm)],[c_0_371]) ).
fof(c_0_1282,plain,
! [X70,X14,X12,X49,X50,X51,X3] :
( hBOOL(hAPP(hAPP(X49,X12),X14))
| ~ hBOOL(hAPP(hAPP(X49,X12),hAPP(hAPP(X51,X14),X70)))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
inference(fof_simplification,[status(thm)],[c_0_372]) ).
fof(c_0_1283,plain,
! [X12,X49,X50,X51,X19,X8,X3] :
( hBOOL(hAPP(hAPP(X49,X12),X8))
| ~ hBOOL(hAPP(hAPP(X49,X12),hAPP(hAPP(X51,X8),X19)))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
inference(fof_simplification,[status(thm)],[c_0_373]) ).
fof(c_0_1284,plain,
! [X12,X49,X50,X51,X19,X8,X3] :
( hBOOL(hAPP(hAPP(X49,X12),X19))
| ~ hBOOL(hAPP(hAPP(X49,X12),hAPP(hAPP(X51,X8),X19)))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
inference(fof_simplification,[status(thm)],[c_0_374]) ).
fof(c_0_1285,plain,
! [X23,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X23),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X23),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_375]) ).
fof(c_0_1286,plain,
! [X23,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X23),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X23),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_376]) ).
fof(c_0_1287,axiom,
! [X42,X43,X44,X21,X3] :
( hAPP(c_Map_Omap__add(X44,X43,X3,X21),X42) = hAPP(X44,X42)
| hBOOL(hAPP(hAPP(c_in(X3),X42),c_Map_Odom(X43,X3,X21))) ),
c_0_377 ).
fof(c_0_1288,axiom,
! [X42,X43,X44,X21,X3] :
( hAPP(c_Map_Omap__add(X44,X43,X3,X21),X42) = hAPP(X43,X42)
| hBOOL(hAPP(hAPP(c_in(X3),X42),c_Map_Odom(X44,X3,X21))) ),
c_0_378 ).
fof(c_0_1289,plain,
! [X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X8)),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_379]) ).
fof(c_0_1290,plain,
! [X17,X12,X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X17))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X9))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X3),X3),X9)))
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_380]) ).
fof(c_0_1291,plain,
! [X17,X12,X9,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X17))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X17),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X3),X3),X9)))
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_381]) ).
fof(c_0_1292,axiom,
! [X55,X42,X56,X21,X3] :
( hAPP(c_Map_Omap__add(X42,X55,X21,X3),X56) != c_Option_Ooption_ONone(X3)
| hAPP(X55,X56) = c_Option_Ooption_ONone(X3) ),
c_0_382 ).
fof(c_0_1293,axiom,
! [X55,X42,X56,X21,X3] :
( hAPP(c_Map_Omap__add(X42,X55,X21,X3),X56) != c_Option_Ooption_ONone(X3)
| hAPP(X42,X56) = c_Option_Ooption_ONone(X3) ),
c_0_383 ).
fof(c_0_1294,plain,
! [X19,X8,X3] :
( X19 = X8
| ~ hBOOL(hAPP(hAPP(c_in(X3),X19),hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))))) ),
inference(fof_simplification,[status(thm)],[c_0_384]) ).
fof(c_0_1295,axiom,
! [X24,X23,X19,X8,X3] :
( hAPP(hAPP(c_Set_Oinsert(X3),X8),hAPP(hAPP(c_Set_Oinsert(X3),X19),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X3),X23),hAPP(hAPP(c_Set_Oinsert(X3),X24),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))))
| X19 = X23
| X19 = X24 ),
c_0_385 ).
fof(c_0_1296,axiom,
! [X24,X23,X19,X8,X3] :
( hAPP(hAPP(c_Set_Oinsert(X3),X8),hAPP(hAPP(c_Set_Oinsert(X3),X19),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X3),X23),hAPP(hAPP(c_Set_Oinsert(X3),X24),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))))
| X8 = X24
| X19 = X24 ),
c_0_386 ).
fof(c_0_1297,axiom,
! [X24,X23,X19,X8,X3] :
( hAPP(hAPP(c_Set_Oinsert(X3),X8),hAPP(hAPP(c_Set_Oinsert(X3),X19),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X3),X23),hAPP(hAPP(c_Set_Oinsert(X3),X24),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))))
| X19 = X23
| X8 = X23 ),
c_0_387 ).
fof(c_0_1298,axiom,
! [X24,X23,X19,X8,X3] :
( hAPP(hAPP(c_Set_Oinsert(X3),X8),hAPP(hAPP(c_Set_Oinsert(X3),X19),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X3),X23),hAPP(hAPP(c_Set_Oinsert(X3),X24),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))))
| X8 = X24
| X8 = X23 ),
c_0_388 ).
fof(c_0_1299,plain,
! [X57,X38,X21,X3] :
( ~ class_HOL_Oord(X21)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,X21)),X38),X57))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,X21)),X38),X57)) ),
inference(fof_simplification,[status(thm)],[c_0_389]) ).
fof(c_0_1300,plain,
! [X23,X13,X9,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X3),X23),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X23),c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(X3,tc_bool)))) ),
inference(fof_simplification,[status(thm)],[c_0_390]) ).
fof(c_0_1301,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OlessThan(X12,X3)),c_SetInterval_Oord__class_OlessThan(X14,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_391]) ).
fof(c_0_1302,plain,
! [X13,X9,X3] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X3),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X3),X3),X9)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X3),X3),X13))
| X13 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X13,X3)
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_392]) ).
fof(c_0_1303,plain,
! [X8,X9,X3] :
( hAPP(hAPP(c_Set_Oinsert(X3),X8),c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))) = X9
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_393]) ).
fof(c_0_1304,plain,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),c_HOL_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19))) ),
inference(fof_simplification,[status(thm)],[c_0_394]) ).
fof(c_0_1305,plain,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19))) ),
inference(fof_simplification,[status(thm)],[c_0_395]) ).
fof(c_0_1306,plain,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),c_HOL_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19))) ),
inference(fof_simplification,[status(thm)],[c_0_396]) ).
fof(c_0_1307,plain,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19))) ),
inference(fof_simplification,[status(thm)],[c_0_397]) ).
fof(c_0_1308,plain,
! [X14,X12,X49,X50,X51,X3] :
( hBOOL(hAPP(hAPP(X49,hAPP(hAPP(X51,X12),X14)),X14))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
inference(fof_simplification,[status(thm)],[c_0_398]) ).
fof(c_0_1309,plain,
! [X14,X12,X49,X50,X51,X3] :
( hBOOL(hAPP(hAPP(X49,hAPP(hAPP(X51,X12),X14)),X12))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
inference(fof_simplification,[status(thm)],[c_0_399]) ).
fof(c_0_1310,plain,
! [X57,X38,X21,X3] :
( X38 = X57
| ~ c_Map_Omap__le(X57,X38,X3,X21)
| ~ c_Map_Omap__le(X38,X57,X3,X21) ),
inference(fof_simplification,[status(thm)],[c_0_400]) ).
fof(c_0_1311,axiom,
! [X25,X26,X27,X28,X29,X30,X3] :
( c_Hoare__Mirabelle_Otriple_Otriple(X28,X30,X26,X3) != c_Hoare__Mirabelle_Otriple_Otriple(X27,X29,X25,X3)
| X26 = X25 ),
c_0_401 ).
fof(c_0_1312,axiom,
! [X25,X26,X27,X28,X29,X30,X3] :
( c_Hoare__Mirabelle_Otriple_Otriple(X28,X30,X26,X3) != c_Hoare__Mirabelle_Otriple_Otriple(X27,X29,X25,X3)
| X30 = X29 ),
c_0_402 ).
fof(c_0_1313,axiom,
! [X25,X26,X27,X28,X29,X30,X3] :
( c_Hoare__Mirabelle_Otriple_Otriple(X28,X30,X26,X3) != c_Hoare__Mirabelle_Otriple_Otriple(X27,X29,X25,X3)
| X28 = X27 ),
c_0_403 ).
fof(c_0_1314,plain,
! [X12,X57,X38,X21,X3] :
( ~ class_HOL_Oord(X21)
| hBOOL(hAPP(hAPP(c_lessequals(X21),hAPP(X38,X12)),hAPP(X57,X12)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,X21)),X38),X57)) ),
inference(fof_simplification,[status(thm)],[c_0_404]) ).
fof(c_0_1315,plain,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_405]) ).
fof(c_0_1316,plain,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_406]) ).
fof(c_0_1317,plain,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_407]) ).
fof(c_0_1318,plain,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_408]) ).
fof(c_0_1319,plain,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_409]) ).
fof(c_0_1320,plain,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_410]) ).
fof(c_0_1321,plain,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_411]) ).
fof(c_0_1322,plain,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_412]) ).
fof(c_0_1323,plain,
! [X23,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X23),X9))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X23),c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(X3,tc_bool)))) ),
inference(fof_simplification,[status(thm)],[c_0_413]) ).
fof(c_0_1324,plain,
! [X12,X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(c_Finite__Set_Olinorder__class_OMin(X3),X9) = X12
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(X9,X12,X3)),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_414]) ).
fof(c_0_1325,plain,
! [X12,X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(c_Finite__Set_Olinorder__class_OMax(X3),X9) = X12
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| hBOOL(hAPP(hAPP(c_in(X3),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(X9,X12,X3)),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_415]) ).
fof(c_0_1326,plain,
! [X13,X9,X3] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),c_HOL_Ominus__class_Ominus(X13,X9,tc_fun(X3,tc_bool))) = X13
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_416]) ).
fof(c_0_1327,plain,
! [X8,X13,X9,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X8),X13)) = hAPP(hAPP(c_Set_Oinsert(X3),X8),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_417]) ).
fof(c_0_1328,plain,
! [X8,X13,X9,X3] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X8),X13),tc_fun(X3,tc_bool)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_418]) ).
fof(c_0_1329,plain,
! [X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),X13))
| X9 = X13
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_419]) ).
fof(c_0_1330,plain,
! [X13,X9,X3] :
( X9 = X13
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),X13))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_420]) ).
fof(c_0_1331,plain,
! [X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_421]) ).
fof(c_0_1332,plain,
! [X12,X24,X23,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X24)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X24)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_422]) ).
fof(c_0_1333,plain,
! [X70,X14,X12,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X14)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X70)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X70)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_423]) ).
fof(c_0_1334,plain,
! [X24,X23,X19,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X23,X24,X3)) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X8),X23),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X19),X24),X3) ),
inference(fof_simplification,[status(thm)],[c_0_424]) ).
fof(c_0_1335,plain,
! [X6,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X6),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X6),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_425]) ).
fof(c_0_1336,plain,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X12),X13))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_426]) ).
fof(c_0_1337,plain,
! [X23,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X23),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X23),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_427]) ).
fof(c_0_1338,plain,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X12),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_428]) ).
fof(c_0_1339,plain,
! [X23,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X23),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X23),X9))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_429]) ).
fof(c_0_1340,plain,
! [X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(X9,X3)),c_Finite__Set_Ocard(X13,X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X9),X13))
| ~ c_Finite__Set_Ofinite(X13,X3) ),
inference(fof_simplification,[status(thm)],[c_0_430]) ).
fof(c_0_1341,plain,
! [X83,X84,X86,X85,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X85),X86)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X84),X83)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X85),X84)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X86),X83)) ),
inference(fof_simplification,[status(thm)],[c_0_431]) ).
fof(c_0_1342,plain,
! [X83,X84,X86,X85,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X85),X86)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X84),X83)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X85),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X86),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X84),X83))) ),
inference(fof_simplification,[status(thm)],[c_0_432]) ).
fof(c_0_1343,plain,
! [X24,X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X24)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X24)) ),
inference(fof_simplification,[status(thm)],[c_0_433]) ).
fof(c_0_1344,plain,
! [X37,X13,X9,X3] :
( hAPP(c_Finite__Set_Ofold1(X37,X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13)) = hAPP(hAPP(X37,hAPP(c_Finite__Set_Ofold1(X37,X3),X9)),hAPP(c_Finite__Set_Ofold1(X37,X3),X13))
| X13 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X13,X3)
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X37,X3) ),
inference(fof_simplification,[status(thm)],[c_0_434]) ).
fof(c_0_1345,plain,
! [X12,X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(c_Finite__Set_Olinorder__class_OMin(X3),X9) = X12
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(X9,X12,X3)))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_435]) ).
fof(c_0_1346,plain,
! [X12,X9,X3] :
( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)),X3) = c_Finite__Set_Ocard(X9,X3)
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_436]) ).
fof(c_0_1347,plain,
! [X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X8)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_437]) ).
fof(c_0_1348,plain,
! [X8,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X8)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_438]) ).
fof(c_0_1349,plain,
! [X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X8)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_439]) ).
fof(c_0_1350,plain,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ominus__class_Ominus(X8,X19,X3)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_440]) ).
fof(c_0_1351,plain,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ominus__class_Ominus(X8,X19,X3)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_441]) ).
fof(c_0_1352,plain,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_442]) ).
fof(c_0_1353,plain,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_443]) ).
fof(c_0_1354,plain,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_444]) ).
fof(c_0_1355,plain,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),c_HOL_Ozero__class_Ozero(X3))) ),
inference(fof_simplification,[status(thm)],[c_0_445]) ).
fof(c_0_1356,plain,
! [X8,X9,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X3),X3),X9)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_446]) ).
fof(c_0_1357,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X70),X14))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X70),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X70),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14))) ),
inference(fof_simplification,[status(thm)],[c_0_447]) ).
fof(c_0_1358,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),X14))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14))) ),
inference(fof_simplification,[status(thm)],[c_0_448]) ).
fof(c_0_1359,plain,
! [X70,X14,X12,X49,X50,X51,X3] :
( hAPP(hAPP(X51,hAPP(hAPP(X51,X12),X14)),X70) = hAPP(hAPP(X51,X12),hAPP(hAPP(X51,X14),X70))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
inference(fof_simplification,[status(thm)],[c_0_449]) ).
fof(c_0_1360,plain,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_450]) ).
fof(c_0_1361,plain,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X23))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_451]) ).
fof(c_0_1362,plain,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X23))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_452]) ).
fof(c_0_1363,plain,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X23))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_453]) ).
fof(c_0_1364,plain,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13),X12))
| ~ hBOOL(hAPP(X13,X12))
| ~ hBOOL(hAPP(X9,X12)) ),
inference(fof_simplification,[status(thm)],[c_0_454]) ).
fof(c_0_1365,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X23))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_455]) ).
fof(c_0_1366,plain,
! [X12,X19,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X8),X19)),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_456]) ).
fof(c_0_1367,plain,
! [X12,X19,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X8),X19)),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_457]) ).
fof(c_0_1368,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14)),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_458]) ).
fof(c_0_1369,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14)),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_459]) ).
fof(c_0_1370,plain,
! [X12,X19,X8,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X8),X19)),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_460]) ).
fof(c_0_1371,plain,
! [X12,X19,X8,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X8),X19)),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_461]) ).
fof(c_0_1372,plain,
! [X12,X19,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X8),X19)),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_462]) ).
fof(c_0_1373,plain,
! [X12,X19,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X8),X19)),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_463]) ).
fof(c_0_1374,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14)),X70))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_464]) ).
fof(c_0_1375,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14)),X70))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_465]) ).
fof(c_0_1376,plain,
! [X12,X19,X8,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X8),X19)),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_466]) ).
fof(c_0_1377,plain,
! [X12,X19,X8,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X8),X19)),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_467]) ).
fof(c_0_1378,plain,
! [X12,X42,X9,X21,X3] :
( hAPP(c_Map_Orestrict__map(X42,X9,X3,X21),X12) = hAPP(X42,X12)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_468]) ).
fof(c_0_1379,plain,
! [X23,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X23),c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(X3,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(X3),X23),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X23),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_469]) ).
fof(c_0_1380,plain,
! [X23,X13,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X23),c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(X3,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(X3),X23),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X23),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_470]) ).
fof(c_0_1381,plain,
! [X15,X6,X16,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X6),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool))),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X6),X15),X3) ),
inference(fof_simplification,[status(thm)],[c_0_471]) ).
fof(c_0_1382,plain,
! [X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X8))) ),
inference(fof_simplification,[status(thm)],[c_0_472]) ).
fof(c_0_1383,plain,
! [X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X8))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X8))) ),
inference(fof_simplification,[status(thm)],[c_0_473]) ).
fof(c_0_1384,plain,
! [X12,X19,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_474]) ).
fof(c_0_1385,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X14),X70)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_475]) ).
fof(c_0_1386,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X14),X70)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_476]) ).
fof(c_0_1387,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),X14))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_477]) ).
fof(c_0_1388,plain,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X14),X70)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_478]) ).
fof(c_0_1389,plain,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X14),X70)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_479]) ).
fof(c_0_1390,plain,
! [X12,X19,X8,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_480]) ).
fof(c_0_1391,plain,
! [X76,X35,X36,X77,X78] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X78,X77)),X36),X76))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X77),X35),X76))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X78),X36),X35)) ),
inference(fof_simplification,[status(thm)],[c_0_481]) ).
fof(c_0_1392,plain,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13),X12))
| ~ hBOOL(hAPP(X13,X12)) ),
inference(fof_simplification,[status(thm)],[c_0_482]) ).
fof(c_0_1393,plain,
! [X12,X13,X9,X3] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13),X12))
| ~ hBOOL(hAPP(X9,X12)) ),
inference(fof_simplification,[status(thm)],[c_0_483]) ).
fof(c_0_1394,plain,
! [X9,X3] :
( X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) ),
inference(fof_simplification,[status(thm)],[c_0_484]) ).
fof(c_0_1395,plain,
! [X8,X13,X9,X3] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X9,hAPP(hAPP(c_Set_Oinsert(X3),X8),X13),tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(X3,tc_bool)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_485]) ).
fof(c_0_1396,plain,
! [X70,X14,X12,X49,X50,X51,X3] :
( hAPP(hAPP(X51,X12),hAPP(hAPP(X51,X14),X70)) = hAPP(hAPP(X51,X14),hAPP(hAPP(X51,X12),X70))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
inference(fof_simplification,[status(thm)],[c_0_486]) ).
fof(c_0_1397,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X14),X70)),X12) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X14),X12)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X70),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_487]) ).
fof(c_0_1398,plain,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Odistrib__lattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X14),X70)),X12) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X14),X12)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X70),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_488]) ).
fof(c_0_1399,plain,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add__join(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X8),X19)),X23) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_489]) ).
fof(c_0_1400,plain,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X8),X19)),X23) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_490]) ).
fof(c_0_1401,plain,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X8),X19)),X23) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_491]) ).
fof(c_0_1402,plain,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X8),X19)),X23) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_492]) ).
fof(c_0_1403,plain,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Odistrib__lattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X14),X70)),X12) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X14),X12)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X70),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_493]) ).
fof(c_0_1404,plain,
! [X70,X14,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14)),X70) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X70)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X14),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_494]) ).
fof(c_0_1405,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X14),X70)),X12) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X14),X12)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X70),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_495]) ).
fof(c_0_1406,plain,
! [X70,X14,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14)),X70) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X70)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X14),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_496]) ).
fof(c_0_1407,plain,
! [X42,X19,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X42)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X42)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),X42) ),
inference(fof_simplification,[status(thm)],[c_0_497]) ).
fof(c_0_1408,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),X23) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_498]) ).
fof(c_0_1409,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),X23) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_499]) ).
fof(c_0_1410,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OlessThan(X12,X3)),c_SetInterval_Oord__class_OlessThan(X14,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_500]) ).
fof(c_0_1411,axiom,
! [X12,X42,X9,X21,X3] :
( hAPP(c_Map_Orestrict__map(X42,X9,X3,X21),X12) = c_Option_Ooption_ONone(X21)
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9)) ),
c_0_501 ).
fof(c_0_1412,axiom,
! [X12,X55,X42,X56,X21,X3] :
( hAPP(X42,X56) != hAPP(c_Option_Ooption_OSome(X3),X12)
| hAPP(X55,X56) != c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X42,X55,X21,X3),X56) = hAPP(c_Option_Ooption_OSome(X3),X12) ),
c_0_502 ).
fof(c_0_1413,plain,
! [X12,X13,X9,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_503]) ).
fof(c_0_1414,plain,
! [X12,X19,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X8),X19))) ),
inference(fof_simplification,[status(thm)],[c_0_504]) ).
fof(c_0_1415,plain,
! [X12,X19,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X8),X19))) ),
inference(fof_simplification,[status(thm)],[c_0_505]) ).
fof(c_0_1416,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X14),X70))) ),
inference(fof_simplification,[status(thm)],[c_0_506]) ).
fof(c_0_1417,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X14),X70))) ),
inference(fof_simplification,[status(thm)],[c_0_507]) ).
fof(c_0_1418,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14))) ),
inference(fof_simplification,[status(thm)],[c_0_508]) ).
fof(c_0_1419,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),X14))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14))) ),
inference(fof_simplification,[status(thm)],[c_0_509]) ).
fof(c_0_1420,plain,
! [X12,X19,X8,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X8),X19))) ),
inference(fof_simplification,[status(thm)],[c_0_510]) ).
fof(c_0_1421,plain,
! [X12,X19,X8,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X8),X19))) ),
inference(fof_simplification,[status(thm)],[c_0_511]) ).
fof(c_0_1422,plain,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X14),X70))) ),
inference(fof_simplification,[status(thm)],[c_0_512]) ).
fof(c_0_1423,plain,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X14),X70))) ),
inference(fof_simplification,[status(thm)],[c_0_513]) ).
fof(c_0_1424,plain,
! [X13,X9,X3] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13) = X13
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_514]) ).
fof(c_0_1425,plain,
! [X13,X9,X3] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13) = X9
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X13),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_515]) ).
fof(c_0_1426,plain,
! [X13,X9,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13) = X9
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_516]) ).
fof(c_0_1427,plain,
! [X13,X9,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13) = X13
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X13),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_517]) ).
fof(c_0_1428,axiom,
! [X8,X80,X13,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X3),X8),X13)),X80) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X13),X80)
| hBOOL(hAPP(hAPP(c_in(X3),X8),X80)) ),
c_0_518 ).
fof(c_0_1429,plain,
! [X19,X8,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| X8 = X19
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),hAPP(hAPP(c_Set_Oinsert(X3),X19),X9))) ),
inference(fof_simplification,[status(thm)],[c_0_519]) ).
fof(c_0_1430,plain,
! [X19,X8,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X3),X8),hAPP(hAPP(c_Set_Oinsert(X3),X19),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X8),X19) ),
inference(fof_simplification,[status(thm)],[c_0_520]) ).
fof(c_0_1431,plain,
! [X19,X8,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X3),X8),hAPP(hAPP(c_Set_Oinsert(X3),X19),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X8),X19) ),
inference(fof_simplification,[status(thm)],[c_0_521]) ).
fof(c_0_1432,plain,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X12)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X14),X14)) != c_HOL_Ozero__class_Ozero(X3)
| X14 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_522]) ).
fof(c_0_1433,plain,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X12)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X14),X14)) != c_HOL_Ozero__class_Ozero(X3)
| X12 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_523]) ).
fof(c_0_1434,plain,
! [X13,X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(c_Finite__Set_Olinorder__class_OMax(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),hAPP(c_Finite__Set_Olinorder__class_OMax(X3),X9)),hAPP(c_Finite__Set_Olinorder__class_OMax(X3),X13))
| X13 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X13,X3)
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_524]) ).
fof(c_0_1435,plain,
! [X13,X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(c_Finite__Set_Olinorder__class_OMin(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),hAPP(c_Finite__Set_Olinorder__class_OMin(X3),X9)),hAPP(c_Finite__Set_Olinorder__class_OMin(X3),X13))
| X13 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X13,X3)
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_525]) ).
fof(c_0_1436,axiom,
! [X12,X55,X42,X56,X21,X3] :
( hAPP(X55,X56) != hAPP(c_Option_Ooption_OSome(X3),X12)
| hAPP(c_Map_Omap__add(X42,X55,X21,X3),X56) = hAPP(c_Option_Ooption_OSome(X3),X12) ),
c_0_526 ).
fof(c_0_1437,axiom,
! [X71,X55,X42,X56,X21,X3] :
( hAPP(X55,X56) != hAPP(c_Option_Ooption_OSome(X3),X71)
| hAPP(c_Map_Omap__add(X42,X55,X21,X3),X56) = hAPP(c_Option_Ooption_OSome(X3),X71) ),
c_0_527 ).
fof(c_0_1438,axiom,
! [X55,X42,X56,X21,X3] :
( hAPP(X42,X56) != c_Option_Ooption_ONone(X3)
| hAPP(X55,X56) != c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X42,X55,X21,X3),X56) = c_Option_Ooption_ONone(X3) ),
c_0_528 ).
fof(c_0_1439,axiom,
! [X12,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))))
| c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),X3) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) ),
c_0_529 ).
fof(c_0_1440,plain,
! [X14,X12,X49,X50,X51,X3] :
( hAPP(hAPP(X51,X12),X14) = X14
| ~ hBOOL(hAPP(hAPP(X49,X14),X12))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
inference(fof_simplification,[status(thm)],[c_0_530]) ).
fof(c_0_1441,plain,
! [X14,X12,X49,X50,X51,X3] :
( hAPP(hAPP(X51,X12),X14) = X12
| ~ hBOOL(hAPP(hAPP(X49,X12),X14))
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
inference(fof_simplification,[status(thm)],[c_0_531]) ).
fof(c_0_1442,plain,
! [X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X8)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_532]) ).
fof(c_0_1443,plain,
! [X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X8)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),c_HOL_Ozero__class_Ozero(X3)),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_533]) ).
fof(c_0_1444,plain,
! [X14,X12,X49,X50,X51,X3] :
( hAPP(hAPP(X51,X12),hAPP(hAPP(X51,X12),X14)) = hAPP(hAPP(X51,X12),X14)
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
inference(fof_simplification,[status(thm)],[c_0_534]) ).
fof(c_0_1445,plain,
! [X14,X12,X49,X50,X51,X3] :
( hAPP(hAPP(X51,X12),X14) != X12
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3)
| hBOOL(hAPP(hAPP(X49,X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_535]) ).
fof(c_0_1446,plain,
! [X70,X14,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14),X70,X3) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),c_HOL_Ominus__class_Ominus(X12,X70,X3)),c_HOL_Ominus__class_Ominus(X14,X70,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_536]) ).
fof(c_0_1447,plain,
! [X70,X14,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14),X70,X3) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),c_HOL_Ominus__class_Ominus(X12,X70,X3)),c_HOL_Ominus__class_Ominus(X14,X70,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_537]) ).
fof(c_0_1448,plain,
! [X12,X33,X18,X3] :
( hBOOL(hAPP(X33,X12))
| ~ hBOOL(hAPP(X18,X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X18),X33)) ),
inference(fof_simplification,[status(thm)],[c_0_538]) ).
fof(c_0_1449,plain,
! [X12,X33,X18,X3] :
( hBOOL(hAPP(X33,X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X18),X33))
| ~ hBOOL(hAPP(X18,X12)) ),
inference(fof_simplification,[status(thm)],[c_0_539]) ).
fof(c_0_1450,plain,
! [X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3)))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3)) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_540]) ).
fof(c_0_1451,plain,
! [X42,X8,X21,X3] :
( hAPP(X42,X8) != c_Option_Ooption_ONone(X21)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),c_Map_Odom(X42,X3,X21))) ),
inference(fof_simplification,[status(thm)],[c_0_541]) ).
fof(c_0_1452,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14)),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_542]) ).
fof(c_0_1453,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14)),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_543]) ).
fof(c_0_1454,plain,
! [X14,X12,X3] :
( ~ class_Lattices_Olattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14)),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_544]) ).
fof(c_0_1455,plain,
! [X14,X12,X3] :
( ~ class_Lattices_Olattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14)),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_545]) ).
fof(c_0_1456,plain,
! [X14,X12,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14)),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_546]) ).
fof(c_0_1457,plain,
! [X14,X12,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14)),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_547]) ).
fof(c_0_1458,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X14),X70)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_548]) ).
fof(c_0_1459,plain,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Odistrib__lattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X14),X70)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_549]) ).
fof(c_0_1460,plain,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add__join(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X19),X23)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_550]) ).
fof(c_0_1461,plain,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X19),X23)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_551]) ).
fof(c_0_1462,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),X23) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),X19) ),
inference(fof_simplification,[status(thm)],[c_0_552]) ).
fof(c_0_1463,plain,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X19),X23)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_553]) ).
fof(c_0_1464,plain,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X19),X23)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_554]) ).
fof(c_0_1465,plain,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Odistrib__lattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X14),X70)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_555]) ).
fof(c_0_1466,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X14),X70)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_556]) ).
fof(c_0_1467,plain,
! [X84,X86,X85,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X85),X86)),X84) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X85),X84)),X86) ),
inference(fof_simplification,[status(thm)],[c_0_557]) ).
fof(c_0_1468,plain,
! [X70,X14,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X14),X70)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X14)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_558]) ).
fof(c_0_1469,axiom,
! [X13,X9,X3] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13) != X13
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
c_0_559 ).
fof(c_0_1470,plain,
! [X14,X12,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X14) != c_HOL_Ozero__class_Ozero(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X14))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X12))
| X14 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_560]) ).
fof(c_0_1471,plain,
! [X14,X12,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X14) != c_HOL_Ozero__class_Ozero(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X14))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),X12))
| X12 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_561]) ).
fof(c_0_1472,plain,
! [X38,X9,X3] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X38,X9,X3),c_ATP__Linkup_Osko__Finite__Set__Xfinite__nonempty__imp__fold1Set__1__1(X9,X38,X3)))
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_562]) ).
fof(c_0_1473,plain,
! [X12,X89,X24,X23,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X89),X23)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X89),X24))
| X23 = X24
| X89 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_563]) ).
fof(c_0_1474,axiom,
! [X12,X38,X9,X21,X3] :
( hAPP(X38,X12) != c_Option_Ooption_ONone(X3)
| c_HOL_Ominus__class_Ominus(c_Map_Odom(X38,X21,X3),hAPP(hAPP(c_Set_Oinsert(X21),X12),X9),tc_fun(X21,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Map_Odom(X38,X21,X3),X9,tc_fun(X21,tc_bool)) ),
c_0_564 ).
fof(c_0_1475,axiom,
! [X8,X13,X9,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),hAPP(hAPP(c_Set_Oinsert(X3),X8),X13)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13)
| hBOOL(hAPP(hAPP(c_in(X3),X8),X9)) ),
c_0_565 ).
fof(c_0_1476,axiom,
! [X12,X9,X3] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X3),X12),X9),hAPP(hAPP(c_Set_Oinsert(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool)) = X9
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9)) ),
c_0_566 ).
fof(c_0_1477,plain,
! [X13,X9,X3] :
( c_Finite__Set_Ofinite(X9,X3)
| ~ c_Finite__Set_Ofinite(X13,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_567]) ).
fof(c_0_1478,plain,
! [X13,X9,X3] :
( c_Finite__Set_Ofinite(X9,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X9),X13))
| ~ c_Finite__Set_Ofinite(X13,X3) ),
inference(fof_simplification,[status(thm)],[c_0_568]) ).
fof(c_0_1479,axiom,
! [X12,X13,X9,X3] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X3),X12),X9),X13,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X3),X12),c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(X3,tc_bool)))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X13)) ),
c_0_569 ).
fof(c_0_1480,axiom,
! [X23,X9,X21,X3] :
( c_Set_Ovimage(c_COMBK(X23,X21,X3),X9,X3,X21) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X21),X23),X9)) ),
c_0_570 ).
fof(c_0_1481,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X70),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X70),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_571]) ).
fof(c_0_1482,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X70),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X70),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_572]) ).
fof(c_0_1483,plain,
! [X12,X19,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_573]) ).
fof(c_0_1484,plain,
! [X12,X19,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_574]) ).
fof(c_0_1485,plain,
! [X12,X19,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_575]) ).
fof(c_0_1486,plain,
! [X12,X19,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_576]) ).
fof(c_0_1487,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_577]) ).
fof(c_0_1488,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_578]) ).
fof(c_0_1489,plain,
! [X12,X19,X8,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_579]) ).
fof(c_0_1490,plain,
! [X12,X19,X8,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_580]) ).
fof(c_0_1491,plain,
! [X12,X19,X8,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_581]) ).
fof(c_0_1492,plain,
! [X12,X19,X8,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X8),X19)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_582]) ).
fof(c_0_1493,plain,
! [X16,X58,X3] :
( c_Finite__Set_Ofinite(X58,X3)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X58),X16),X3) ),
inference(fof_simplification,[status(thm)],[c_0_583]) ).
fof(c_0_1494,plain,
! [X16,X58,X3] :
( c_Finite__Set_Ofinite(X16,X3)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X58),X16),X3) ),
inference(fof_simplification,[status(thm)],[c_0_584]) ).
fof(c_0_1495,plain,
! [X12,X38,X9,X21,X3] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X21)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X21)
| hAPP(X38,X12) != c_HOL_Ozero__class_Ozero(X21)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Finite__Set_Ofinite(X9,X3)
| c_Finite__Set_Osetprod(X38,X9,X3,X21) = c_HOL_Ozero__class_Ozero(X21) ),
inference(fof_simplification,[status(thm)],[c_0_585]) ).
fof(c_0_1496,plain,
! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3))) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_586]) ).
fof(c_0_1497,plain,
! [X19,X8,X9,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X8),hAPP(hAPP(c_Set_Oinsert(X3),X19),X9)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_587]) ).
fof(c_0_1498,plain,
! [X19,X8,X13,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X8),hAPP(hAPP(c_Set_Oinsert(X3),X19),X13)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_588]) ).
fof(c_0_1499,plain,
! [X12,X38,X9,X21,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X21)
| hAPP(X38,X12) != c_HOL_Ozero__class_Ozero(X21)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Finite__Set_Ofinite(X9,X3)
| c_Finite__Set_Osetprod(X38,X9,X3,X21) = c_HOL_Ozero__class_Ozero(X21) ),
inference(fof_simplification,[status(thm)],[c_0_589]) ).
fof(c_0_1500,plain,
! [X12,X9,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X3),X3),hAPP(hAPP(c_Set_Oinsert(X3),X12),X9)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X3),X3),X9))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Finite__Set_Ofinite(X9,X3)
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_590]) ).
fof(c_0_1501,plain,
! [X12,X9,X3] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X3),X3),hAPP(hAPP(c_Set_Oinsert(X3),X12),X9)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X3),X3),X9))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Finite__Set_Ofinite(X9,X3)
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_591]) ).
fof(c_0_1502,plain,
! [X14,X12,X49,X50,X51,X3] :
( hAPP(hAPP(X51,X12),X14) = hAPP(hAPP(X51,X14),X12)
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
inference(fof_simplification,[status(thm)],[c_0_592]) ).
fof(c_0_1503,plain,
! [X12,X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),hAPP(c_Finite__Set_Olinorder__class_OMin(X3),X9)),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_593]) ).
fof(c_0_1504,plain,
! [X68,X14,X69,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X12,X14,X3) != c_HOL_Ominus__class_Ominus(X69,X68,X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X68),X69))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_594]) ).
fof(c_0_1505,plain,
! [X68,X14,X69,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X12,X14,X3) != c_HOL_Ominus__class_Ominus(X69,X68,X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X68),X69)) ),
inference(fof_simplification,[status(thm)],[c_0_595]) ).
fof(c_0_1506,plain,
! [X68,X14,X69,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X12,X14,X3) != c_HOL_Ominus__class_Ominus(X69,X68,X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X69),X68))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_596]) ).
fof(c_0_1507,plain,
! [X68,X14,X69,X12,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X12,X14,X3) != c_HOL_Ominus__class_Ominus(X69,X68,X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X69),X68)) ),
inference(fof_simplification,[status(thm)],[c_0_597]) ).
fof(c_0_1508,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Opreorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X70))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X70))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_598]) ).
fof(c_0_1509,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),X14))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_599]) ).
fof(c_0_1510,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X70),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X70),X14))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_600]) ).
fof(c_0_1511,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X70),X14))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_601]) ).
fof(c_0_1512,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X70),X14))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_602]) ).
fof(c_0_1513,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Opreorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_603]) ).
fof(c_0_1514,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Opreorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X70))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_604]) ).
fof(c_0_1515,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Opreorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X70))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X70))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_605]) ).
fof(c_0_1516,plain,
! [X12,X37,X9,X3] :
( hAPP(c_Finite__Set_Ofold1(X37,X3),hAPP(hAPP(c_Set_Oinsert(X3),X12),X9)) = hAPP(hAPP(X37,X12),hAPP(c_Finite__Set_Ofold1(X37,X3),X9))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Finite__Set_Ofinite(X9,X3)
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__mult(X37,X3) ),
inference(fof_simplification,[status(thm)],[c_0_606]) ).
fof(c_0_1517,plain,
! [X12,X49,X50,X51,X3] :
( hAPP(hAPP(X51,X12),X12) = X12
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
inference(fof_simplification,[status(thm)],[c_0_607]) ).
fof(c_0_1518,plain,
! [X57,X38,X21] :
( ~ class_Lattices_Olattice(X21)
| hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,X21)),X38),X57),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X21),hAPP(X38,v_x)),hAPP(X57,v_x)) ),
inference(fof_simplification,[status(thm)],[c_0_608]) ).
fof(c_0_1519,plain,
! [X57,X38,X21] :
( ~ class_Lattices_Olattice(X21)
| hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,X21)),X38),X57),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X21),hAPP(X38,v_x)),hAPP(X57,v_x)) ),
inference(fof_simplification,[status(thm)],[c_0_609]) ).
fof(c_0_1520,plain,
! [X12,X13,X9,X3] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X3),X12),X9),X13,tc_fun(X3,tc_bool)) = c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X13)) ),
inference(fof_simplification,[status(thm)],[c_0_610]) ).
fof(c_0_1521,plain,
! [X56,X3] :
( ~ class_Orderings_Oorder(X3)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X3),X56),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),c_SetInterval_Oord__class_OlessThan(X56,X3),tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X3),X56),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) ),
inference(fof_simplification,[status(thm)],[c_0_611]) ).
fof(c_0_1522,plain,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X8),X19)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_612]) ).
fof(c_0_1523,plain,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Olattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14)),X70) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X14),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_613]) ).
fof(c_0_1524,plain,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14)),X70) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X14),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_614]) ).
fof(c_0_1525,plain,
! [X70,X14,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X14),X70)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X14)),X70) ),
inference(fof_simplification,[status(thm)],[c_0_615]) ).
fof(c_0_1526,plain,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),X23) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_616]) ).
fof(c_0_1527,plain,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Oab__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),X23) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_617]) ).
fof(c_0_1528,plain,
! [X24,X23,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X24)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)),X24) ),
inference(fof_simplification,[status(thm)],[c_0_618]) ).
fof(c_0_1529,plain,
! [X23,X19,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19)),X23) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_619]) ).
fof(c_0_1530,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14)),X70) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X14),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_620]) ).
fof(c_0_1531,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14)),X70) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X14),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_621]) ).
fof(c_0_1532,plain,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19)),X23) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_622]) ).
fof(c_0_1533,plain,
! [X84,X86,X85,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X85),X86)),X84) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X85),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X86),X84)) ),
inference(fof_simplification,[status(thm)],[c_0_623]) ).
fof(c_0_1534,plain,
! [X83,X84,X85,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X85),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X84),X83)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X85),X84)),X83) ),
inference(fof_simplification,[status(thm)],[c_0_624]) ).
fof(c_0_1535,plain,
! [X70,X14,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X14),X70)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X14)),X70) ),
inference(fof_simplification,[status(thm)],[c_0_625]) ).
fof(c_0_1536,plain,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Olattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14)),X70) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X14),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_626]) ).
fof(c_0_1537,plain,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14)),X70) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X14),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_627]) ).
fof(c_0_1538,plain,
! [X56,X91,X92] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X92)),X56))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X91),X56))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X92),X91)) ),
inference(fof_simplification,[status(thm)],[c_0_628]) ).
fof(c_0_1539,plain,
! [X49,X50,X51,X3] :
( c_OrderedGroup_Oab__semigroup__idem__mult(X51,X3)
| ~ c_Lattices_Olower__semilattice(X49,X50,X51,X3) ),
inference(fof_simplification,[status(thm)],[c_0_629]) ).
fof(c_0_1540,plain,
! [X14,X12,X9,X3] :
( hBOOL(hAPP(X9,X12))
| X14 = X12
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X14),X9),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_630]) ).
fof(c_0_1541,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Opreorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_631]) ).
fof(c_0_1542,plain,
! [X12,X9,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_Complete__Lattice_OInf__class_OInf(X9,X3)),X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_632]) ).
fof(c_0_1543,plain,
! [X70,X14,X12,X22,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X14),X70)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X14),X22)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X70) = X22 ),
inference(fof_simplification,[status(thm)],[c_0_633]) ).
fof(c_0_1544,plain,
! [X12,X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(c_Finite__Set_Olinorder__class_OMax(X3),X9)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_634]) ).
fof(c_0_1545,axiom,
! [X12,X13,X9,X3] :
( hAPP(hAPP(c_Set_Oinsert(X3),X12),X9) != hAPP(hAPP(c_Set_Oinsert(X3),X12),X13)
| hBOOL(hAPP(hAPP(c_in(X3),X12),X13))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| X9 = X13 ),
c_0_635 ).
fof(c_0_1546,plain,
! [X12,X18,X3] :
( ~ hBOOL(hAPP(X18,X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) ),
inference(fof_simplification,[status(thm)],[c_0_636]) ).
fof(c_0_1547,plain,
! [X15,X6,X16,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,X15,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X6),X15),X3) ),
inference(fof_simplification,[status(thm)],[c_0_637]) ).
fof(c_0_1548,plain,
! [X9,X21,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_Finite__Set_Osetsum(c_COMBK(c_HOL_Ozero__class_Ozero(X3),X3,X21),X9,X21,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_638]) ).
fof(c_0_1549,axiom,
! [X42,X19,X8,X21,X3] :
( hAPP(X42,X8) != hAPP(c_Option_Ooption_OSome(X3),X19)
| hBOOL(hAPP(hAPP(c_in(X21),X8),c_Map_Odom(X42,X21,X3))) ),
c_0_639 ).
fof(c_0_1550,plain,
! [X12,X9,X3] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X3),X3),hAPP(hAPP(c_Set_Oinsert(X3),X12),X9)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X3),X3),X9))
| ~ c_Finite__Set_Ofinite(X9,X3)
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_640]) ).
fof(c_0_1551,plain,
! [X56,X92,X3] :
( ~ class_HOL_Oord(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X92),X56))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X92),c_SetInterval_Oord__class_OlessThan(X56,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_641]) ).
fof(c_0_1552,plain,
! [X12,X18,X3] :
( hBOOL(hAPP(X18,X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) ),
inference(fof_simplification,[status(thm)],[c_0_642]) ).
fof(c_0_1553,axiom,
! [X13,X9,X3] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X9),X13) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(X3,tc_bool)) = X9 ),
c_0_643 ).
fof(c_0_1554,plain,
! [X16,X58,X3] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X58),X16),X3)
| ~ c_Finite__Set_Ofinite(X16,X3)
| ~ c_Finite__Set_Ofinite(X58,X3) ),
inference(fof_simplification,[status(thm)],[c_0_644]) ).
fof(c_0_1555,plain,
! [X16,X58,X3] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X58),X16),X3)
| ~ c_Finite__Set_Ofinite(X16,X3)
| ~ c_Finite__Set_Ofinite(X58,X3) ),
inference(fof_simplification,[status(thm)],[c_0_645]) ).
fof(c_0_1556,plain,
! [X14,X12,X49,X50,X3] :
( ~ hBOOL(hAPP(hAPP(X50,X12),X14))
| ~ hBOOL(hAPP(hAPP(X50,X14),X12))
| ~ c_Orderings_Olinorder(X49,X50,X3) ),
inference(fof_simplification,[status(thm)],[c_0_646]) ).
fof(c_0_1557,plain,
! [X14,X12,X49,X50,X3] :
( ~ hBOOL(hAPP(hAPP(X50,X12),X14))
| ~ hBOOL(hAPP(hAPP(X49,X14),X12))
| ~ c_Orderings_Olinorder(X49,X50,X3) ),
inference(fof_simplification,[status(thm)],[c_0_647]) ).
fof(c_0_1558,plain,
! [X14,X12,X49,X50,X3] :
( ~ hBOOL(hAPP(hAPP(X49,X12),X14))
| ~ hBOOL(hAPP(hAPP(X50,X14),X12))
| ~ c_Orderings_Olinorder(X49,X50,X3) ),
inference(fof_simplification,[status(thm)],[c_0_648]) ).
fof(c_0_1559,plain,
! [X12,X49,X50,X3] :
( ~ hBOOL(hAPP(hAPP(X49,X12),X12))
| ~ c_Orderings_Olinorder(X49,X50,X3)
| ~ hBOOL(hAPP(hAPP(X50,X12),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_649]) ).
fof(c_0_1560,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Oorder(X3)
| X12 = X14
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_650]) ).
fof(c_0_1561,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Oorder(X3)
| X12 = X14
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_651]) ).
fof(c_0_1562,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Oorder(X3)
| X12 = X14
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_652]) ).
fof(c_0_1563,plain,
! [X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_653]) ).
fof(c_0_1564,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_654]) ).
fof(c_0_1565,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_655]) ).
fof(c_0_1566,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_656]) ).
fof(c_0_1567,plain,
! [X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_HOL_Ozero__class_Ozero(X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X8))) ),
inference(fof_simplification,[status(thm)],[c_0_657]) ).
fof(c_0_1568,plain,
! [X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_658]) ).
fof(c_0_1569,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_659]) ).
fof(c_0_1570,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_660]) ).
fof(c_0_1571,plain,
! [X19,X8,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X8))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_661]) ).
fof(c_0_1572,axiom,
! [X42,X8,X21,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X8),c_Map_Odom(X42,X3,X21)))
| hAPP(X42,X8) = c_Option_Ooption_ONone(X21) ),
c_0_662 ).
fof(c_0_1573,plain,
! [X22,X6,X7,X23] :
( X22 = X6
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X23),X7),X22))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X23),X7),X6)) ),
inference(fof_simplification,[status(thm)],[c_0_663]) ).
fof(c_0_1574,plain,
! [X22,X88,X3] :
( ~ class_Orderings_Oorder(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),c_SetInterval_Oord__class_OlessThan(X88,X3)),c_SetInterval_Oord__class_OatLeastAtMost(X88,X22,X3)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_664]) ).
fof(c_0_1575,plain,
! [X37,X23,X19,X8,X3] :
( hAPP(hAPP(X37,hAPP(hAPP(X37,X8),X19)),X23) = hAPP(hAPP(X37,X8),hAPP(hAPP(X37,X19),X23))
| ~ c_OrderedGroup_Oab__semigroup__mult(X37,X3) ),
inference(fof_simplification,[status(thm)],[c_0_665]) ).
fof(c_0_1576,plain,
! [X12,X37,X9,X3] :
( hAPP(c_Finite__Set_Ofold1(X37,X3),hAPP(hAPP(c_Set_Oinsert(X3),X12),X9)) = hAPP(hAPP(X37,X12),hAPP(c_Finite__Set_Ofold1(X37,X3),X9))
| ~ c_Finite__Set_Ofinite(X9,X3)
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X37,X3) ),
inference(fof_simplification,[status(thm)],[c_0_666]) ).
fof(c_0_1577,plain,
! [X56,X92,X3] :
( ~ class_HOL_Oord(X3)
| hBOOL(hAPP(hAPP(c_in(X3),X92),c_SetInterval_Oord__class_OlessThan(X56,X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X92),X56)) ),
inference(fof_simplification,[status(thm)],[c_0_667]) ).
fof(c_0_1578,plain,
! [X12,X9,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),c_Complete__Lattice_OSup__class_OSup(X9,X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_668]) ).
fof(c_0_1579,plain,
! [X49,X50,X38,X8,X21,X3] :
( ~ c_Orderings_Olinorder(X49,X50,X3)
| hAPP(c_Finite__Set_Ofold1(X38,X21),hAPP(hAPP(c_Set_Oinsert(X21),X8),c_Orderings_Obot__class_Obot(tc_fun(X21,tc_bool)))) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_669]) ).
fof(c_0_1580,axiom,
! [X19,X8,X3] :
( hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) != hAPP(hAPP(c_Set_Oinsert(X3),X19),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))
| X8 = X19 ),
c_0_670 ).
fof(c_0_1581,plain,
! [X16,X58,X3] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X58),X16),X3)
| ~ c_Finite__Set_Ofinite(X16,X3) ),
inference(fof_simplification,[status(thm)],[c_0_671]) ).
fof(c_0_1582,plain,
! [X16,X58,X3] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X58),X16),X3)
| ~ c_Finite__Set_Ofinite(X58,X3) ),
inference(fof_simplification,[status(thm)],[c_0_672]) ).
fof(c_0_1583,plain,
! [X70,X14,X12,X38,X21,X3] :
( hAPP(hAPP(X38,X12),hAPP(hAPP(X38,X14),X70)) = hAPP(hAPP(X38,X14),hAPP(hAPP(X38,X12),X70))
| ~ c_Finite__Set_Ofun__left__comm(X38,X3,X21) ),
inference(fof_simplification,[status(thm)],[c_0_673]) ).
fof(c_0_1584,plain,
! [X12,X9,X3] :
( c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(X3),X12),X9),X3) = c_Finite__Set_Ocard(X9,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_674]) ).
fof(c_0_1585,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X14),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14))) ),
inference(fof_simplification,[status(thm)],[c_0_675]) ).
fof(c_0_1586,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14))) ),
inference(fof_simplification,[status(thm)],[c_0_676]) ).
fof(c_0_1587,plain,
! [X14,X12,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14))) ),
inference(fof_simplification,[status(thm)],[c_0_677]) ).
fof(c_0_1588,plain,
! [X14,X12,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X14),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14))) ),
inference(fof_simplification,[status(thm)],[c_0_678]) ).
fof(c_0_1589,plain,
! [X14,X12,X3] :
( ~ class_Lattices_Olattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X14),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14))) ),
inference(fof_simplification,[status(thm)],[c_0_679]) ).
fof(c_0_1590,plain,
! [X14,X12,X3] :
( ~ class_Lattices_Olattice(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14))) ),
inference(fof_simplification,[status(thm)],[c_0_680]) ).
fof(c_0_1591,plain,
! [X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_in(X3),hAPP(c_Finite__Set_Olinorder__class_OMax(X3),X9)),X9))
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_681]) ).
fof(c_0_1592,plain,
! [X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_in(X3),hAPP(c_Finite__Set_Olinorder__class_OMin(X3),X9)),X9))
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_682]) ).
fof(c_0_1593,plain,
! [X55,X42] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X42),X55))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X55),c_Suc(X42))) ),
inference(fof_simplification,[status(thm)],[c_0_683]) ).
fof(c_0_1594,plain,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Olattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X14),X70)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X14),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_684]) ).
fof(c_0_1595,plain,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X14),X70)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X14),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_685]) ).
fof(c_0_1596,plain,
! [X70,X14,X12,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X14),X70)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X14),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_686]) ).
fof(c_0_1597,plain,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X23)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)) ),
inference(fof_simplification,[status(thm)],[c_0_687]) ).
fof(c_0_1598,plain,
! [X24,X23,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X24)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X24)) ),
inference(fof_simplification,[status(thm)],[c_0_688]) ).
fof(c_0_1599,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X14),X70)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X14),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_689]) ).
fof(c_0_1600,plain,
! [X70,X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X14),X70)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X14),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_690]) ).
fof(c_0_1601,plain,
! [X83,X84,X85,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X85),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X84),X83)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X84),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X85),X83)) ),
inference(fof_simplification,[status(thm)],[c_0_691]) ).
fof(c_0_1602,plain,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Olattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X14),X70)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X14),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_692]) ).
fof(c_0_1603,plain,
! [X70,X14,X12,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X14),X70)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X14),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X70)) ),
inference(fof_simplification,[status(thm)],[c_0_693]) ).
fof(c_0_1604,plain,
! [X38,X21,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_Finite__Set_Osetsum(X38,c_Orderings_Obot__class_Obot(tc_fun(X21,tc_bool)),X21,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_694]) ).
fof(c_0_1605,plain,
! [X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_695]) ).
fof(c_0_1606,plain,
! [X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_696]) ).
fof(c_0_1607,plain,
! [X55,X42] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X42),X55))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X42)),c_Suc(X55))) ),
inference(fof_simplification,[status(thm)],[c_0_697]) ).
fof(c_0_1608,plain,
! [X14,X12,X49,X50,X3] :
( X12 = X14
| hBOOL(hAPP(hAPP(X50,X12),X14))
| ~ hBOOL(hAPP(hAPP(X49,X12),X14))
| ~ c_Orderings_Olinorder(X49,X50,X3) ),
inference(fof_simplification,[status(thm)],[c_0_698]) ).
fof(c_0_1609,plain,
! [X14,X12,X49,X50,X3] :
( X12 = X14
| ~ hBOOL(hAPP(hAPP(X49,X12),X14))
| hBOOL(hAPP(hAPP(X50,X12),X14))
| ~ c_Orderings_Olinorder(X49,X50,X3) ),
inference(fof_simplification,[status(thm)],[c_0_699]) ).
fof(c_0_1610,plain,
! [X13,X9,X3] :
( c_Finite__Set_Ofinite(X9,X3)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X13,X3) ),
inference(fof_simplification,[status(thm)],[c_0_700]) ).
fof(c_0_1611,axiom,
! [X13,X9,X3] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X13 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_701 ).
fof(c_0_1612,axiom,
! [X13,X9,X3] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X9),X13) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_702 ).
fof(c_0_1613,plain,
! [X8,X9,X3] :
( ~ class_Lattices_Olattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X8),hAPP(c_Finite__Set_Olattice__class_OInf__fin(X3),X9)) = X8
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_703]) ).
fof(c_0_1614,plain,
! [X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X8))
| X8 = X19
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_704]) ).
fof(c_0_1615,plain,
! [X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X8))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X19),X8))
| X8 = X19 ),
inference(fof_simplification,[status(thm)],[c_0_705]) ).
fof(c_0_1616,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Oorder(X3)
| X12 = X14
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_706]) ).
fof(c_0_1617,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14))
| X12 = X14
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_707]) ).
fof(c_0_1618,plain,
! [X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| X8 = X19
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_708]) ).
fof(c_0_1619,plain,
! [X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X8),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19))
| X8 = X19 ),
inference(fof_simplification,[status(thm)],[c_0_709]) ).
fof(c_0_1620,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| X12 = X14
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_710]) ).
fof(c_0_1621,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| X12 = X14
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_711]) ).
fof(c_0_1622,plain,
! [X14,X12,X9,X3] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X14),X9),X12))
| ~ hBOOL(hAPP(X9,X12)) ),
inference(fof_simplification,[status(thm)],[c_0_712]) ).
fof(c_0_1623,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_713]) ).
fof(c_0_1624,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Opreorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_714]) ).
fof(c_0_1625,plain,
! [X55,X42] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X42),X55))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X42)),X55)) ),
inference(fof_simplification,[status(thm)],[c_0_715]) ).
fof(c_0_1626,plain,
! [X12,X55] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X12)),c_Suc(X55)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X12),X55)) ),
inference(fof_simplification,[status(thm)],[c_0_716]) ).
fof(c_0_1627,plain,
! [X55,X42] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X42)),c_Suc(X55)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X42),X55)) ),
inference(fof_simplification,[status(thm)],[c_0_717]) ).
fof(c_0_1628,plain,
! [X12,X9,X3] :
( c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(X3),X12),X9),X3) = c_Suc(c_Finite__Set_Ocard(X9,X3))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X9))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_718]) ).
fof(c_0_1629,plain,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ominus__class_Ominus(X8,X19,X3)),X19) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_719]) ).
fof(c_0_1630,axiom,
! [X55,X42,X18] :
( hBOOL(hAPP(hAPP(X18,X55),X42))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X55),X42))
| X42 = X55
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X42),X55)) ),
c_0_720 ).
fof(c_0_1631,plain,
! [X38,X9,X21,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_Finite__Set_Osetsum(X38,X9,X21,X3) = c_HOL_Ozero__class_Ozero(X3)
| c_Finite__Set_Ofinite(X9,X21) ),
inference(fof_simplification,[status(thm)],[c_0_721]) ).
fof(c_0_1632,plain,
! [X38,X9,X21,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X21)
| c_Finite__Set_Osetsum(X38,X9,X3,X21) = c_HOL_Ozero__class_Ozero(X21)
| c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_722]) ).
fof(c_0_1633,plain,
! [X55,X42] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X42)),X55))
| c_Suc(X42) = X55
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X42),X55)) ),
inference(fof_simplification,[status(thm)],[c_0_723]) ).
fof(c_0_1634,plain,
! [X13,X9,X21] :
( ~ class_HOL_Ominus(X21)
| hAPP(c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(t_a,X21)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(X9,v_x),hAPP(X13,v_x),X21) ),
inference(fof_simplification,[status(thm)],[c_0_724]) ).
fof(c_0_1635,plain,
! [X12,X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(c_Finite__Set_Olinorder__class_OMin(X3),hAPP(hAPP(c_Set_Oinsert(X3),X12),X9)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),hAPP(c_Finite__Set_Olinorder__class_OMin(X3),X9))
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_725]) ).
fof(c_0_1636,plain,
! [X12,X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(c_Finite__Set_Olinorder__class_OMax(X3),hAPP(hAPP(c_Set_Oinsert(X3),X12),X9)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),hAPP(c_Finite__Set_Olinorder__class_OMax(X3),X9))
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_726]) ).
fof(c_0_1637,plain,
! [X79,X12,X3] :
( X79 = hAPP(c_Option_Ooption_OSome(X3),X12)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),c_Option_Oset(X79,X3))) ),
inference(fof_simplification,[status(thm)],[c_0_727]) ).
fof(c_0_1638,axiom,
! [X14,X12,X38,X21,X3] :
( hAPP(X38,X12) != hAPP(c_Option_Ooption_OSome(X3),X14)
| hAPP(hAPP(c_Set_Oinsert(X21),X12),c_Map_Odom(X38,X21,X3)) = c_Map_Odom(X38,X21,X3) ),
c_0_728 ).
fof(c_0_1639,plain,
! [X55,X42] :
( X42 = X55
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X42),X55))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X42),c_Suc(X55))) ),
inference(fof_simplification,[status(thm)],[c_0_729]) ).
fof(c_0_1640,plain,
! [X55,X42] :
( X42 = X55
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X55),c_Suc(X42)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X55),X42)) ),
inference(fof_simplification,[status(thm)],[c_0_730]) ).
fof(c_0_1641,plain,
! [X55,X42] :
( X55 = X42
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X55),c_Suc(X42)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X55),X42)) ),
inference(fof_simplification,[status(thm)],[c_0_731]) ).
fof(c_0_1642,plain,
! [X37,X23,X19,X8,X3] :
( hAPP(hAPP(X37,X8),hAPP(hAPP(X37,X19),X23)) = hAPP(hAPP(X37,X19),hAPP(hAPP(X37,X8),X23))
| ~ c_OrderedGroup_Oab__semigroup__mult(X37,X3) ),
inference(fof_simplification,[status(thm)],[c_0_732]) ).
fof(c_0_1643,plain,
! [X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X19),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_733]) ).
fof(c_0_1644,plain,
! [X55,X42] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X42),c_Suc(X55)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X42),X55)) ),
inference(fof_simplification,[status(thm)],[c_0_734]) ).
fof(c_0_1645,plain,
! [X17,X12,X37,X21,X3] :
( hAPP(hAPP(c_Set_Oinsert(X21),X12),X17) != c_Orderings_Obot__class_Obot(tc_fun(X21,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X21),X12),X17))
| ~ c_OrderedGroup_Oab__semigroup__mult(X37,X3) ),
inference(fof_simplification,[status(thm)],[c_0_735]) ).
fof(c_0_1646,plain,
! [X14,X12,X49,X50,X3] :
( X12 = X14
| hBOOL(hAPP(hAPP(X50,X14),X12))
| hBOOL(hAPP(hAPP(X50,X12),X14))
| ~ c_Orderings_Olinorder(X49,X50,X3) ),
inference(fof_simplification,[status(thm)],[c_0_736]) ).
fof(c_0_1647,plain,
! [X14,X12,X49,X50,X3] :
( hBOOL(hAPP(hAPP(X50,X14),X12))
| hBOOL(hAPP(hAPP(X50,X12),X14))
| X12 = X14
| ~ c_Orderings_Olinorder(X49,X50,X3) ),
inference(fof_simplification,[status(thm)],[c_0_737]) ).
fof(c_0_1648,plain,
! [X14,X12,X49,X50,X3] :
( hBOOL(hAPP(hAPP(X50,X14),X12))
| X12 = X14
| hBOOL(hAPP(hAPP(X50,X12),X14))
| ~ c_Orderings_Olinorder(X49,X50,X3) ),
inference(fof_simplification,[status(thm)],[c_0_738]) ).
fof(c_0_1649,plain,
! [X14,X12,X49,X50,X3] :
( X12 = X14
| hBOOL(hAPP(hAPP(X50,X12),X14))
| hBOOL(hAPP(hAPP(X50,X14),X12))
| ~ c_Orderings_Olinorder(X49,X50,X3) ),
inference(fof_simplification,[status(thm)],[c_0_739]) ).
fof(c_0_1650,plain,
! [X14,X12,X49,X50,X3] :
( hBOOL(hAPP(hAPP(X49,X14),X12))
| hBOOL(hAPP(hAPP(X50,X12),X14))
| ~ c_Orderings_Olinorder(X49,X50,X3) ),
inference(fof_simplification,[status(thm)],[c_0_740]) ).
fof(c_0_1651,plain,
! [X14,X12,X49,X50,X3] :
( hBOOL(hAPP(hAPP(X49,X14),X12))
| hBOOL(hAPP(hAPP(X49,X12),X14))
| ~ c_Orderings_Olinorder(X49,X50,X3) ),
inference(fof_simplification,[status(thm)],[c_0_741]) ).
fof(c_0_1652,plain,
! [X14,X12,X49,X50,X3] :
( hBOOL(hAPP(hAPP(X50,X14),X12))
| hBOOL(hAPP(hAPP(X49,X12),X14))
| ~ c_Orderings_Olinorder(X49,X50,X3) ),
inference(fof_simplification,[status(thm)],[c_0_742]) ).
fof(c_0_1653,plain,
! [X14,X12,X49,X50,X3] :
( hBOOL(hAPP(hAPP(X50,X12),X14))
| hBOOL(hAPP(hAPP(X49,X14),X12))
| ~ c_Orderings_Olinorder(X49,X50,X3) ),
inference(fof_simplification,[status(thm)],[c_0_743]) ).
fof(c_0_1654,plain,
! [X12,X49,X50,X3] :
( hBOOL(hAPP(hAPP(X50,X12),X12))
| ~ c_Orderings_Olinorder(X49,X50,X3)
| hBOOL(hAPP(hAPP(X49,X12),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_744]) ).
fof(c_0_1655,plain,
! [X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(c_Finite__Set_Olinorder__class_OMin(X3),hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_745]) ).
fof(c_0_1656,plain,
! [X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(c_Finite__Set_Olinorder__class_OMax(X3),hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_746]) ).
fof(c_0_1657,axiom,
! [X17,X12,X3] :
( hAPP(hAPP(c_Set_Oinsert(X3),X12),X17) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X3),X12),X17)) ),
c_0_747 ).
fof(c_0_1658,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14) = X14
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_748]) ).
fof(c_0_1659,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14) = X12
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_749]) ).
fof(c_0_1660,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14) = X12
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_750]) ).
fof(c_0_1661,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14) = X14
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_751]) ).
fof(c_0_1662,plain,
! [X14,X12,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14) = X12
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_752]) ).
fof(c_0_1663,plain,
! [X14,X12,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14) = X14
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_753]) ).
fof(c_0_1664,plain,
! [X14,X12,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14) = X12
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_754]) ).
fof(c_0_1665,plain,
! [X14,X12,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14) = X14
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_755]) ).
fof(c_0_1666,plain,
! [X8,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),X3) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_756]) ).
fof(c_0_1667,plain,
! [X8,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),X3) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_757]) ).
fof(c_0_1668,plain,
! [X15,X31,X16,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X16,X15,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,X31,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X31,X15,X3) ),
inference(fof_simplification,[status(thm)],[c_0_758]) ).
fof(c_0_1669,plain,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14))
| X12 = X14 ),
inference(fof_simplification,[status(thm)],[c_0_759]) ).
fof(c_0_1670,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| X12 = X14
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_760]) ).
fof(c_0_1671,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14))
| X12 = X14 ),
inference(fof_simplification,[status(thm)],[c_0_761]) ).
fof(c_0_1672,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X12))
| X12 = X14
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_762]) ).
fof(c_0_1673,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| X12 = X14
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_763]) ).
fof(c_0_1674,plain,
! [X8,X9,X3] :
( hAPP(hAPP(c_Set_Oinsert(X3),X8),X9) = X9
| ~ hBOOL(hAPP(hAPP(c_in(X3),X8),X9)) ),
inference(fof_simplification,[status(thm)],[c_0_764]) ).
fof(c_0_1675,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_765]) ).
fof(c_0_1676,plain,
! [X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X12))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_766]) ).
fof(c_0_1677,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_767]) ).
fof(c_0_1678,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X14),X12))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_768]) ).
fof(c_0_1679,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X14),X12))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_769]) ).
fof(c_0_1680,plain,
! [X12,X49,X50,X3] :
( ~ hBOOL(hAPP(hAPP(X50,X12),X12))
| ~ c_Orderings_Olinorder(X49,X50,X3) ),
inference(fof_simplification,[status(thm)],[c_0_770]) ).
fof(c_0_1681,plain,
! [X12,X49,X50,X3] :
( ~ c_Orderings_Olinorder(X49,X50,X3)
| ~ hBOOL(hAPP(hAPP(X50,X12),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_771]) ).
fof(c_0_1682,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14) ),
inference(fof_simplification,[status(thm)],[c_0_772]) ).
fof(c_0_1683,plain,
! [X14,X12,X3] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X14)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X14) ),
inference(fof_simplification,[status(thm)],[c_0_773]) ).
fof(c_0_1684,plain,
! [X14,X12,X3] :
( ~ class_Lattices_Olattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14) ),
inference(fof_simplification,[status(thm)],[c_0_774]) ).
fof(c_0_1685,plain,
! [X14,X12,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14) ),
inference(fof_simplification,[status(thm)],[c_0_775]) ).
fof(c_0_1686,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14) ),
inference(fof_simplification,[status(thm)],[c_0_776]) ).
fof(c_0_1687,plain,
! [X14,X12,X3] :
( ~ class_Lattices_Olattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14) ),
inference(fof_simplification,[status(thm)],[c_0_777]) ).
fof(c_0_1688,plain,
! [X14,X12,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14) ),
inference(fof_simplification,[status(thm)],[c_0_778]) ).
fof(c_0_1689,plain,
! [X13,X9,X3] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X9,X3)
| ~ c_Finite__Set_Ofinite(X13,X3) ),
inference(fof_simplification,[status(thm)],[c_0_779]) ).
fof(c_0_1690,plain,
! [X8,X9,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X3),X8),X9),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X8),c_Complete__Lattice_OSup__class_OSup(X9,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_780]) ).
fof(c_0_1691,plain,
! [X8,X9,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X3),X8),X9),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X8),c_Complete__Lattice_OInf__class_OInf(X9,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_781]) ).
fof(c_0_1692,axiom,
! [X12] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X12),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X12),c_Suc(X12))) ),
c_0_782 ).
fof(c_0_1693,axiom,
! [X55,X42] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X55),c_Suc(X42)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X42),X55)) ),
c_0_783 ).
fof(c_0_1694,plain,
! [X12,X20,X3] :
( hBOOL(hAPP(X20,X12))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X12),X20)) ),
inference(fof_simplification,[status(thm)],[c_0_784]) ).
fof(c_0_1695,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14) != X14
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_785]) ).
fof(c_0_1696,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14) != X12
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_786]) ).
fof(c_0_1697,plain,
! [X14,X12,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14) != X14
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_787]) ).
fof(c_0_1698,plain,
! [X14,X12,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14) != X12
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X14)) ),
inference(fof_simplification,[status(thm)],[c_0_788]) ).
fof(c_0_1699,plain,
! [X8,X9,X3] :
( c_Finite__Set_Ofinite(X9,X3)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X3),X8),X9),X3) ),
inference(fof_simplification,[status(thm)],[c_0_789]) ).
fof(c_0_1700,axiom,
! [X38,X21,X3] :
( c_Map_Odom(X38,X3,X21) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X38 = c_COMBK(c_Option_Ooption_ONone(X21),tc_Option_Ooption(X21),X3) ),
c_0_790 ).
fof(c_0_1701,plain,
! [X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_791]) ).
fof(c_0_1702,plain,
! [X19,X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X8,X19,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X3),X8),X19)) ),
inference(fof_simplification,[status(thm)],[c_0_792]) ).
fof(c_0_1703,axiom,
! [X55,X42] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X55),X42))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X42),X55))
| X42 = X55 ),
c_0_793 ).
fof(c_0_1704,axiom,
! [X14,X12] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X14),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X12),X14))
| X12 = X14 ),
c_0_794 ).
fof(c_0_1705,plain,
! [X13,X9,X3] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X9,X13,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_795]) ).
fof(c_0_1706,plain,
! [X70,X14,X12,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X14) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X70)
| X14 = X70 ),
inference(fof_simplification,[status(thm)],[c_0_796]) ).
fof(c_0_1707,plain,
! [X68,X69,X12,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X12,X12,X3) != c_HOL_Ominus__class_Ominus(X69,X68,X3)
| X69 = X68 ),
inference(fof_simplification,[status(thm)],[c_0_797]) ).
fof(c_0_1708,plain,
! [X14,X17,X12,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X17,X14,X3) != c_HOL_Ominus__class_Ominus(X12,X12,X3)
| X17 = X14 ),
inference(fof_simplification,[status(thm)],[c_0_798]) ).
fof(c_0_1709,plain,
! [X14,X12,X37,X3] :
( hAPP(hAPP(X37,X12),hAPP(hAPP(X37,X12),X14)) = hAPP(hAPP(X37,X12),X14)
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X37,X3) ),
inference(fof_simplification,[status(thm)],[c_0_799]) ).
fof(c_0_1710,plain,
! [X12,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_800]) ).
fof(c_0_1711,plain,
! [X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_801]) ).
fof(c_0_1712,plain,
! [X12,X3] :
( ~ class_Orderings_Opreorder(X3)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X12),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_802]) ).
fof(c_0_1713,plain,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)
| X19 = X23 ),
inference(fof_simplification,[status(thm)],[c_0_803]) ).
fof(c_0_1714,plain,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23)
| X19 = X23 ),
inference(fof_simplification,[status(thm)],[c_0_804]) ).
fof(c_0_1715,plain,
! [X23,X19,X8,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X8) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X8)
| X19 = X23 ),
inference(fof_simplification,[status(thm)],[c_0_805]) ).
fof(c_0_1716,plain,
! [X1,X2,X3] :
( X2 = X1
| ~ hBOOL(hAPP(hAPP(c_fequal(X3),X2),X1)) ),
inference(fof_simplification,[status(thm)],[c_0_806]) ).
fof(c_0_1717,plain,
! [X8,X3] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_Oord__class_OatLeastAtMost(X8,X8,X3) = hAPP(hAPP(c_Set_Oinsert(X3),X8),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) ),
inference(fof_simplification,[status(thm)],[c_0_807]) ).
fof(c_0_1718,plain,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19),X19,X3) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_808]) ).
fof(c_0_1719,plain,
! [X14,X12,X3] :
( ~ class_Lattices_Olattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14)) = X12 ),
inference(fof_simplification,[status(thm)],[c_0_809]) ).
fof(c_0_1720,plain,
! [X14,X12,X3] :
( ~ class_Lattices_Olattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14)) = X12 ),
inference(fof_simplification,[status(thm)],[c_0_810]) ).
fof(c_0_1721,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14)) = X12 ),
inference(fof_simplification,[status(thm)],[c_0_811]) ).
fof(c_0_1722,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14)) = X12 ),
inference(fof_simplification,[status(thm)],[c_0_812]) ).
fof(c_0_1723,plain,
! [X12,X20,X3] :
( hBOOL(hAPP(hAPP(c_in(X3),X12),X20))
| ~ hBOOL(hAPP(X20,X12)) ),
inference(fof_simplification,[status(thm)],[c_0_813]) ).
fof(c_0_1724,plain,
! [X6,X7] :
( X6 = X7
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X7),X6)) ),
inference(fof_simplification,[status(thm)],[c_0_814]) ).
fof(c_0_1725,plain,
! [X15,X16,X3] :
( c_Hoare__Mirabelle_Ohoare__valids(X16,X15,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16,X15,X3) ),
inference(fof_simplification,[status(thm)],[c_0_815]) ).
fof(c_0_1726,plain,
! [X8,X9,X3] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X3),X8),X9),X3)
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_816]) ).
fof(c_0_1727,plain,
! [X12,X3] :
( ~ class_Orderings_Obot(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),c_Orderings_Obot__class_Obot(X3)),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_817]) ).
fof(c_0_1728,plain,
! [X12,X3] :
( ~ class_Orderings_Oorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_818]) ).
fof(c_0_1729,plain,
! [X12,X3] :
( ~ class_Orderings_Opreorder(X3)
| hBOOL(hAPP(hAPP(c_lessequals(X3),X12),X12)) ),
inference(fof_simplification,[status(thm)],[c_0_819]) ).
fof(c_0_1730,plain,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X14) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X14),X12) ),
inference(fof_simplification,[status(thm)],[c_0_820]) ).
fof(c_0_1731,plain,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X19) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X19),X8) ),
inference(fof_simplification,[status(thm)],[c_0_821]) ).
fof(c_0_1732,plain,
! [X23,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X23) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X23),X8) ),
inference(fof_simplification,[status(thm)],[c_0_822]) ).
fof(c_0_1733,plain,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X14) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X14),X12) ),
inference(fof_simplification,[status(thm)],[c_0_823]) ).
fof(c_0_1734,plain,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X19),X8) ),
inference(fof_simplification,[status(thm)],[c_0_824]) ).
fof(c_0_1735,plain,
! [X14,X12,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X14),X12) ),
inference(fof_simplification,[status(thm)],[c_0_825]) ).
fof(c_0_1736,plain,
! [X14,X12,X3] :
( ~ class_Lattices_Olattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X14) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X14),X12) ),
inference(fof_simplification,[status(thm)],[c_0_826]) ).
fof(c_0_1737,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X14) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X14),X12) ),
inference(fof_simplification,[status(thm)],[c_0_827]) ).
fof(c_0_1738,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X14) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X14),X12) ),
inference(fof_simplification,[status(thm)],[c_0_828]) ).
fof(c_0_1739,plain,
! [X14,X12,X3] :
( ~ class_Lattices_Olattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X14),X12) ),
inference(fof_simplification,[status(thm)],[c_0_829]) ).
fof(c_0_1740,plain,
! [X14,X12,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X14) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X14),X12) ),
inference(fof_simplification,[status(thm)],[c_0_830]) ).
fof(c_0_1741,plain,
! [X14,X12,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X12,X14,X3) != c_HOL_Ozero__class_Ozero(X3)
| X12 = X14 ),
inference(fof_simplification,[status(thm)],[c_0_831]) ).
fof(c_0_1742,plain,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19) != c_HOL_Ozero__class_Ozero(X3)
| X19 = c_HOL_Ozero__class_Ozero(X3)
| X8 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_832]) ).
fof(c_0_1743,plain,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19) != c_HOL_Ozero__class_Ozero(X3)
| X19 = c_HOL_Ozero__class_Ozero(X3)
| X8 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_833]) ).
fof(c_0_1744,plain,
! [X19,X8,X3] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),X19) != c_HOL_Ozero__class_Ozero(X3)
| X8 = c_HOL_Ozero__class_Ozero(X3)
| X19 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_834]) ).
fof(c_0_1745,plain,
! [X12,X8,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X12 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),X8)
| X8 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_835]) ).
fof(c_0_1746,plain,
! [X37,X19,X8,X3] :
( hAPP(hAPP(X37,X8),X19) = hAPP(hAPP(X37,X19),X8)
| ~ c_OrderedGroup_Oab__semigroup__mult(X37,X3) ),
inference(fof_simplification,[status(thm)],[c_0_836]) ).
fof(c_0_1747,plain,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X8,X19,X3) != c_HOL_Ozero__class_Ozero(X3)
| X8 = X19 ),
inference(fof_simplification,[status(thm)],[c_0_837]) ).
fof(c_0_1748,plain,
! [X19,X8,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X8,X19,X3) != c_HOL_Ozero__class_Ozero(X3)
| X8 = X19 ),
inference(fof_simplification,[status(thm)],[c_0_838]) ).
fof(c_0_1749,plain,
! [X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),X8) != c_HOL_Ozero__class_Ozero(X3)
| X8 = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_839]) ).
fof(c_0_1750,plain,
! [X13,X9,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X9),X13) != c_Orderings_Obot__class_Obot(X3)
| X13 = c_Orderings_Obot__class_Obot(X3) ),
inference(fof_simplification,[status(thm)],[c_0_840]) ).
fof(c_0_1751,plain,
! [X13,X9,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X9),X13) != c_Orderings_Obot__class_Obot(X3)
| X9 = c_Orderings_Obot__class_Obot(X3) ),
inference(fof_simplification,[status(thm)],[c_0_841]) ).
fof(c_0_1752,plain,
! [X9,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| hAPP(c_Finite__Set_Olattice__class_OInf__fin(X3),X9) = c_Complete__Lattice_OInf__class_OInf(X9,X3)
| X9 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_842]) ).
fof(c_0_1753,plain,
! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),c_HOL_Ozero__class_Ozero(X3)) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_843]) ).
fof(c_0_1754,plain,
! [X37,X3] :
( c_Finite__Set_Ofun__left__comm(X37,X3,X3)
| ~ c_OrderedGroup_Oab__semigroup__mult(X37,X3) ),
inference(fof_simplification,[status(thm)],[c_0_844]) ).
fof(c_0_1755,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_845]) ).
fof(c_0_1756,plain,
! [X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X8) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_846]) ).
fof(c_0_1757,plain,
! [X19,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X19) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_847]) ).
fof(c_0_1758,plain,
! [X8,X3] :
( ~ class_Ring__and__Field_Omult__zero(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X8) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_848]) ).
fof(c_0_1759,plain,
! [X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),c_HOL_Ozero__class_Ozero(X3)),X12) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_849]) ).
fof(c_0_1760,plain,
! [X12,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),c_Orderings_Obot__class_Obot(X3)),X12) = c_Orderings_Obot__class_Obot(X3) ),
inference(fof_simplification,[status(thm)],[c_0_850]) ).
fof(c_0_1761,plain,
! [X21] :
( ~ class_Orderings_Obot(X21)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X21)),v_x) = c_Orderings_Obot__class_Obot(X21) ),
inference(fof_simplification,[status(thm)],[c_0_851]) ).
fof(c_0_1762,plain,
! [X12,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| X12 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X12),c_HOL_Ozero__class_Ozero(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_852]) ).
fof(c_0_1763,plain,
! [X12,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X12,X12,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_853]) ).
fof(c_0_1764,plain,
! [X12,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X12) = X12 ),
inference(fof_simplification,[status(thm)],[c_0_854]) ).
fof(c_0_1765,plain,
! [X8,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X8) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_855]) ).
fof(c_0_1766,plain,
! [X8,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X8) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_856]) ).
fof(c_0_1767,plain,
! [X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),c_HOL_Ozero__class_Ozero(X3)),X8) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_857]) ).
fof(c_0_1768,plain,
! [X12,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),c_Orderings_Obot__class_Obot(X3)),X12) = X12 ),
inference(fof_simplification,[status(thm)],[c_0_858]) ).
fof(c_0_1769,axiom,
! [X79,X3] :
( c_Option_Oset(X79,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X79 = c_Option_Ooption_ONone(X3) ),
c_0_859 ).
fof(c_0_1770,plain,
! [X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),c_HOL_Ozero__class_Ozero(X3)) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_860]) ).
fof(c_0_1771,plain,
! [X8,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),c_HOL_Ozero__class_Ozero(X3)) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_861]) ).
fof(c_0_1772,plain,
! [X8,X3] :
( ~ class_Ring__and__Field_Omult__zero(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X8),c_HOL_Ozero__class_Ozero(X3)) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_862]) ).
fof(c_0_1773,plain,
! [X12,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),c_Orderings_Obot__class_Obot(X3)) = c_Orderings_Obot__class_Obot(X3) ),
inference(fof_simplification,[status(thm)],[c_0_863]) ).
fof(c_0_1774,plain,
! [X8,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X8,c_HOL_Ozero__class_Ozero(X3),X3) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_864]) ).
fof(c_0_1775,plain,
! [X3] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
| c_Finite__Set_Ofun__left__comm(c_HOL_Otimes__class_Otimes(X3),X3,X3) ),
inference(fof_simplification,[status(thm)],[c_0_865]) ).
fof(c_0_1776,plain,
! [X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_Finite__Set_Ofun__left__comm(c_HOL_Oplus__class_Oplus(X3),X3,X3) ),
inference(fof_simplification,[status(thm)],[c_0_866]) ).
fof(c_0_1777,plain,
! [X8,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),c_HOL_Ozero__class_Ozero(X3)) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_867]) ).
fof(c_0_1778,plain,
! [X8,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),c_HOL_Ozero__class_Ozero(X3)) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_868]) ).
fof(c_0_1779,plain,
! [X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X8),c_HOL_Ozero__class_Ozero(X3)) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_869]) ).
fof(c_0_1780,plain,
! [X12,X3] :
( ~ class_Lattices_Obounded__lattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),c_Orderings_Obot__class_Obot(X3)) = X12 ),
inference(fof_simplification,[status(thm)],[c_0_870]) ).
fof(c_0_1781,plain,
! [X8,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X8,X8,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_871]) ).
fof(c_0_1782,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X12,X12,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_872]) ).
fof(c_0_1783,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X12,X12,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(fof_simplification,[status(thm)],[c_0_873]) ).
fof(c_0_1784,axiom,
! [X59,X8,X3] :
( hAPP(c_Option_Ooption_OSome(X3),X8) != hAPP(c_Option_Ooption_OSome(X3),X59)
| X8 = X59 ),
c_0_874 ).
fof(c_0_1785,plain,
! [X12,X37,X3] :
( hAPP(hAPP(X37,X12),X12) = X12
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X37,X3) ),
inference(fof_simplification,[status(thm)],[c_0_875]) ).
fof(c_0_1786,plain,
! [X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X3),X12),X12) = X12 ),
inference(fof_simplification,[status(thm)],[c_0_876]) ).
fof(c_0_1787,plain,
! [X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X3),X12),X12) = X12 ),
inference(fof_simplification,[status(thm)],[c_0_877]) ).
fof(c_0_1788,plain,
! [X12,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3),X12),X12) = X12 ),
inference(fof_simplification,[status(thm)],[c_0_878]) ).
fof(c_0_1789,plain,
! [X12,X3] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X3)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X3),X12),X12) = X12 ),
inference(fof_simplification,[status(thm)],[c_0_879]) ).
fof(c_0_1790,plain,
! [X12,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3),X12),X12) = X12 ),
inference(fof_simplification,[status(thm)],[c_0_880]) ).
fof(c_0_1791,plain,
! [X14,X12,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_SetInterval_Oord__class_OlessThan(X12,X3) != c_SetInterval_Oord__class_OlessThan(X14,X3)
| X12 = X14 ),
inference(fof_simplification,[status(thm)],[c_0_881]) ).
fof(c_0_1792,axiom,
! [X64,X65,X66,X67] :
( c_Com_Ocom_OSemi(X67,X65) != c_Com_Ocom_OSemi(X66,X64)
| X65 = X64 ),
c_0_882 ).
fof(c_0_1793,axiom,
! [X64,X65,X66,X67] :
( c_Com_Ocom_OSemi(X67,X65) != c_Com_Ocom_OSemi(X66,X64)
| X67 = X66 ),
c_0_883 ).
fof(c_0_1794,plain,
! [X5,X4] :
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X5,X4))
| ~ class_Finite__Set_Ofinite_Ofinite(X4)
| ~ class_Finite__Set_Ofinite_Ofinite(X5) ),
inference(fof_simplification,[status(thm)],[c_0_884]) ).
fof(c_0_1795,plain,
! [X5,X4] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X5,X4))
| ~ class_Complete__Lattice_Ocomplete__lattice(X4) ),
inference(fof_simplification,[status(thm)],[c_0_885]) ).
fof(c_0_1796,plain,
! [X5,X4] :
( class_Lattices_Oupper__semilattice(tc_fun(X5,X4))
| ~ class_Lattices_Olattice(X4) ),
inference(fof_simplification,[status(thm)],[c_0_886]) ).
fof(c_0_1797,plain,
! [X5,X4] :
( class_Lattices_Olower__semilattice(tc_fun(X5,X4))
| ~ class_Lattices_Olattice(X4) ),
inference(fof_simplification,[status(thm)],[c_0_887]) ).
fof(c_0_1798,plain,
! [X5,X4] :
( class_Lattices_Odistrib__lattice(tc_fun(X5,X4))
| ~ class_Lattices_Odistrib__lattice(X4) ),
inference(fof_simplification,[status(thm)],[c_0_888]) ).
fof(c_0_1799,plain,
! [X5,X4] :
( class_Lattices_Obounded__lattice(tc_fun(X5,X4))
| ~ class_Lattices_Obounded__lattice(X4) ),
inference(fof_simplification,[status(thm)],[c_0_889]) ).
fof(c_0_1800,plain,
! [X5,X4] :
( class_Orderings_Opreorder(tc_fun(X5,X4))
| ~ class_Orderings_Opreorder(X4) ),
inference(fof_simplification,[status(thm)],[c_0_890]) ).
fof(c_0_1801,plain,
! [X5,X4] :
( class_Lattices_Olattice(tc_fun(X5,X4))
| ~ class_Lattices_Olattice(X4) ),
inference(fof_simplification,[status(thm)],[c_0_891]) ).
fof(c_0_1802,plain,
! [X5,X4] :
( class_Orderings_Oorder(tc_fun(X5,X4))
| ~ class_Orderings_Oorder(X4) ),
inference(fof_simplification,[status(thm)],[c_0_892]) ).
fof(c_0_1803,plain,
! [X5,X4] :
( class_Orderings_Obot(tc_fun(X5,X4))
| ~ class_Orderings_Obot(X4) ),
inference(fof_simplification,[status(thm)],[c_0_893]) ).
fof(c_0_1804,plain,
! [X5,X4] :
( class_HOL_Ominus(tc_fun(X5,X4))
| ~ class_HOL_Ominus(X4) ),
inference(fof_simplification,[status(thm)],[c_0_894]) ).
fof(c_0_1805,plain,
! [X5,X4] :
( class_HOL_Oord(tc_fun(X5,X4))
| ~ class_HOL_Oord(X4) ),
inference(fof_simplification,[status(thm)],[c_0_895]) ).
fof(c_0_1806,plain,
! [X3] :
( ~ class_Lattices_Olattice(X3)
| c_Finite__Set_Olattice__class_OInf__fin(X3) = c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_896]) ).
fof(c_0_1807,plain,
! [X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Finite__Set_Olinorder__class_OMax(X3) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_897]) ).
fof(c_0_1808,plain,
! [X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Finite__Set_Olinorder__class_OMin(X3) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_898]) ).
fof(c_0_1809,plain,
! [X3] :
( ~ class_Orderings_Olinorder(X3)
| c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omin(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_899]) ).
fof(c_0_1810,plain,
! [X3] :
( ~ class_Orderings_Olinorder(X3)
| c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omax(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_900]) ).
fof(c_0_1811,plain,
! [X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Oupper__semilattice__class_Osup(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_901]) ).
fof(c_0_1812,plain,
! [X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Olower__semilattice__class_Oinf(X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_902]) ).
fof(c_0_1813,plain,
! [X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X3) = c_Orderings_Oord__class_Omax(X3) ),
inference(fof_simplification,[status(thm)],[c_0_903]) ).
fof(c_0_1814,plain,
! [X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X3) = c_Orderings_Oord__class_Omin(X3) ),
inference(fof_simplification,[status(thm)],[c_0_904]) ).
fof(c_0_1815,plain,
! [X9,X3] :
( ~ class_Finite__Set_Ofinite_Ofinite(X3)
| c_Finite__Set_Ofinite(X9,X3) ),
inference(fof_simplification,[status(thm)],[c_0_905]) ).
fof(c_0_1816,plain,
! [X4] :
( class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(X4))
| ~ class_Finite__Set_Ofinite_Ofinite(X4) ),
inference(fof_simplification,[status(thm)],[c_0_906]) ).
fof(c_0_1817,axiom,
! [X14,X12] :
( c_Suc(X12) != c_Suc(X14)
| X12 = X14 ),
c_0_907 ).
fof(c_0_1818,axiom,
! [X96,X97] :
( c_Suc(X97) != c_Suc(X96)
| X97 = X96 ),
c_0_908 ).
fof(c_0_1819,axiom,
! [X10,X11] :
( c_Com_Ocom_OBODY(X11) != c_Com_Ocom_OBODY(X10)
| X11 = X10 ),
c_0_909 ).
fof(c_0_1820,plain,
! [X55,X56,X57,X58,X59,X60,X61,X62,X63] :
( c_Complete__Lattice_Ocomplete__lattice(X61,X62,c_COMBC(X57,X63,X63,tc_bool),c_COMBC(X58,X63,X63,tc_bool),X56,X59,X55,X60,X63)
| ~ c_Complete__Lattice_Ocomplete__lattice(X62,X61,X57,X58,X59,X56,X60,X55,X63) ),
inference(variable_rename,[status(thm)],[c_0_910]) ).
fof(c_0_1821,plain,
! [X55,X56,X57,X58,X59,X60,X61,X62,X63,X64,X65] :
( hAPP(hAPP(X56,X63),hAPP(X61,X64)) = c_Finite__Set_Ofold(X56,X63,X64,X65,X65)
| ~ c_Finite__Set_Ofinite(X64,X65)
| ~ c_Complete__Lattice_Ocomplete__lattice(X62,X61,X57,X58,X59,X56,X60,X55,X65) ),
inference(variable_rename,[status(thm)],[c_0_911]) ).
fof(c_0_1822,plain,
! [X55,X56,X57,X58,X59,X60,X61,X62,X63,X64,X65] :
( hAPP(hAPP(X59,X63),hAPP(X62,X64)) = c_Finite__Set_Ofold(X59,X63,X64,X65,X65)
| ~ c_Finite__Set_Ofinite(X64,X65)
| ~ c_Complete__Lattice_Ocomplete__lattice(X62,X61,X57,X58,X59,X56,X60,X55,X65) ),
inference(variable_rename,[status(thm)],[c_0_912]) ).
fof(c_0_1823,plain,
! [X55,X56,X57,X58,X59,X60,X61,X62,X63,X64] :
( hAPP(X61,X63) = c_Finite__Set_Ofold(X56,X60,X63,X64,X64)
| ~ c_Finite__Set_Ofinite(X63,X64)
| ~ c_Complete__Lattice_Ocomplete__lattice(X62,X61,X57,X58,X59,X56,X60,X55,X64) ),
inference(variable_rename,[status(thm)],[c_0_913]) ).
fof(c_0_1824,plain,
! [X55,X56,X57,X58,X59,X60,X61,X62,X63,X64] :
( hAPP(X62,X63) = c_Finite__Set_Ofold(X59,X55,X63,X64,X64)
| ~ c_Finite__Set_Ofinite(X63,X64)
| ~ c_Complete__Lattice_Ocomplete__lattice(X62,X61,X57,X58,X59,X56,X60,X55,X64) ),
inference(variable_rename,[status(thm)],[c_0_914]) ).
fof(c_0_1825,plain,
! [X55,X56,X57,X58,X59,X60,X61,X62,X63,X64,X65] :
( hAPP(X64,hAPP(hAPP(c_Set_Oinsert(X65),X62),hAPP(hAPP(c_Set_Oinsert(X65),X61),c_Orderings_Obot__class_Obot(tc_fun(X65,tc_bool))))) = hAPP(hAPP(X59,X62),X61)
| ~ c_Complete__Lattice_Ocomplete__lattice(X64,X63,X57,X58,X59,X56,X60,X55,X65) ),
inference(variable_rename,[status(thm)],[c_0_915]) ).
fof(c_0_1826,plain,
! [X55,X56,X57,X58,X59,X60,X61,X62,X63,X64,X65] :
( hAPP(X63,hAPP(hAPP(c_Set_Oinsert(X65),X62),hAPP(hAPP(c_Set_Oinsert(X65),X61),c_Orderings_Obot__class_Obot(tc_fun(X65,tc_bool))))) = hAPP(hAPP(X56,X62),X61)
| ~ c_Complete__Lattice_Ocomplete__lattice(X64,X63,X57,X58,X59,X56,X60,X55,X65) ),
inference(variable_rename,[status(thm)],[c_0_916]) ).
fof(c_0_1827,plain,
! [X55,X56,X57,X58,X59,X60,X61,X62,X63,X64,X65] :
( hBOOL(hAPP(hAPP(X58,hAPP(X63,X64)),X55))
| ~ hBOOL(hAPP(hAPP(c_in(X65),X55),X64))
| ~ c_Complete__Lattice_Ocomplete__lattice(X63,X62,X58,X59,X60,X57,X61,X56,X65) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_917])])]) ).
fof(c_0_1828,plain,
! [X55,X56,X57,X58,X59,X60,X61,X62,X63,X64,X65] :
( hBOOL(hAPP(hAPP(X58,X55),hAPP(X62,X64)))
| ~ hBOOL(hAPP(hAPP(c_in(X65),X55),X64))
| ~ c_Complete__Lattice_Ocomplete__lattice(X63,X62,X58,X59,X60,X57,X61,X56,X65) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_918])])]) ).
fof(c_0_1829,plain,
! [X55,X56,X57,X58,X59,X60,X61,X62,X63,X64] :
( hAPP(X63,hAPP(hAPP(c_Set_Oinsert(X64),X61),c_Orderings_Obot__class_Obot(tc_fun(X64,tc_bool)))) = X61
| ~ c_Complete__Lattice_Ocomplete__lattice(X63,X62,X57,X58,X59,X56,X60,X55,X64) ),
inference(variable_rename,[status(thm)],[c_0_919]) ).
fof(c_0_1830,plain,
! [X55,X56,X57,X58,X59,X60,X61,X62,X63,X64] :
( hAPP(X62,hAPP(hAPP(c_Set_Oinsert(X64),X61),c_Orderings_Obot__class_Obot(tc_fun(X64,tc_bool)))) = X61
| ~ c_Complete__Lattice_Ocomplete__lattice(X63,X62,X57,X58,X59,X56,X60,X55,X64) ),
inference(variable_rename,[status(thm)],[c_0_920]) ).
fof(c_0_1831,plain,
! [X55,X56,X57,X58,X59,X60,X61,X62,X63,X64,X65] :
( hAPP(X63,hAPP(hAPP(c_Set_Oinsert(X65),X61),X64)) = hAPP(hAPP(X59,X61),hAPP(X63,X64))
| ~ c_Complete__Lattice_Ocomplete__lattice(X63,X62,X57,X58,X59,X56,X60,X55,X65) ),
inference(variable_rename,[status(thm)],[c_0_921]) ).
fof(c_0_1832,plain,
! [X55,X56,X57,X58,X59,X60,X61,X62,X63,X64,X65] :
( hAPP(X62,hAPP(hAPP(c_Set_Oinsert(X65),X61),X64)) = hAPP(hAPP(X56,X61),hAPP(X62,X64))
| ~ c_Complete__Lattice_Ocomplete__lattice(X63,X62,X57,X58,X59,X56,X60,X55,X65) ),
inference(variable_rename,[status(thm)],[c_0_922]) ).
fof(c_0_1833,plain,
! [X55,X56,X57,X58,X59,X60,X61,X62,X63,X64] :
( c_Finite__Set_Olattice_OSup__fin(X56,X63,X64) = hAPP(X61,X63)
| X63 = c_Orderings_Obot__class_Obot(tc_fun(X64,tc_bool))
| ~ c_Finite__Set_Ofinite(X63,X64)
| ~ c_Complete__Lattice_Ocomplete__lattice(X62,X61,X57,X58,X59,X56,X60,X55,X64) ),
inference(variable_rename,[status(thm)],[c_0_923]) ).
fof(c_0_1834,plain,
! [X55,X56,X57,X58,X59,X60,X61,X62,X63,X64] :
( c_Finite__Set_Olattice_OInf__fin(X59,X63,X64) = hAPP(X62,X63)
| X63 = c_Orderings_Obot__class_Obot(tc_fun(X64,tc_bool))
| ~ c_Finite__Set_Ofinite(X63,X64)
| ~ c_Complete__Lattice_Ocomplete__lattice(X62,X61,X57,X58,X59,X56,X60,X55,X64) ),
inference(variable_rename,[status(thm)],[c_0_924]) ).
fof(c_0_1835,plain,
! [X55,X56,X57,X58,X59,X60,X61,X62,X63] :
( hAPP(X61,c_Orderings_Obot__class_Obot(tc_fun(X63,tc_bool))) = X60
| ~ c_Complete__Lattice_Ocomplete__lattice(X62,X61,X57,X58,X59,X56,X60,X55,X63) ),
inference(variable_rename,[status(thm)],[c_0_925]) ).
fof(c_0_1836,plain,
! [X55,X56,X57,X58,X59,X60,X61,X62,X63] :
( hAPP(X62,c_Orderings_Obot__class_Obot(tc_fun(X63,tc_bool))) = X55
| ~ c_Complete__Lattice_Ocomplete__lattice(X62,X61,X57,X58,X59,X56,X60,X55,X63) ),
inference(variable_rename,[status(thm)],[c_0_926]) ).
fof(c_0_1837,plain,
! [X34,X35,X36,X37] :
( c_Hoare__Mirabelle_Ohoare__derivs(X37,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X36,X34,X35,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X37,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X37,X36,X35,X34)),tc_fun(tc_Com_Ostate,tc_bool),t_a),X34,c_COMBK(hAPP(X35,v_sko__Hoare__Mirabelle__Xescape__1(X37,X36,X35,X34)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(variable_rename,[status(thm)],[c_0_927]) ).
fof(c_0_1838,plain,
! [X58,X59,X60,X61,X62] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X61)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X61),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X61),X58,c_HOL_Ozero__class_Ozero(X61),X60,X61,X62)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X61),X58,c_HOL_Ozero__class_Ozero(X61),X59,X61,X62)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X61),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X61),X58,c_HOL_Ozero__class_Ozero(X61),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X62,tc_bool)),X60),X59),X61,X62)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X61),X58,c_HOL_Ozero__class_Ozero(X61),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X62,tc_bool)),X60),X59),X61,X62))
| ~ c_Finite__Set_Ofinite(X59,X62)
| ~ c_Finite__Set_Ofinite(X60,X62) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_928])])]) ).
fof(c_0_1839,plain,
! [X34,X35,X36,X37,X38,X39] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X38,X36,X37,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X37,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X39,X38,X37,X36)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X39,X38,X37,X36,X35,X34)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X35,X36,X34,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(variable_rename,[status(thm)],[c_0_929]) ).
fof(c_0_1840,plain,
! [X34,X35,X36,X37,X38,X39] :
( c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X38,X36,X37,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X37,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X39,X38,X37,X36)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X39,X38,X37,X36,X35,X34)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X39,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X35,X36,X34,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(variable_rename,[status(thm)],[c_0_930]) ).
fof(c_0_1841,plain,
! [X58,X59,X60,X61,X62] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X61)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X62,tc_bool)),X60),X59) != c_Orderings_Obot__class_Obot(tc_fun(X62,tc_bool))
| ~ c_Finite__Set_Ofinite(X59,X62)
| ~ c_Finite__Set_Ofinite(X60,X62)
| c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X61),X58,c_HOL_Ozero__class_Ozero(X61),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X62,tc_bool)),X60),X59),X61,X62) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X61),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X61),X58,c_HOL_Ozero__class_Ozero(X61),X60,X61,X62)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X61),X58,c_HOL_Ozero__class_Ozero(X61),X59,X61,X62)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_931])])]) ).
fof(c_0_1842,plain,
! [X42,X43,X44,X45,X46,X47,X48] :
( c_Hoare__Mirabelle_Ohoare__derivs(X48,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X47,X44,X46,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X42,X45),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X48,X47,X46,X44,X43,X42)))
| ~ hBOOL(hAPP(hAPP(X43,X45),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X48,X47,X46,X44)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X48,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X43,X44,X42,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(variable_rename,[status(thm)],[c_0_932]) ).
fof(c_0_1843,plain,
! [X42,X43,X44,X45,X46,X47,X48] :
( c_Hoare__Mirabelle_Ohoare__derivs(X48,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X47,X44,X46,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X42,X45),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X48,X47,X46,X44,X43,X42)))
| ~ hBOOL(hAPP(hAPP(X43,X45),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X48,X47,X46,X44)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X48,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X43,X44,X42,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(variable_rename,[status(thm)],[c_0_933]) ).
fof(c_0_1844,plain,
! [X71,X72,X73,X74,X75,X76] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X75)
| c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X75),X72,X71,hAPP(hAPP(c_Set_Oinsert(X76),X73),X74),X75,X76) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X75),hAPP(X72,X73)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X75),X72,X71,X74,X75,X76))
| hBOOL(hAPP(hAPP(c_in(X76),X73),X74))
| ~ c_Finite__Set_Ofinite(X74,X76) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_934])])]) ).
fof(c_0_1845,plain,
! [X71,X72,X73,X74,X75,X76] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X75)
| c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(X75),X72,X71,hAPP(hAPP(c_Set_Oinsert(X76),X73),X74),X75,X76) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X75),hAPP(X72,X73)),c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(X75),X72,X71,X74,X75,X76))
| hBOOL(hAPP(hAPP(c_in(X76),X73),X74))
| ~ c_Finite__Set_Ofinite(X74,X76) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_935])])]) ).
fof(c_0_1846,plain,
! [X71,X72,X73,X74,X75,X76,X77] :
( c_Finite__Set_Ofold__image(X72,X73,X71,hAPP(hAPP(c_Set_Oinsert(X76),X74),X75),X77,X76) = hAPP(hAPP(X72,hAPP(X73,X74)),c_Finite__Set_Ofold__image(X72,X73,X71,X75,X77,X76))
| hBOOL(hAPP(hAPP(c_in(X76),X74),X75))
| ~ c_Finite__Set_Ofinite(X75,X76)
| ~ c_OrderedGroup_Oab__semigroup__mult(X72,X77) ),
inference(variable_rename,[status(thm)],[c_0_936]) ).
fof(c_0_1847,plain,
! [X20,X21,X22,X23,X24] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X24)
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X24),X22,hAPP(hAPP(c_Set_Oinsert(X24),X21),c_HOL_Ominus__class_Ominus(X23,hAPP(hAPP(c_Set_Oinsert(X24),X22),c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool))),tc_fun(X24,tc_bool))),X24,X24),X20))
| hBOOL(hAPP(hAPP(c_in(X24),X21),X23))
| ~ hBOOL(hAPP(hAPP(c_in(X24),X22),X23))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X24),X21,X23,X24,X24),X20)) ),
inference(variable_rename,[status(thm)],[c_0_937]) ).
fof(c_0_1848,plain,
! [X20,X21,X22,X23,X24] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X24)
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X24),X22,hAPP(hAPP(c_Set_Oinsert(X24),X21),c_HOL_Ominus__class_Ominus(X23,hAPP(hAPP(c_Set_Oinsert(X24),X22),c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool))),tc_fun(X24,tc_bool))),X24,X24),X20))
| hBOOL(hAPP(hAPP(c_in(X24),X21),X23))
| ~ hBOOL(hAPP(hAPP(c_in(X24),X22),X23))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X24),X21,X23,X24,X24),X20)) ),
inference(variable_rename,[status(thm)],[c_0_938]) ).
fof(c_0_1849,plain,
! [X38,X39,X40,X41,X42,X43] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X39,X41,hAPP(hAPP(c_Set_Oinsert(X43),X40),c_HOL_Ominus__class_Ominus(X42,hAPP(hAPP(c_Set_Oinsert(X43),X41),c_Orderings_Obot__class_Obot(tc_fun(X43,tc_bool))),tc_fun(X43,tc_bool))),X43,X43),X38))
| hBOOL(hAPP(hAPP(c_in(X43),X40),X42))
| ~ hBOOL(hAPP(hAPP(c_in(X43),X41),X42))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X39,X40,X42,X43,X43),X38))
| ~ c_OrderedGroup_Oab__semigroup__mult(X39,X43) ),
inference(variable_rename,[status(thm)],[c_0_939]) ).
fof(c_0_1850,plain,
! [X91,X92,X93,X94,X95,X96] :
( ~ class_Ring__and__Field_Opordered__ring(X96)
| hBOOL(hAPP(hAPP(c_lessequals(X96),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X96),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X96),X95),X91)),X93)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X96),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X96),X94),X91)),X92)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X96),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X96),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X96),c_HOL_Ominus__class_Ominus(X95,X94,X96)),X91)),X93)),X92)) ),
inference(variable_rename,[status(thm)],[c_0_940]) ).
fof(c_0_1851,plain,
! [X91,X92,X93,X94,X95,X96] :
( ~ class_Ring__and__Field_Opordered__ring(X96)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X96),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X96),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X96),X95),X91)),X93)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X96),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X96),X94),X91)),X92)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X96),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X96),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X96),c_HOL_Ominus__class_Ominus(X95,X94,X96)),X91)),X93)),X92)) ),
inference(variable_rename,[status(thm)],[c_0_941]) ).
fof(c_0_1852,plain,
! [X71,X72,X73,X74,X75,X76,X77] :
( c_Nitpick_Ofold__graph_H(X74,X71,X75,hAPP(hAPP(X74,X73),X72),X77,X76)
| ~ c_Nitpick_Ofold__graph_H(X74,X71,c_HOL_Ominus__class_Ominus(X75,hAPP(hAPP(c_Set_Oinsert(X77),X73),c_Orderings_Obot__class_Obot(tc_fun(X77,tc_bool))),tc_fun(X77,tc_bool)),X72,X77,X76)
| ~ hBOOL(hAPP(hAPP(c_in(X77),X73),X75)) ),
inference(variable_rename,[status(thm)],[c_0_942]) ).
fof(c_0_1853,plain,
! [X71,X72,X73,X74,X75,X76,X77] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X74,X71,X75,X77,X76),hAPP(hAPP(X74,X73),X72)))
| ~ hBOOL(hAPP(hAPP(c_in(X77),X73),X75))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X74,X71,c_HOL_Ominus__class_Ominus(X75,hAPP(hAPP(c_Set_Oinsert(X77),X73),c_Orderings_Obot__class_Obot(tc_fun(X77,tc_bool))),tc_fun(X77,tc_bool)),X77,X76),X72)) ),
inference(variable_rename,[status(thm)],[c_0_943]) ).
fof(c_0_1854,plain,
! [X71,X72,X73,X74,X75,X76,X77] :
( X72 = X73
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X74,X71,X75,X77,X76),X72))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X74,X71,X75,X77,X76),X73))
| ~ c_Finite__Set_Ofun__left__comm(X74,X77,X76) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_944])])]) ).
fof(c_0_1855,plain,
! [X15,X16,X17,X18] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X17,hAPP(hAPP(c_Set_Oinsert(X18),X16),c_Orderings_Obot__class_Obot(tc_fun(X18,tc_bool))),tc_fun(X18,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X18),X15),c_Orderings_Obot__class_Obot(tc_fun(X18,tc_bool))),tc_fun(X18,tc_bool)),X18)),c_Finite__Set_Ocard(X17,X18)))
| ~ hBOOL(hAPP(hAPP(c_in(X18),X15),X17))
| ~ hBOOL(hAPP(hAPP(c_in(X18),X16),X17))
| ~ c_Finite__Set_Ofinite(X17,X18) ),
inference(variable_rename,[status(thm)],[c_0_945]) ).
fof(c_0_1856,plain,
! [X91,X92,X93,X94,X95,X96] :
( ~ class_Ring__and__Field_Opordered__ring(X96)
| hBOOL(hAPP(hAPP(c_lessequals(X96),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X96),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X96),c_HOL_Ominus__class_Ominus(X95,X94,X96)),X91)),X93)),X92))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X96),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X96),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X96),X95),X91)),X93)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X96),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X96),X94),X91)),X92))) ),
inference(variable_rename,[status(thm)],[c_0_946]) ).
fof(c_0_1857,plain,
! [X91,X92,X93,X94,X95,X96] :
( ~ class_Ring__and__Field_Opordered__ring(X96)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X96),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X96),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X96),c_HOL_Ominus__class_Ominus(X95,X94,X96)),X91)),X93)),X92))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X96),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X96),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X96),X95),X91)),X93)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X96),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X96),X94),X91)),X92))) ),
inference(variable_rename,[status(thm)],[c_0_947]) ).
fof(c_0_1858,plain,
! [X71,X72,X73,X74,X75] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X75)
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X75),X71,hAPP(hAPP(c_Set_Oinsert(X75),X73),X74),X75,X75),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X75),X71),X72)))
| hBOOL(hAPP(hAPP(c_in(X75),X73),X74))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X75),X73,X74,X75,X75),X72)) ),
inference(variable_rename,[status(thm)],[c_0_948]) ).
fof(c_0_1859,plain,
! [X71,X72,X73,X74,X75] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X75)
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X75),X71,hAPP(hAPP(c_Set_Oinsert(X75),X73),X74),X75,X75),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X75),X71),X72)))
| hBOOL(hAPP(hAPP(c_in(X75),X73),X74))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X75),X73,X74,X75,X75),X72)) ),
inference(variable_rename,[status(thm)],[c_0_949]) ).
fof(c_0_1860,plain,
! [X88,X89,X90,X91,X92,X93,X94] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X91,X88,X92,X93,X94),X89))
| hBOOL(hAPP(hAPP(c_in(X93),X90),X92))
| ~ c_Finite__Set_Ofun__left__comm(X91,X93,X94)
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X91,X88,hAPP(hAPP(c_Set_Oinsert(X93),X90),X92),X93,X94),hAPP(hAPP(X91,X90),X89))) ),
inference(variable_rename,[status(thm)],[c_0_950]) ).
fof(c_0_1861,plain,
! [X71,X72,X73,X74,X75,X76] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X73,X71,hAPP(hAPP(c_Set_Oinsert(X76),X74),X75),X76,X76),hAPP(hAPP(X73,X71),X72)))
| hBOOL(hAPP(hAPP(c_in(X76),X74),X75))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X73,X74,X75,X76,X76),X72))
| ~ c_OrderedGroup_Oab__semigroup__mult(X73,X76) ),
inference(variable_rename,[status(thm)],[c_0_951]) ).
fof(c_0_1862,plain,
! [X71,X72,X73,X74,X75,X76,X77] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X74,X71,hAPP(hAPP(c_Set_Oinsert(X77),X73),X75),X77,X76),hAPP(hAPP(X74,X73),X72)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X74,X71,X75,X77,X76),X72))
| hBOOL(hAPP(hAPP(c_in(X77),X73),X75)) ),
inference(variable_rename,[status(thm)],[c_0_952]) ).
fof(c_0_1863,plain,
! [X35,X36,X37] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X37,tc_bool)),X36),X35))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X37,tc_bool)),hAPP(c_COMBC(c_in(X37),X37,tc_fun(X37,tc_bool),tc_bool),X36)),hAPP(c_COMBC(c_in(X37),X37,tc_fun(X37,tc_bool),tc_bool),X35))) ),
inference(variable_rename,[status(thm)],[c_0_953]) ).
fof(c_0_1864,plain,
! [X41,X42,X43,X44,X45,X46] :
( c_Hoare__Mirabelle_Ohoare__derivs(X46,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X45,X41,X43,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X43,v_sko__Hoare__Mirabelle__Xconseq12__1(X45,X44,X43,X42)),v_sko__Hoare__Mirabelle__Xconseq12__3(X45,X44,X43,X42)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X46,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X44,X41,X42,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(variable_rename,[status(thm)],[c_0_954]) ).
fof(c_0_1865,plain,
! [X52,X53,X54,X55,X56,X57,X58] :
( hBOOL(hAPP(hAPP(X52,c_Finite__Set_Ofold(X54,X55,X57,X58,X58)),hAPP(hAPP(X54,X56),X55)))
| ~ hBOOL(hAPP(hAPP(c_in(X58),X56),X57))
| ~ c_Finite__Set_Ofinite(X57,X58)
| ~ c_Lattices_Olower__semilattice(X52,X53,X54,X58) ),
inference(variable_rename,[status(thm)],[c_0_955]) ).
fof(c_0_1866,plain,
! [X91,X92,X93,X94,X95,X96] :
( ~ class_Ring__and__Field_Opordered__ring(X96)
| hBOOL(hAPP(hAPP(c_lessequals(X96),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X96),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X96),X95),X91)),X93)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X96),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X96),X94),X91)),X92)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X96),X93),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X96),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X96),c_HOL_Ominus__class_Ominus(X94,X95,X96)),X91)),X92))) ),
inference(variable_rename,[status(thm)],[c_0_956]) ).
fof(c_0_1867,plain,
! [X91,X92,X93,X94,X95,X96] :
( ~ class_Ring__and__Field_Opordered__ring(X96)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X96),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X96),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X96),X95),X91)),X93)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X96),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X96),X94),X91)),X92)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X96),X93),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X96),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X96),c_HOL_Ominus__class_Ominus(X94,X95,X96)),X91)),X92))) ),
inference(variable_rename,[status(thm)],[c_0_957]) ).
fof(c_0_1868,plain,
! [X34,X35,X36,X37,X38] :
( c_Hoare__Mirabelle_Ohoare__derivs(X37,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X38)),c_Hoare__Mirabelle_Otriple_Otriple(X36,c_Com_Ocom_OBODY(X34),X35,X38)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X38),tc_bool))),X38)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X38)),c_Hoare__Mirabelle_Otriple_Otriple(X36,c_Com_Ocom_OBODY(X34),X35,X38)),X37),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X38)),c_Hoare__Mirabelle_Otriple_Otriple(X36,c_Option_Othe(hAPP(c_Com_Obody,X34),tc_Com_Ocom),X35,X38)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X38),tc_bool))),X38) ),
inference(variable_rename,[status(thm)],[c_0_958]) ).
fof(c_0_1869,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Olower__semilattice(X23)
| hBOOL(hAPP(hAPP(c_lessequals(X23),c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X23),X20,X22,X23,X23)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X23),X21),X20)))
| ~ hBOOL(hAPP(hAPP(c_in(X23),X21),X22))
| ~ c_Finite__Set_Ofinite(X22,X23) ),
inference(variable_rename,[status(thm)],[c_0_959]) ).
fof(c_0_1870,plain,
! [X35,X36,X37,X38,X39,X40,X41] :
( c_Hoare__Mirabelle_Ohoare__derivs(X40,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X41)),c_Hoare__Mirabelle_Otriple_Otriple(X39,c_Com_Ocom_OSemi(X36,X35),X37,X41)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X41),tc_bool))),X41)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X40,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X41)),c_Hoare__Mirabelle_Otriple_Otriple(X38,X35,X37,X41)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X41),tc_bool))),X41)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X40,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X41)),c_Hoare__Mirabelle_Otriple_Otriple(X39,X36,X38,X41)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X41),tc_bool))),X41) ),
inference(variable_rename,[status(thm)],[c_0_960]) ).
fof(c_0_1871,plain,
! [X91,X92,X93,X94,X95,X96] :
( ~ class_Ring__and__Field_Opordered__ring(X96)
| hBOOL(hAPP(hAPP(c_lessequals(X96),X93),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X96),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X96),c_HOL_Ominus__class_Ominus(X94,X95,X96)),X91)),X92)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X96),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X96),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X96),X95),X91)),X93)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X96),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X96),X94),X91)),X92))) ),
inference(variable_rename,[status(thm)],[c_0_961]) ).
fof(c_0_1872,plain,
! [X91,X92,X93,X94,X95,X96] :
( ~ class_Ring__and__Field_Opordered__ring(X96)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X96),X93),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X96),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X96),c_HOL_Ominus__class_Ominus(X94,X95,X96)),X91)),X92)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X96),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X96),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X96),X95),X91)),X93)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X96),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X96),X94),X91)),X92))) ),
inference(variable_rename,[status(thm)],[c_0_962]) ).
fof(c_0_1873,plain,
! [X71,X72,X73,X74,X75,X76] :
( c_Finite__Set_Ofold(X73,X71,X74,X76,X75) = X72
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X73,X71,X74,X76,X75),X72))
| ~ c_Finite__Set_Ofun__left__comm(X73,X76,X75) ),
inference(variable_rename,[status(thm)],[c_0_963]) ).
fof(c_0_1874,plain,
! [X41,X42,X43,X44,X45,X46] :
( c_Hoare__Mirabelle_Ohoare__derivs(X46,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X45,X41,X43,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X45,v_sko__Hoare__Mirabelle__Xconseq12__1(X45,X44,X43,X42)),v_sko__Hoare__Mirabelle__Xconseq12__2(X45,X44,X43,X42)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X46,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X44,X41,X42,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(variable_rename,[status(thm)],[c_0_964]) ).
fof(c_0_1875,plain,
! [X42,X43,X44,X45,X46,X47,X48] :
( c_Hoare__Mirabelle_Ohoare__derivs(X48,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X47,X42,X45,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X44,X43),v_sko__Hoare__Mirabelle__Xconseq12__3(X47,X46,X45,X44)))
| ~ hBOOL(hAPP(hAPP(X46,X43),v_sko__Hoare__Mirabelle__Xconseq12__2(X47,X46,X45,X44)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X48,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X46,X42,X44,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(variable_rename,[status(thm)],[c_0_965]) ).
fof(c_0_1876,plain,
! [X39,X40,X41,X42,X43] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X40,hAPP(hAPP(c_Set_Oinsert(X43),X41),X42),X43),X39))
| hBOOL(hAPP(hAPP(c_in(X43),X41),X42))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X40,X41,X42,X43,X43),X39)) ),
inference(variable_rename,[status(thm)],[c_0_966]) ).
fof(c_0_1877,plain,
! [X71,X72,X73,X74,X75] :
( X72 = X71
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X73,X71,c_Orderings_Obot__class_Obot(tc_fun(X75,tc_bool)),X75,X74),X72)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_967])])]) ).
fof(c_0_1878,plain,
! [X95,X96,X97,X98] :
( ~ hBOOL(hAPP(X98,c_Option_Ooption_Ooption__case(X96,X95,hAPP(c_Option_Ooption_OSome(t_b),X97),t_a,t_b)))
| hBOOL(hAPP(X98,hAPP(X95,X97))) ),
inference(variable_rename,[status(thm)],[c_0_968]) ).
fof(c_0_1879,plain,
! [X95,X96,X97,X98] :
( ~ hBOOL(hAPP(X98,c_Option_Ooption_Ooption__case(X97,X96,hAPP(c_Option_Ooption_OSome(t_b),X95),t_a,t_b)))
| hBOOL(hAPP(X98,hAPP(X96,X95))) ),
inference(variable_rename,[status(thm)],[c_0_969]) ).
fof(c_0_1880,plain,
! [X95,X96,X97] :
( ~ hBOOL(hAPP(X97,c_Option_Ooption_Ooption__case(X96,X95,c_Option_Ooption_ONone(t_b),t_a,t_b)))
| hBOOL(hAPP(X97,X96)) ),
inference(variable_rename,[status(thm)],[c_0_970]) ).
fof(c_0_1881,plain,
! [X71,X72,X73,X74,X75,X76] :
( c_Finite__Set_Ofinite(X74,X76)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X73,X71,X74,X76,X75),X72)) ),
inference(variable_rename,[status(thm)],[c_0_971]) ).
fof(c_0_1882,plain,
! [X35,X36,X37] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X37,tc_bool)),hAPP(c_COMBC(c_in(X37),X37,tc_fun(X37,tc_bool),tc_bool),X36)),hAPP(c_COMBC(c_in(X37),X37,tc_fun(X37,tc_bool),tc_bool),X35)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X37,tc_bool)),X36),X35)) ),
inference(variable_rename,[status(thm)],[c_0_972]) ).
fof(c_0_1883,plain,
! [X43,X44,X45,X46,X47,X48,X49] :
( c_Fun_Ofun__upd(c_Fun_Ofun__upd(X43,X47,X46,X49,X48),X45,X44,X49,X48) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X43,X45,X44,X49,X48),X47,X46,X49,X48)
| X47 = X45 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_973])])]) ).
fof(c_0_1884,plain,
! [X34,X35,X36,X37,X38] :
( c_Hoare__Mirabelle_Ohoare__derivs(X37,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X38)),c_Hoare__Mirabelle_Otriple_Otriple(X36,c_Com_Ocom_OBODY(X34),X35,X38)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X38),tc_bool))),X38)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X37,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X38)),c_Hoare__Mirabelle_Otriple_Otriple(X36,c_Option_Othe(hAPP(c_Com_Obody,X34),tc_Com_Ocom),X35,X38)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X38),tc_bool))),X38) ),
inference(variable_rename,[status(thm)],[c_0_974]) ).
fof(c_0_1885,plain,
! [X34,X35,X36] :
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_Otriple_Otriple(X36,X34,X35,tc_Com_Ostate)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_Otriple_Otriple(X36,X34,X35,tc_Com_Ostate)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(X34)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))),tc_Com_Ostate) ),
inference(variable_rename,[status(thm)],[c_0_975]) ).
fof(c_0_1886,plain,
! [X39,X40,X41,X42] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X42)
| c_Finite__Set_Osetsum(X39,X40,X41,X42) = c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X42),X39,c_HOL_Ozero__class_Ozero(X42),X40,X42,X41)
| ~ c_Finite__Set_Ofinite(X40,X41) ),
inference(variable_rename,[status(thm)],[c_0_976]) ).
fof(c_0_1887,plain,
! [X41,X42,X43,X44,X45] :
( c_Hoare__Mirabelle_Ohoare__derivs(X45,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X44,X41,X42,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X43,v_sko__Hoare__Mirabelle__Xconseq1__1(X44,X43)),v_sko__Hoare__Mirabelle__Xconseq1__2(X44,X43)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X45,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X43,X41,X42,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(variable_rename,[status(thm)],[c_0_977]) ).
fof(c_0_1888,plain,
! [X40,X41,X42,X43,X44] :
( c_Hoare__Mirabelle_Ohoare__derivs(X44,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X43,X40,X42,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X42,v_sko__Hoare__Mirabelle__Xconseq2__1(X42,X41)),v_sko__Hoare__Mirabelle__Xconseq2__2(X42,X41)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X44,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X43,X40,X41,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(variable_rename,[status(thm)],[c_0_978]) ).
fof(c_0_1889,plain,
! [X40,X41,X42,X43,X44] :
( c_Hoare__Mirabelle_Ohoare__derivs(X44,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X43,X40,X42,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X41,v_sko__Hoare__Mirabelle__Xconseq2__1(X42,X41)),v_sko__Hoare__Mirabelle__Xconseq2__2(X42,X41)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X44,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X43,X40,X41,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(variable_rename,[status(thm)],[c_0_979]) ).
fof(c_0_1890,plain,
! [X41,X42,X43,X44,X45] :
( c_Hoare__Mirabelle_Ohoare__derivs(X45,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X44,X41,X42,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X44,v_sko__Hoare__Mirabelle__Xconseq1__1(X44,X43)),v_sko__Hoare__Mirabelle__Xconseq1__2(X44,X43)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X45,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X43,X41,X42,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(variable_rename,[status(thm)],[c_0_980]) ).
fof(c_0_1891,plain,
! [X73,X74,X75,X76,X77,X78] :
( c_Map_Orestrict__map(c_Fun_Ofun__upd(X75,X74,X73,X78,tc_Option_Ooption(X77)),X76,X78,X77) = c_Fun_Ofun__upd(c_Map_Orestrict__map(X75,c_HOL_Ominus__class_Ominus(X76,hAPP(hAPP(c_Set_Oinsert(X78),X74),c_Orderings_Obot__class_Obot(tc_fun(X78,tc_bool))),tc_fun(X78,tc_bool)),X78,X77),X74,X73,X78,tc_Option_Ooption(X77))
| ~ hBOOL(hAPP(hAPP(c_in(X78),X74),X76)) ),
inference(variable_rename,[status(thm)],[c_0_981]) ).
fof(c_0_1892,plain,
! [X63,X64,X65,X66,X67,X68] :
( c_Map_Omap__le(c_Fun_Ofun__upd(X66,X64,c_Option_Ooption_ONone(X67),X68,tc_Option_Ooption(X67)),c_Fun_Ofun__upd(X65,X64,hAPP(c_Option_Ooption_OSome(X67),X63),X68,tc_Option_Ooption(X67)),X68,X67)
| ~ c_Map_Omap__le(X66,X65,X68,X67) ),
inference(variable_rename,[status(thm)],[c_0_982]) ).
fof(c_0_1893,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Oupper__semilattice(X23)
| hBOOL(hAPP(hAPP(c_lessequals(X23),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X23),X21),X20)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X23),X20,X22,X23,X23)))
| ~ hBOOL(hAPP(hAPP(c_in(X23),X21),X22))
| ~ c_Finite__Set_Ofinite(X22,X23) ),
inference(variable_rename,[status(thm)],[c_0_983]) ).
fof(c_0_1894,plain,
! [X58,X59,X60,X61,X62,X63] :
( c_Map_Omap__le(c_Fun_Ofun__upd(X59,X61,X60,X63,tc_Option_Ooption(X62)),c_Fun_Ofun__upd(X58,X61,X60,X63,tc_Option_Ooption(X62)),X63,X62)
| ~ c_Map_Omap__le(X59,X58,X63,X62) ),
inference(variable_rename,[status(thm)],[c_0_984]) ).
fof(c_0_1895,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X17,tc_bool)),X16),hAPP(hAPP(c_Set_Oinsert(X17),X14),X15)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X17,tc_bool)),X16),X15))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X17,tc_bool)),c_HOL_Ominus__class_Ominus(X16,hAPP(hAPP(c_Set_Oinsert(X17),X14),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_bool))),tc_fun(X17,tc_bool))),X15))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X17,tc_bool)),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_985]) ).
fof(c_0_1896,plain,
! [X34,X35,X36,X37] :
( c_Hoare__Mirabelle_Ohoare__derivs(X37,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X36,X34,X35,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X36,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X37,X36,X35,X34)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X37,X36,X35,X34))) ),
inference(variable_rename,[status(thm)],[c_0_986]) ).
fof(c_0_1897,plain,
! [X34,X35,X36,X37] :
( c_Hoare__Mirabelle_Ohoare__derivs(X37,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X36,X34,X35,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X36,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X37,X36,X35,X34)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X37,X36,X35,X34))) ),
inference(variable_rename,[status(thm)],[c_0_987]) ).
fof(c_0_1898,plain,
! [X34,X35,X36,X37] :
( c_Hoare__Mirabelle_Ohoare__derivs(X37,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X36,X34,X35,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X36,v_sko__Hoare__Mirabelle__Xescape__1(X37,X36,X35,X34)),v_sko__Hoare__Mirabelle__Xescape__2(X37,X36,X35,X34))) ),
inference(variable_rename,[status(thm)],[c_0_988]) ).
fof(c_0_1899,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X17,tc_bool)),X16),hAPP(hAPP(c_Set_Oinsert(X17),X14),X15)))
| ~ hBOOL(hAPP(hAPP(c_in(X17),X14),X16))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X17,tc_bool)),c_HOL_Ominus__class_Ominus(X16,hAPP(hAPP(c_Set_Oinsert(X17),X14),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_bool))),tc_fun(X17,tc_bool))),X15))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X17,tc_bool)),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_989]) ).
fof(c_0_1900,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X17,tc_bool)),X16),hAPP(hAPP(c_Set_Oinsert(X17),X14),X15)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X17,tc_bool)),X16),X15))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X17,tc_bool)),c_HOL_Ominus__class_Ominus(X16,hAPP(hAPP(c_Set_Oinsert(X17),X14),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_bool))),tc_fun(X17,tc_bool))),X15))
| hBOOL(hAPP(hAPP(c_in(X17),X14),X15)) ),
inference(variable_rename,[status(thm)],[c_0_990]) ).
fof(c_0_1901,plain,
! [X71,X72,X73,X74,X75,X76] :
( c_Finite__Set_Ofold(X73,X71,X74,X76,X75) = hAPP(hAPP(X73,X72),c_Finite__Set_Ofold(X73,X71,c_HOL_Ominus__class_Ominus(X74,hAPP(hAPP(c_Set_Oinsert(X76),X72),c_Orderings_Obot__class_Obot(tc_fun(X76,tc_bool))),tc_fun(X76,tc_bool)),X76,X75))
| ~ hBOOL(hAPP(hAPP(c_in(X76),X72),X74))
| ~ c_Finite__Set_Ofinite(X74,X76)
| ~ c_Finite__Set_Ofun__left__comm(X73,X76,X75) ),
inference(variable_rename,[status(thm)],[c_0_991]) ).
fof(c_0_1902,plain,
! [X71,X72,X73,X74,X75,X76] :
( c_Finite__Set_Ofold(X73,X71,hAPP(hAPP(c_Set_Oinsert(X76),X72),X74),X76,X75) = hAPP(hAPP(X73,X72),c_Finite__Set_Ofold(X73,X71,c_HOL_Ominus__class_Ominus(X74,hAPP(hAPP(c_Set_Oinsert(X76),X72),c_Orderings_Obot__class_Obot(tc_fun(X76,tc_bool))),tc_fun(X76,tc_bool)),X76,X75))
| ~ c_Finite__Set_Ofinite(X74,X76)
| ~ c_Finite__Set_Ofun__left__comm(X73,X76,X75) ),
inference(variable_rename,[status(thm)],[c_0_992]) ).
fof(c_0_1903,plain,
! [X13,X14,X15] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X14,hAPP(hAPP(c_Set_Oinsert(X15),X13),c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool))),tc_fun(X15,tc_bool)),X15)),c_Finite__Set_Ocard(X14,X15)))
| ~ hBOOL(hAPP(hAPP(c_in(X15),X13),X14))
| ~ c_Finite__Set_Ofinite(X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_993]) ).
fof(c_0_1904,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X17,tc_bool)),X16),hAPP(hAPP(c_Set_Oinsert(X17),X14),X15)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X17,tc_bool)),X16),X15))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X17,tc_bool)),c_HOL_Ominus__class_Ominus(X16,hAPP(hAPP(c_Set_Oinsert(X17),X14),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_bool))),tc_fun(X17,tc_bool))),X15)) ),
inference(variable_rename,[status(thm)],[c_0_994]) ).
fof(c_0_1905,plain,
! [X58,X59,X60,X61,X62] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X61)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X61),c_Finite__Set_Osetsum(X58,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X62,tc_bool)),X60),X59),X62,X61)),c_Finite__Set_Osetsum(X58,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X62,tc_bool)),X60),X59),X62,X61)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X61),c_Finite__Set_Osetsum(X58,X60,X62,X61)),c_Finite__Set_Osetsum(X58,X59,X62,X61))
| ~ c_Finite__Set_Ofinite(X59,X62)
| ~ c_Finite__Set_Ofinite(X60,X62) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_995])])]) ).
fof(c_0_1906,plain,
! [X58,X59,X60,X61,X62] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X61)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X61),c_Finite__Set_Osetprod(X58,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X62,tc_bool)),X60),X59),X62,X61)),c_Finite__Set_Osetprod(X58,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X62,tc_bool)),X60),X59),X62,X61)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X61),c_Finite__Set_Osetprod(X58,X60,X62,X61)),c_Finite__Set_Osetprod(X58,X59,X62,X61))
| ~ c_Finite__Set_Ofinite(X59,X62)
| ~ c_Finite__Set_Ofinite(X60,X62) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_996])])]) ).
fof(c_0_1907,plain,
! [X76,X77,X78,X79,X80,X81] :
( c_Map_Omap__add(c_Fun_Ofun__upd(X79,X77,hAPP(c_Option_Ooption_OSome(X80),X76),X81,tc_Option_Ooption(X80)),X78,X81,X80) = c_Fun_Ofun__upd(c_Map_Omap__add(X79,X78,X81,X80),X77,hAPP(c_Option_Ooption_OSome(X80),X76),X81,tc_Option_Ooption(X80))
| hBOOL(hAPP(hAPP(c_in(X81),X77),c_Map_Odom(X78,X81,X80))) ),
inference(variable_rename,[status(thm)],[c_0_997]) ).
fof(c_0_1908,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X17,tc_bool)),X16),hAPP(hAPP(c_Set_Oinsert(X17),X14),X15)))
| ~ hBOOL(hAPP(hAPP(c_in(X17),X14),X16))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X17,tc_bool)),c_HOL_Ominus__class_Ominus(X16,hAPP(hAPP(c_Set_Oinsert(X17),X14),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_bool))),tc_fun(X17,tc_bool))),X15))
| hBOOL(hAPP(hAPP(c_in(X17),X14),X15)) ),
inference(variable_rename,[status(thm)],[c_0_998]) ).
fof(c_0_1909,plain,
! [X39,X40,X41,X42,X43] :
( ~ class_OrderedGroup_Oab__group__add(X42)
| c_Finite__Set_Osetsum(X39,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X43,tc_bool)),X41),X40),X43,X42) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X42),c_Finite__Set_Osetsum(X39,X41,X43,X42)),c_Finite__Set_Osetsum(X39,X40,X43,X42)),c_Finite__Set_Osetsum(X39,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X43,tc_bool)),X41),X40),X43,X42),X42)
| ~ c_Finite__Set_Ofinite(X40,X43)
| ~ c_Finite__Set_Ofinite(X41,X43) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_999])])]) ).
fof(c_0_1910,plain,
! [X38,X39,X40] :
( hBOOL(hAPP(hAPP(c_in(X40),hAPP(c_Finite__Set_Ofold1(X38,X40),X39)),X39))
| ~ hBOOL(hAPP(hAPP(c_in(X40),hAPP(hAPP(X38,c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1(X38,X40)),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2(X38,X40))),hAPP(hAPP(c_Set_Oinsert(X40),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1(X38,X40)),hAPP(hAPP(c_Set_Oinsert(X40),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2(X38,X40)),c_Orderings_Obot__class_Obot(tc_fun(X40,tc_bool))))))
| X39 = c_Orderings_Obot__class_Obot(tc_fun(X40,tc_bool))
| ~ c_Finite__Set_Ofinite(X39,X40)
| ~ c_OrderedGroup_Oab__semigroup__mult(X38,X40) ),
inference(variable_rename,[status(thm)],[c_0_1000]) ).
fof(c_0_1911,plain,
! [X73,X74,X75,X76,X77,X78] :
( c_Fun_Ofun__upd(c_Map_Orestrict__map(X75,X76,X78,X77),X74,X73,X78,tc_Option_Ooption(X77)) = c_Fun_Ofun__upd(c_Map_Orestrict__map(X75,c_HOL_Ominus__class_Ominus(X76,hAPP(hAPP(c_Set_Oinsert(X78),X74),c_Orderings_Obot__class_Obot(tc_fun(X78,tc_bool))),tc_fun(X78,tc_bool)),X78,X77),X74,X73,X78,tc_Option_Ooption(X77))
| ~ hBOOL(hAPP(hAPP(c_in(X78),X74),X76)) ),
inference(variable_rename,[status(thm)],[c_0_1001]) ).
fof(c_0_1912,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| X16 = c_HOL_Ozero__class_Ozero(X17)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X17),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X16),X16)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X15),X15))),c_HOL_Ozero__class_Ozero(X17))) ),
inference(variable_rename,[status(thm)],[c_0_1002]) ).
fof(c_0_1913,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| X15 = c_HOL_Ozero__class_Ozero(X17)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X17),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X16),X16)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X15),X15))),c_HOL_Ozero__class_Ozero(X17))) ),
inference(variable_rename,[status(thm)],[c_0_1003]) ).
fof(c_0_1914,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X17),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X16),X16)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X15),X15))),c_HOL_Ozero__class_Ozero(X17))) ),
inference(variable_rename,[status(thm)],[c_0_1004]) ).
fof(c_0_1915,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X17,tc_bool)),X16),hAPP(hAPP(c_Set_Oinsert(X17),X14),X15)))
| ~ hBOOL(hAPP(hAPP(c_in(X17),X14),X16))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X17,tc_bool)),c_HOL_Ominus__class_Ominus(X16,hAPP(hAPP(c_Set_Oinsert(X17),X14),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_bool))),tc_fun(X17,tc_bool))),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1005]) ).
fof(c_0_1916,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X17,tc_bool)),X16),hAPP(hAPP(c_Set_Oinsert(X17),X14),X15)))
| ~ hBOOL(hAPP(hAPP(c_in(X17),X14),X16))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X17,tc_bool)),c_HOL_Ominus__class_Ominus(X16,hAPP(hAPP(c_Set_Oinsert(X17),X14),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_bool))),tc_fun(X17,tc_bool))),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1006]) ).
fof(c_0_1917,plain,
! [X52,X53,X54,X55,X56,X57,X58] :
( c_Finite__Set_Ofold(X54,X55,hAPP(hAPP(c_Set_Oinsert(X58),X56),X57),X58,X58) = hAPP(hAPP(X54,X56),c_Finite__Set_Ofold(X54,X55,X57,X58,X58))
| ~ c_Finite__Set_Ofinite(X57,X58)
| ~ c_Lattices_Olower__semilattice(X52,X53,X54,X58) ),
inference(variable_rename,[status(thm)],[c_0_1007]) ).
fof(c_0_1918,plain,
! [X43,X44,X45,X46,X47,X48,X49] :
( hAPP(c_Fun_Ofun__upd(X45,X47,hAPP(c_Option_Ooption_OSome(X49),X46),X48,tc_Option_Ooption(X49)),X44) != hAPP(c_Option_Ooption_OSome(X49),X43)
| hAPP(X45,X44) = hAPP(c_Option_Ooption_OSome(X49),X43)
| X46 = X43 ),
inference(variable_rename,[status(thm)],[c_0_1008]) ).
fof(c_0_1919,plain,
! [X43,X44,X45,X46,X47,X48,X49] :
( hAPP(c_Fun_Ofun__upd(X45,X47,hAPP(c_Option_Ooption_OSome(X49),X46),X48,tc_Option_Ooption(X49)),X44) != hAPP(c_Option_Ooption_OSome(X49),X43)
| hAPP(X45,X44) = hAPP(c_Option_Ooption_OSome(X49),X43)
| X44 = X47 ),
inference(variable_rename,[status(thm)],[c_0_1009]) ).
fof(c_0_1920,plain,
! [X88,X89,X90,X91,X92,X93] :
( X91 = X88
| hAPP(c_Fun_Ofun__upd(X90,X89,hAPP(c_Option_Ooption_OSome(X92),X91),X93,tc_Option_Ooption(X92)),X89) != hAPP(c_Option_Ooption_OSome(X92),X88) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1010])])]) ).
fof(c_0_1921,plain,
! [X71,X72,X73,X74,X75,X76] :
( c_Finite__Set_Ofold(X73,X71,hAPP(hAPP(c_Set_Oinsert(X76),X72),X74),X76,X75) = hAPP(hAPP(X73,X72),c_Finite__Set_Ofold(X73,X71,X74,X76,X75))
| hBOOL(hAPP(hAPP(c_in(X76),X72),X74))
| ~ c_Finite__Set_Ofinite(X74,X76)
| ~ c_Finite__Set_Ofun__left__comm(X73,X76,X75) ),
inference(variable_rename,[status(thm)],[c_0_1011]) ).
fof(c_0_1922,plain,
! [X56,X57,X58,X59,X60,X61,X62] :
( c_Fun_Ofun__upd(X59,X60,hAPP(c_Option_Ooption_OSome(X61),X57),X62,tc_Option_Ooption(X61)) != c_Fun_Ofun__upd(X58,X60,hAPP(c_Option_Ooption_OSome(X61),X56),X62,tc_Option_Ooption(X61))
| X57 = X56 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1012])])]) ).
fof(c_0_1923,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| hBOOL(hAPP(hAPP(c_lessequals(X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),c_HOL_Ozero__class_Ozero(X4)),c_HOL_Ozero__class_Ozero(X4))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),c_HOL_Ozero__class_Ozero(X4)),c_HOL_Ozero__class_Ozero(X4)))),c_HOL_Ozero__class_Ozero(X4))) ),
inference(variable_rename,[status(thm)],[c_0_1013]) ).
fof(c_0_1924,plain,
! [X71,X72,X73,X74,X75,X76] :
( hAPP(hAPP(X73,X72),c_Finite__Set_Ofold(X73,X71,X74,X76,X75)) = c_Finite__Set_Ofold(X73,hAPP(hAPP(X73,X72),X71),X74,X76,X75)
| ~ c_Finite__Set_Ofinite(X74,X76)
| ~ c_Finite__Set_Ofun__left__comm(X73,X76,X75) ),
inference(variable_rename,[status(thm)],[c_0_1014]) ).
fof(c_0_1925,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Olower__semilattice(X23)
| c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X23),X20,hAPP(hAPP(c_Set_Oinsert(X23),X21),X22),X23,X23) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X23),X21),c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X23),X20,X22,X23,X23))
| ~ c_Finite__Set_Ofinite(X22,X23) ),
inference(variable_rename,[status(thm)],[c_0_1015]) ).
fof(c_0_1926,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Oupper__semilattice(X23)
| c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X23),X20,hAPP(hAPP(c_Set_Oinsert(X23),X21),X22),X23,X23) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X23),X21),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X23),X20,X22,X23,X23))
| ~ c_Finite__Set_Ofinite(X22,X23) ),
inference(variable_rename,[status(thm)],[c_0_1016]) ).
fof(c_0_1927,plain,
! [X39,X40,X41,X42,X43] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X42,tc_bool)),c_Set_Ovimage(X39,X41,X42,X43)),c_Set_Ovimage(X39,X40,X42,X43)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X43,tc_bool)),X41),X40)) ),
inference(variable_rename,[status(thm)],[c_0_1017]) ).
fof(c_0_1928,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X17,tc_bool)),c_HOL_Ominus__class_Ominus(X16,hAPP(hAPP(c_Set_Oinsert(X17),X14),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_bool))),tc_fun(X17,tc_bool))),X15))
| ~ hBOOL(hAPP(hAPP(c_in(X17),X14),X16))
| hBOOL(hAPP(hAPP(c_in(X17),X14),X15))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X17,tc_bool)),X16),hAPP(hAPP(c_Set_Oinsert(X17),X14),X15))) ),
inference(variable_rename,[status(thm)],[c_0_1018]) ).
fof(c_0_1929,plain,
! [X71,X72,X73,X74] :
( ~ class_Lattices_Olattice(X74)
| hBOOL(hAPP(hAPP(c_lessequals(X74),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),X73),X72)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),X73),X71))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),X73),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),X72),X71)))) ),
inference(variable_rename,[status(thm)],[c_0_1019]) ).
fof(c_0_1930,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hBOOL(hAPP(hAPP(c_lessequals(X74),hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X73),X72)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X73),X71))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X73),hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X72),X71)))) ),
inference(variable_rename,[status(thm)],[c_0_1020]) ).
fof(c_0_1931,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X17,tc_bool)),c_HOL_Ominus__class_Ominus(X16,hAPP(hAPP(c_Set_Oinsert(X17),X14),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_bool))),tc_fun(X17,tc_bool))),X15))
| ~ hBOOL(hAPP(hAPP(c_in(X17),X14),X16))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X17,tc_bool)),X16),hAPP(hAPP(c_Set_Oinsert(X17),X14),X15))) ),
inference(variable_rename,[status(thm)],[c_0_1021]) ).
fof(c_0_1932,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X4),c_HOL_Ozero__class_Ozero(X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),c_HOL_Ozero__class_Ozero(X4)),c_HOL_Ozero__class_Ozero(X4))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),c_HOL_Ozero__class_Ozero(X4)),c_HOL_Ozero__class_Ozero(X4))))) ),
inference(variable_rename,[status(thm)],[c_0_1022]) ).
fof(c_0_1933,plain,
! [X39,X40,X41,X42,X43] :
( hAPP(X39,X41) = X40
| ~ hBOOL(hAPP(hAPP(c_in(X43),X41),c_Set_Ovimage(X39,hAPP(hAPP(c_Set_Oinsert(X42),X40),c_Orderings_Obot__class_Obot(tc_fun(X42,tc_bool))),X43,X42))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1023])])]) ).
fof(c_0_1934,plain,
! [X73,X74,X75,X76,X77,X78] :
( c_Map_Orestrict__map(c_Fun_Ofun__upd(X75,X74,X73,X78,tc_Option_Ooption(X77)),X76,X78,X77) = c_Map_Orestrict__map(X75,X76,X78,X77)
| hBOOL(hAPP(hAPP(c_in(X78),X74),X76)) ),
inference(variable_rename,[status(thm)],[c_0_1024]) ).
fof(c_0_1935,plain,
! [X81,X82,X83,X84,X85] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X85,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X85,tc_bool)),X84),X83)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X85,tc_bool)),X82),X81)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X85,tc_bool)),X83),X81))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X85,tc_bool)),X84),X82)) ),
inference(variable_rename,[status(thm)],[c_0_1025]) ).
fof(c_0_1936,plain,
! [X81,X82,X83,X84,X85] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X85,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X85,tc_bool)),X84),X83)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X85,tc_bool)),X82),X81)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X85,tc_bool)),X83),X81))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X85,tc_bool)),X84),X82)) ),
inference(variable_rename,[status(thm)],[c_0_1026]) ).
fof(c_0_1937,plain,
! [X71,X72,X73,X74,X75,X76] :
( c_Finite__Set_Ofold(X73,X71,hAPP(hAPP(c_Set_Oinsert(X76),X72),X74),X76,X75) = c_Finite__Set_Ofold(X73,hAPP(hAPP(X73,X72),X71),X74,X76,X75)
| hBOOL(hAPP(hAPP(c_in(X76),X72),X74))
| ~ c_Finite__Set_Ofinite(X74,X76)
| ~ c_Finite__Set_Ofun__left__comm(X73,X76,X75) ),
inference(variable_rename,[status(thm)],[c_0_1027]) ).
fof(c_0_1938,plain,
! [X71,X72,X73,X74] :
( ~ class_Lattices_Olattice(X74)
| hBOOL(hAPP(hAPP(c_lessequals(X74),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),X73),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),X72),X71))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),X73),X72)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),X73),X71)))) ),
inference(variable_rename,[status(thm)],[c_0_1028]) ).
fof(c_0_1939,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hBOOL(hAPP(hAPP(c_lessequals(X74),hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X73),hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X72),X71))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X73),X72)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X73),X71)))) ),
inference(variable_rename,[status(thm)],[c_0_1029]) ).
fof(c_0_1940,plain,
! [X91,X92,X93,X94,X95] :
( ~ class_Ring__and__Field_Oring(X95)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X95),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X95),X94),X91)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X95),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X95),c_HOL_Ominus__class_Ominus(X93,X94,X95)),X91)),X92)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X95),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X95),X93),X91)),X92) ),
inference(variable_rename,[status(thm)],[c_0_1030]) ).
fof(c_0_1941,plain,
! [X91,X92,X93,X94,X95] :
( ~ class_Ring__and__Field_Oring(X95)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X95),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X95),X94),X91)),X92) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X95),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X95),X93),X91)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X95),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X95),c_HOL_Ominus__class_Ominus(X94,X93,X95)),X91)),X92)) ),
inference(variable_rename,[status(thm)],[c_0_1031]) ).
fof(c_0_1942,plain,
! [X73,X74,X75,X76,X77] :
( c_Fun_Ofun__upd(c_Map_Orestrict__map(X74,X75,X77,X76),X73,c_Option_Ooption_ONone(X76),X77,tc_Option_Ooption(X76)) = c_Map_Orestrict__map(X74,c_HOL_Ominus__class_Ominus(X75,hAPP(hAPP(c_Set_Oinsert(X77),X73),c_Orderings_Obot__class_Obot(tc_fun(X77,tc_bool))),tc_fun(X77,tc_bool)),X77,X76)
| ~ hBOOL(hAPP(hAPP(c_in(X77),X73),X75)) ),
inference(variable_rename,[status(thm)],[c_0_1032]) ).
fof(c_0_1943,plain,
! [X64,X65,X66,X67,X68] :
( c_Map_Omap__le(c_Map_Omap__add(X66,X65,X68,X67),X64,X68,X67)
| ~ c_Map_Omap__le(X66,c_Map_Omap__add(X66,X65,X68,X67),X68,X67)
| ~ c_Map_Omap__le(X65,X64,X68,X67)
| ~ c_Map_Omap__le(X66,X64,X68,X67) ),
inference(variable_rename,[status(thm)],[c_0_1033]) ).
fof(c_0_1944,plain,
! [X39,X40,X41,X42,X43] :
( c_Map_Odom(c_Fun_Ofun__upd(X41,X40,X39,X43,tc_Option_Ooption(X42)),X43,X42) = hAPP(hAPP(c_Set_Oinsert(X43),X40),c_Map_Odom(X41,X43,X42))
| X39 = c_Option_Ooption_ONone(X42) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1034])])]) ).
fof(c_0_1945,plain,
! [X43,X44,X45,X46,X47,X48,X49] :
( hAPP(X45,X44) != hAPP(c_Option_Ooption_OSome(X49),X43)
| X44 = X47
| hAPP(c_Fun_Ofun__upd(X45,X47,hAPP(c_Option_Ooption_OSome(X49),X46),X48,tc_Option_Ooption(X49)),X44) = hAPP(c_Option_Ooption_OSome(X49),X43) ),
inference(variable_rename,[status(thm)],[c_0_1035]) ).
fof(c_0_1946,plain,
! [X47,X48,X49,X50] :
( c_Map_Omap__le(X48,X47,X50,X49)
| hBOOL(hAPP(hAPP(c_in(X50),c_Map_Osko__Map__Xmap__le__def__1__1(X48,X47,X50,X49)),c_Map_Odom(X48,X50,X49))) ),
inference(variable_rename,[status(thm)],[c_0_1036]) ).
fof(c_0_1947,plain,
! [X81,X82,X83,X84] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),X83),X81))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X84,tc_bool)),X83),X82)),X81)) ),
inference(variable_rename,[status(thm)],[c_0_1037]) ).
fof(c_0_1948,plain,
! [X81,X82,X83,X84] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),X82),X81))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X84,tc_bool)),X83),X82)),X81)) ),
inference(variable_rename,[status(thm)],[c_0_1038]) ).
fof(c_0_1949,plain,
! [X71,X72,X73,X74,X75,X76] :
( hAPP(c_Fun_Ofun__upd(X74,X73,X72,X75,X76),X71) = hAPP(X74,X71)
| X71 = X73 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1039])])]) ).
fof(c_0_1950,plain,
! [X71,X72,X73,X74,X75,X76] :
( hAPP(c_Fun_Ofun__upd(X74,X73,X72,X76,X75),X71) = hAPP(X74,X71)
| X71 = X73 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1040])])]) ).
fof(c_0_1951,plain,
! [X58,X59,X60,X61,X62] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X61)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X62,tc_bool)),X60),X59) != c_Orderings_Obot__class_Obot(tc_fun(X62,tc_bool))
| ~ c_Finite__Set_Ofinite(X59,X62)
| ~ c_Finite__Set_Ofinite(X60,X62)
| c_Finite__Set_Osetsum(X58,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X62,tc_bool)),X60),X59),X62,X61) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X61),c_Finite__Set_Osetsum(X58,X60,X62,X61)),c_Finite__Set_Osetsum(X58,X59,X62,X61)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1041])])]) ).
fof(c_0_1952,plain,
! [X58,X59,X60,X61,X62] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X61)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X62,tc_bool)),X60),X59) != c_Orderings_Obot__class_Obot(tc_fun(X62,tc_bool))
| ~ c_Finite__Set_Ofinite(X59,X62)
| ~ c_Finite__Set_Ofinite(X60,X62)
| c_Finite__Set_Osetprod(X58,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X62,tc_bool)),X60),X59),X62,X61) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X61),c_Finite__Set_Osetprod(X58,X60,X62,X61)),c_Finite__Set_Osetprod(X58,X59,X62,X61)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1042])])]) ).
fof(c_0_1953,plain,
! [X81,X82,X83,X84] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X84,tc_bool)),X83),X82)),X81))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),X82),X81))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),X83),X81)) ),
inference(variable_rename,[status(thm)],[c_0_1043]) ).
fof(c_0_1954,plain,
! [X81,X82,X83,X84] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X84,tc_bool)),X83),X82)),X81))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),X82),X81))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),X83),X81)) ),
inference(variable_rename,[status(thm)],[c_0_1044]) ).
fof(c_0_1955,plain,
! [X81,X82,X83,X84] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),X83),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X84,tc_bool)),X82),X81)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),c_HOL_Ominus__class_Ominus(X83,X82,tc_fun(X84,tc_bool))),X81)) ),
inference(variable_rename,[status(thm)],[c_0_1045]) ).
fof(c_0_1956,plain,
! [X81,X82,X83,X84] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),c_HOL_Ominus__class_Ominus(X83,X82,tc_fun(X84,tc_bool))),X81))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),X83),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X84,tc_bool)),X82),X81))) ),
inference(variable_rename,[status(thm)],[c_0_1046]) ).
fof(c_0_1957,plain,
! [X39,X40,X41,X42,X43] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X42)
| c_Finite__Set_Osetsum(X39,X41,X43,X42) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X42),hAPP(X39,X40)),c_Finite__Set_Osetsum(X39,c_HOL_Ominus__class_Ominus(X41,hAPP(hAPP(c_Set_Oinsert(X43),X40),c_Orderings_Obot__class_Obot(tc_fun(X43,tc_bool))),tc_fun(X43,tc_bool)),X43,X42))
| ~ hBOOL(hAPP(hAPP(c_in(X43),X40),X41))
| ~ c_Finite__Set_Ofinite(X41,X43) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1047])])]) ).
fof(c_0_1958,plain,
! [X81,X82,X83,X84,X85] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X85,tc_bool)),c_HOL_Ominus__class_Ominus(X84,X83,tc_fun(X85,tc_bool))),c_HOL_Ominus__class_Ominus(X82,X81,tc_fun(X85,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X85,tc_bool)),X81),X83))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X85,tc_bool)),X84),X82)) ),
inference(variable_rename,[status(thm)],[c_0_1048]) ).
fof(c_0_1959,plain,
! [X81,X82,X83,X84] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X84,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X84,tc_bool)),X83),X82)),X81) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X84,tc_bool)),X83),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X84,tc_bool)),X82),X81))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),X81),X83)) ),
inference(variable_rename,[status(thm)],[c_0_1049]) ).
fof(c_0_1960,plain,
! [X73,X74,X75,X76,X77] :
( c_Fun_Ofun__upd(c_Map_Orestrict__map(X74,X75,X77,X76),X73,c_Option_Ooption_ONone(X76),X77,tc_Option_Ooption(X76)) = c_Map_Orestrict__map(X74,X75,X77,X76)
| hBOOL(hAPP(hAPP(c_in(X77),X73),X75)) ),
inference(variable_rename,[status(thm)],[c_0_1050]) ).
fof(c_0_1961,plain,
! [X39,X40,X41,X42,X43] :
( hBOOL(hAPP(hAPP(c_in(X42),hAPP(X39,X40)),X41))
| ~ hBOOL(hAPP(hAPP(c_in(X43),X40),c_Set_Ovimage(X39,X41,X43,X42))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1051])])]) ).
fof(c_0_1962,plain,
! [X39,X40,X41,X42,X43] :
( hBOOL(hAPP(hAPP(c_in(X42),hAPP(X39,X40)),X41))
| ~ hBOOL(hAPP(hAPP(c_in(X43),X40),c_Set_Ovimage(X39,X41,X43,X42))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1052])])]) ).
fof(c_0_1963,plain,
! [X91,X92,X93,X94,X95,X96] :
( ~ class_Ring__and__Field_Oring(X96)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X96),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X96),X95),X91)),X93) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X96),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X96),X94),X91)),X92)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X96),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X96),c_HOL_Ominus__class_Ominus(X95,X94,X96)),X91)),X93) = X92 ),
inference(variable_rename,[status(thm)],[c_0_1053]) ).
fof(c_0_1964,plain,
! [X91,X92,X93,X94,X95,X96] :
( ~ class_Ring__and__Field_Oring(X96)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X96),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X96),X95),X91)),X93) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X96),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X96),X94),X91)),X92)
| X93 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X96),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X96),c_HOL_Ominus__class_Ominus(X94,X95,X96)),X91)),X92) ),
inference(variable_rename,[status(thm)],[c_0_1054]) ).
fof(c_0_1965,plain,
! [X39,X40,X41,X42,X43] :
( ~ class_OrderedGroup_Oab__group__add(X42)
| c_Finite__Set_Osetsum(X39,c_HOL_Ominus__class_Ominus(X41,X40,tc_fun(X43,tc_bool)),X43,X42) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X39,X41,X43,X42),c_Finite__Set_Osetsum(X39,X40,X43,X42),X42)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X43,tc_bool)),X40),X41))
| ~ c_Finite__Set_Ofinite(X41,X43) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1055])])]) ).
fof(c_0_1966,plain,
! [X39,X40,X41,X42,X43] :
( c_Fun_Ofun__upd(X41,X40,X39,X43,X42) != X41
| hAPP(X41,X40) = X39 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1056])])]) ).
fof(c_0_1967,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_Orderings_Oorder(X29)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X29),X27),X25))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X29),X26),X28))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),X28),X27))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X29,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X28,X27,X29)),c_SetInterval_Oord__class_OatLeastAtMost(X26,X25,X29))) ),
inference(variable_rename,[status(thm)],[c_0_1057]) ).
fof(c_0_1968,plain,
! [X91,X92,X93,X94,X95] :
( ~ class_Ring__and__Field_Osemiring(X95)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X95),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X95),X94),X91)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X95),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X95),X93),X91)),X92)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X95),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X95),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X95),X94),X93)),X91)),X92) ),
inference(variable_rename,[status(thm)],[c_0_1058]) ).
fof(c_0_1969,plain,
! [X47,X48,X49,X50] :
( hAPP(X48,c_Map_Osko__Map__Xmap__le__def__1__1(X48,X47,X50,X49)) != hAPP(X47,c_Map_Osko__Map__Xmap__le__def__1__1(X48,X47,X50,X49))
| c_Map_Omap__le(X48,X47,X50,X49) ),
inference(variable_rename,[status(thm)],[c_0_1059]) ).
fof(c_0_1970,plain,
! [X81,X82,X83,X84] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),X81),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X84,tc_bool)),X83),X82)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),X81),X82))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),X81),X83)) ),
inference(variable_rename,[status(thm)],[c_0_1060]) ).
fof(c_0_1971,plain,
! [X81,X82,X83,X84] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),X81),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X84,tc_bool)),X83),X82)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),X81),X82))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),X81),X83)) ),
inference(variable_rename,[status(thm)],[c_0_1061]) ).
fof(c_0_1972,plain,
! [X35,X36,X37] :
( hAPP(c_COMBC(c_in(X37),X37,tc_fun(X37,tc_bool),tc_bool),X36) != hAPP(c_COMBC(c_in(X37),X37,tc_fun(X37,tc_bool),tc_bool),X35)
| X36 = X35 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1062])])]) ).
fof(c_0_1973,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_Orderings_Oorder(X29)
| hBOOL(hAPP(hAPP(c_lessequals(X29),X26),X28))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),X28),X27))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X29,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X28,X27,X29)),c_SetInterval_Oord__class_OatLeastAtMost(X26,X25,X29))) ),
inference(variable_rename,[status(thm)],[c_0_1063]) ).
fof(c_0_1974,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_Orderings_Oorder(X29)
| hBOOL(hAPP(hAPP(c_lessequals(X29),X27),X25))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),X28),X27))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X29,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X28,X27,X29)),c_SetInterval_Oord__class_OatLeastAtMost(X26,X25,X29))) ),
inference(variable_rename,[status(thm)],[c_0_1064]) ).
fof(c_0_1975,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_Orderings_Oorder(X29)
| hBOOL(hAPP(hAPP(c_lessequals(X29),X26),X28))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),X28),X27))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X29,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X28,X27,X29)),c_SetInterval_Oord__class_OatLeastAtMost(X26,X25,X29))) ),
inference(variable_rename,[status(thm)],[c_0_1065]) ).
fof(c_0_1976,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_Orderings_Oorder(X29)
| hBOOL(hAPP(hAPP(c_lessequals(X29),X27),X25))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),X28),X27))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X29,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X28,X27,X29)),c_SetInterval_Oord__class_OatLeastAtMost(X26,X25,X29))) ),
inference(variable_rename,[status(thm)],[c_0_1066]) ).
fof(c_0_1977,plain,
! [X39,X40,X41,X42] :
( X41 = X40
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X39,hAPP(hAPP(c_Set_Oinsert(X42),X41),c_Orderings_Obot__class_Obot(tc_fun(X42,tc_bool))),X42),X40)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1067])])]) ).
fof(c_0_1978,plain,
! [X39,X40,X41,X42,X43] :
( hBOOL(hAPP(X41,hAPP(X40,X39)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X40,X41,X43,X42),X39)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1068])])]) ).
fof(c_0_1979,plain,
! [X58,X59,X60,X61] :
( c_Map_Omap__add(X59,X58,X61,X60) = c_Map_Omap__add(X58,X59,X61,X60)
| ~ c_Map_Omap__le(X59,c_Map_Omap__add(X59,X58,X61,X60),X61,X60) ),
inference(variable_rename,[status(thm)],[c_0_1069]) ).
fof(c_0_1980,plain,
! [X81,X82,X83,X84] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),X81),X82))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),X81),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X84,tc_bool)),X83),X82))) ),
inference(variable_rename,[status(thm)],[c_0_1070]) ).
fof(c_0_1981,plain,
! [X81,X82,X83,X84] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),X81),X83))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),X81),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X84,tc_bool)),X83),X82))) ),
inference(variable_rename,[status(thm)],[c_0_1071]) ).
fof(c_0_1982,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_Orderings_Oorder(X29)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X29,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X28,X27,X29)),c_SetInterval_Oord__class_OatLeastAtMost(X26,X25,X29)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X29),X27),X25))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),X27),X25))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),X26),X28)) ),
inference(variable_rename,[status(thm)],[c_0_1072]) ).
fof(c_0_1983,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_Orderings_Oorder(X29)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X29,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X28,X27,X29)),c_SetInterval_Oord__class_OatLeastAtMost(X26,X25,X29)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X29),X26),X28))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),X27),X25))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),X26),X28)) ),
inference(variable_rename,[status(thm)],[c_0_1073]) ).
fof(c_0_1984,plain,
! [X81,X82,X83,X84] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X84,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X84,tc_bool)),X83),X82)),X81) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X84,tc_bool)),X83),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X84,tc_bool)),X82),X81))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),X81),X83)) ),
inference(variable_rename,[status(thm)],[c_0_1074]) ).
fof(c_0_1985,plain,
! [X39,X40,X41,X42,X43] :
( ~ class_Ring__and__Field_Oring(X42)
| c_Finite__Set_Osetsum(X39,c_HOL_Ominus__class_Ominus(X41,hAPP(hAPP(c_Set_Oinsert(X43),X40),c_Orderings_Obot__class_Obot(tc_fun(X43,tc_bool))),tc_fun(X43,tc_bool)),X43,X42) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X39,X41,X43,X42),hAPP(X39,X40),X42)
| ~ hBOOL(hAPP(hAPP(c_in(X43),X40),X41))
| ~ c_Finite__Set_Ofinite(X41,X43) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1075])])]) ).
fof(c_0_1986,plain,
! [X39,X40,X41,X42,X43] :
( ~ class_OrderedGroup_Oab__group__add(X42)
| c_Finite__Set_Osetsum(X39,c_HOL_Ominus__class_Ominus(X41,hAPP(hAPP(c_Set_Oinsert(X43),X40),c_Orderings_Obot__class_Obot(tc_fun(X43,tc_bool))),tc_fun(X43,tc_bool)),X43,X42) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X39,X41,X43,X42),hAPP(X39,X40),X42)
| ~ hBOOL(hAPP(hAPP(c_in(X43),X40),X41))
| ~ c_Finite__Set_Ofinite(X41,X43) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1076])])]) ).
fof(c_0_1987,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_Orderings_Oorder(X29)
| hBOOL(hAPP(hAPP(c_lessequals(X29),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X29,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X28,X27,X29)),c_SetInterval_Oord__class_OatLeastAtMost(X26,X25,X29))) ),
inference(variable_rename,[status(thm)],[c_0_1077]) ).
fof(c_0_1988,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X17),c_HOL_Ozero__class_Ozero(X17)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X16),X16)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X15),X15))))
| X16 = c_HOL_Ozero__class_Ozero(X17) ),
inference(variable_rename,[status(thm)],[c_0_1078]) ).
fof(c_0_1989,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X17),c_HOL_Ozero__class_Ozero(X17)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X16),X16)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X15),X15))))
| X15 = c_HOL_Ozero__class_Ozero(X17) ),
inference(variable_rename,[status(thm)],[c_0_1079]) ).
fof(c_0_1990,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| hBOOL(hAPP(hAPP(c_lessequals(X17),c_HOL_Ozero__class_Ozero(X17)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X16),X16)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X15),X15)))) ),
inference(variable_rename,[status(thm)],[c_0_1080]) ).
fof(c_0_1991,plain,
! [X58,X59,X60,X61] :
( c_Map_Omap__add(X59,X58,X61,X60) != c_Map_Omap__add(X58,X59,X61,X60)
| c_Map_Omap__le(X59,c_Map_Omap__add(X59,X58,X61,X60),X61,X60) ),
inference(variable_rename,[status(thm)],[c_0_1081]) ).
fof(c_0_1992,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X17,tc_bool)),X16),hAPP(hAPP(c_Set_Oinsert(X17),X14),X15)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X17,tc_bool)),X16),X15))
| hBOOL(hAPP(hAPP(c_in(X17),X14),X16))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X17,tc_bool)),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1082]) ).
fof(c_0_1993,plain,
! [X10,X11,X12] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X12)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X12),X12),hAPP(hAPP(c_Set_Oinsert(X12),X10),X11)) = c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(X12),X10,X11,X12,X12)
| hBOOL(hAPP(hAPP(c_in(X12),X10),X11))
| ~ c_Finite__Set_Ofinite(X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1083]) ).
fof(c_0_1994,plain,
! [X10,X11,X12] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X12)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X12),X12),hAPP(hAPP(c_Set_Oinsert(X12),X10),X11)) = c_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(X12),X10,X11,X12,X12)
| hBOOL(hAPP(hAPP(c_in(X12),X10),X11))
| ~ c_Finite__Set_Ofinite(X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1084]) ).
fof(c_0_1995,plain,
! [X38,X39,X40,X41] :
( hAPP(c_Finite__Set_Ofold1(X38,X41),hAPP(hAPP(c_Set_Oinsert(X41),X39),X40)) = c_Finite__Set_Ofold(X38,X39,X40,X41,X41)
| hBOOL(hAPP(hAPP(c_in(X41),X39),X40))
| ~ c_Finite__Set_Ofinite(X40,X41)
| ~ c_OrderedGroup_Oab__semigroup__mult(X38,X41) ),
inference(variable_rename,[status(thm)],[c_0_1085]) ).
fof(c_0_1996,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X29)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X29),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X29),X28),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X29),X27),X25)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),c_HOL_Ozero__class_Ozero(X29)),X26))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X29),c_HOL_Ozero__class_Ozero(X29)),X27))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X29),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X29),X28),X27)) ),
inference(variable_rename,[status(thm)],[c_0_1086]) ).
fof(c_0_1997,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X29)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X29),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X29),X28),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X29),X27),X25)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X29),c_HOL_Ozero__class_Ozero(X29)),X26))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),c_HOL_Ozero__class_Ozero(X29)),X28))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X29),X28),X27)) ),
inference(variable_rename,[status(thm)],[c_0_1087]) ).
fof(c_0_1998,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X29)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X29),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X29),X28),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X29),X27),X25)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),c_HOL_Ozero__class_Ozero(X29)),X26))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X29),c_HOL_Ozero__class_Ozero(X29)),X28))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X29),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),X28),X27)) ),
inference(variable_rename,[status(thm)],[c_0_1088]) ).
fof(c_0_1999,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X29)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X29),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X29),X28),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X29),X27),X25)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),c_HOL_Ozero__class_Ozero(X29)),X26))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),c_HOL_Ozero__class_Ozero(X29)),X28))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X29),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X29),X28),X27)) ),
inference(variable_rename,[status(thm)],[c_0_1089]) ).
fof(c_0_2000,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_Ring__and__Field_Opordered__semiring(X29)
| hBOOL(hAPP(hAPP(c_lessequals(X29),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X29),X28),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X29),X27),X25)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),c_HOL_Ozero__class_Ozero(X29)),X26))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),c_HOL_Ozero__class_Ozero(X29)),X27))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),X28),X27)) ),
inference(variable_rename,[status(thm)],[c_0_1090]) ).
fof(c_0_2001,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_Ring__and__Field_Opordered__semiring(X29)
| hBOOL(hAPP(hAPP(c_lessequals(X29),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X29),X28),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X29),X27),X25)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),c_HOL_Ozero__class_Ozero(X29)),X26))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),c_HOL_Ozero__class_Ozero(X29)),X28))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),X28),X27)) ),
inference(variable_rename,[status(thm)],[c_0_1091]) ).
fof(c_0_2002,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Oordered__semiring(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X27),c_HOL_Ozero__class_Ozero(X27)),X24))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X25))) ),
inference(variable_rename,[status(thm)],[c_0_1092]) ).
fof(c_0_2003,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Oordered__semiring(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X27),c_HOL_Ozero__class_Ozero(X27)),X24))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X26),X24)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X25),X24))) ),
inference(variable_rename,[status(thm)],[c_0_1093]) ).
fof(c_0_2004,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X27),c_HOL_Ozero__class_Ozero(X27)),X24))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X25))) ),
inference(variable_rename,[status(thm)],[c_0_1094]) ).
fof(c_0_2005,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X27),c_HOL_Ozero__class_Ozero(X27)),X24))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X26),X24)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X25),X24))) ),
inference(variable_rename,[status(thm)],[c_0_1095]) ).
fof(c_0_2006,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X27)
| hBOOL(hAPP(hAPP(c_lessequals(X27),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X25)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),c_HOL_Ozero__class_Ozero(X27)),X24)) ),
inference(variable_rename,[status(thm)],[c_0_1096]) ).
fof(c_0_2007,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X27)
| hBOOL(hAPP(hAPP(c_lessequals(X27),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),c_HOL_Ozero__class_Ozero(X27)),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X25))) ),
inference(variable_rename,[status(thm)],[c_0_1097]) ).
fof(c_0_2008,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X27)
| hBOOL(hAPP(hAPP(c_lessequals(X27),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),c_HOL_Ozero__class_Ozero(X27)),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X26),X24)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X25),X24))) ),
inference(variable_rename,[status(thm)],[c_0_1098]) ).
fof(c_0_2009,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X25)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),c_HOL_Ozero__class_Ozero(X27)),X24)) ),
inference(variable_rename,[status(thm)],[c_0_1099]) ).
fof(c_0_2010,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X27)
| hBOOL(hAPP(hAPP(c_lessequals(X27),X25),X26))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X25)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X24),c_HOL_Ozero__class_Ozero(X27))) ),
inference(variable_rename,[status(thm)],[c_0_1100]) ).
fof(c_0_2011,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X25),X26))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X25)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X24),c_HOL_Ozero__class_Ozero(X27))) ),
inference(variable_rename,[status(thm)],[c_0_1101]) ).
fof(c_0_2012,plain,
! [X39,X40,X41,X42,X43] :
( hBOOL(hAPP(hAPP(c_in(X42),X40),c_Set_Ovimage(X39,X41,X42,X43)))
| ~ hBOOL(hAPP(hAPP(c_in(X43),hAPP(X39,X40)),X41)) ),
inference(variable_rename,[status(thm)],[c_0_1102]) ).
fof(c_0_2013,plain,
! [X39,X40,X41,X42,X43] :
( hBOOL(hAPP(hAPP(c_in(X42),X40),c_Set_Ovimage(X39,X41,X42,X43)))
| ~ hBOOL(hAPP(hAPP(c_in(X43),hAPP(X39,X40)),X41)) ),
inference(variable_rename,[status(thm)],[c_0_1103]) ).
fof(c_0_2014,plain,
! [X39,X40,X41,X42,X43] :
( hBOOL(hAPP(hAPP(c_in(X43),X40),c_Set_Ovimage(X39,X41,X43,X42)))
| ~ hBOOL(hAPP(hAPP(c_in(X42),hAPP(X39,X40)),X41)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1104])])]) ).
fof(c_0_2015,plain,
! [X64,X65,X66,X67,X68] :
( c_Map_Omap__le(X65,X64,X68,X67)
| ~ c_Map_Omap__le(c_Map_Omap__add(X66,X65,X68,X67),X64,X68,X67) ),
inference(variable_rename,[status(thm)],[c_0_1105]) ).
fof(c_0_2016,plain,
! [X14,X15,X16] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X16,tc_bool)),X15),X14) = c_Finite__Set_Ofold(c_Set_Oinsert(X16),X14,X15,X16,tc_fun(X16,tc_bool))
| ~ c_Finite__Set_Ofinite(X15,X16) ),
inference(variable_rename,[status(thm)],[c_0_1106]) ).
fof(c_0_2017,plain,
! [X10,X11,X12] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X12)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X12),X12),hAPP(hAPP(c_Set_Oinsert(X12),X10),X11)) = c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(X12),X10,X11,X12,X12)
| ~ c_Finite__Set_Ofinite(X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1107]) ).
fof(c_0_2018,plain,
! [X38,X39,X40,X41] :
( hAPP(c_Finite__Set_Ofold1(X38,X41),hAPP(hAPP(c_Set_Oinsert(X41),X39),X40)) = c_Finite__Set_Ofold(X38,X39,X40,X41,X41)
| ~ c_Finite__Set_Ofinite(X40,X41)
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X38,X41) ),
inference(variable_rename,[status(thm)],[c_0_1108]) ).
fof(c_0_2019,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X24),c_HOL_Ozero__class_Ozero(X27)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),c_HOL_Ozero__class_Ozero(X27)),X24))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X25))) ),
inference(variable_rename,[status(thm)],[c_0_1109]) ).
fof(c_0_2020,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X24),c_HOL_Ozero__class_Ozero(X27)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),c_HOL_Ozero__class_Ozero(X27)),X24))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X26),X24)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X25),X24))) ),
inference(variable_rename,[status(thm)],[c_0_1110]) ).
fof(c_0_2021,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X17,tc_bool)),X16),X15))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X17,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X17),X14),X16)),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1111]) ).
fof(c_0_2022,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X25),X26))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),c_HOL_Ozero__class_Ozero(X27)),X24))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X26),X24)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X25),X24))) ),
inference(variable_rename,[status(thm)],[c_0_1112]) ).
fof(c_0_2023,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X25),X26))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),c_HOL_Ozero__class_Ozero(X27)),X24))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X25))) ),
inference(variable_rename,[status(thm)],[c_0_1113]) ).
fof(c_0_2024,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X24),c_HOL_Ozero__class_Ozero(X27)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X26),X24)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X25),X24))) ),
inference(variable_rename,[status(thm)],[c_0_1114]) ).
fof(c_0_2025,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X24),c_HOL_Ozero__class_Ozero(X27)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X25))) ),
inference(variable_rename,[status(thm)],[c_0_1115]) ).
fof(c_0_2026,plain,
! [X13,X14,X15] :
( c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X14,hAPP(hAPP(c_Set_Oinsert(X15),X13),c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool))),tc_fun(X15,tc_bool)),X15)) = c_Finite__Set_Ocard(X14,X15)
| ~ hBOOL(hAPP(hAPP(c_in(X15),X13),X14))
| ~ c_Finite__Set_Ofinite(X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_1116]) ).
fof(c_0_2027,plain,
! [X81,X82,X83,X84] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X84),X81),X83)),hAPP(hAPP(c_Set_Oinsert(X84),X81),X82)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),X83),X82)) ),
inference(variable_rename,[status(thm)],[c_0_1117]) ).
fof(c_0_2028,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X25),X26))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X25))) ),
inference(variable_rename,[status(thm)],[c_0_1118]) ).
fof(c_0_2029,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X25),X26))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X26),X24)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X25),X24))) ),
inference(variable_rename,[status(thm)],[c_0_1119]) ).
fof(c_0_2030,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X17,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X17),X14),X16)),X15))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X17,tc_bool)),X16),X15))
| ~ hBOOL(hAPP(hAPP(c_in(X17),X14),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1120]) ).
fof(c_0_2031,plain,
! [X58,X59,X60,X61] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X61,tc_bool)),c_Map_Odom(X59,X61,X60)),c_Map_Odom(X58,X61,X60)))
| ~ c_Map_Omap__le(X59,X58,X61,X60) ),
inference(variable_rename,[status(thm)],[c_0_1121]) ).
fof(c_0_2032,plain,
! [X14,X15,X16] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X16)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X16),X14),c_Complete__Lattice_OInf__class_OInf(X15,X16)) = c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X16),X14,X15,X16,X16)
| ~ c_Finite__Set_Ofinite(X15,X16) ),
inference(variable_rename,[status(thm)],[c_0_1122]) ).
fof(c_0_2033,plain,
! [X14,X15,X16] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X16)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X16),X14),c_Complete__Lattice_OSup__class_OSup(X15,X16)) = c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X16),X14,X15,X16,X16)
| ~ c_Finite__Set_Ofinite(X15,X16) ),
inference(variable_rename,[status(thm)],[c_0_1123]) ).
fof(c_0_2034,plain,
! [X57,X58,X59,X60,X61] :
( hAPP(X58,X59) != hAPP(c_Option_Ooption_OSome(X61),X57)
| c_Fun_Ofun__upd(X58,X59,hAPP(c_Option_Ooption_OSome(X61),X57),X60,tc_Option_Ooption(X61)) = X58 ),
inference(variable_rename,[status(thm)],[c_0_1124]) ).
fof(c_0_2035,plain,
! [X13,X14,X15] :
( c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(X15),X13),X14),X15) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X14,hAPP(hAPP(c_Set_Oinsert(X15),X13),c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool))),tc_fun(X15,tc_bool)),X15))
| ~ c_Finite__Set_Ofinite(X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_1125]) ).
fof(c_0_2036,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X17,tc_bool)),X16),X15))
| hBOOL(hAPP(hAPP(c_in(X17),X14),X16))
| hBOOL(hAPP(hAPP(c_in(X17),X14),X15))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X17,tc_bool)),X16),hAPP(hAPP(c_Set_Oinsert(X17),X14),X15))) ),
inference(variable_rename,[status(thm)],[c_0_1126]) ).
fof(c_0_2037,plain,
! [X24,X25,X26,X27] :
( hBOOL(hAPP(hAPP(c_in(X27),X24),X25))
| hBOOL(hAPP(hAPP(c_in(X27),X24),X26))
| ~ hBOOL(hAPP(hAPP(c_in(X27),X24),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X27,tc_bool)),X26),X25))) ),
inference(variable_rename,[status(thm)],[c_0_1127]) ).
fof(c_0_2038,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_Orderings_Oorder(X29)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X29,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X28,X27,X29)),c_SetInterval_Oord__class_OatLeastAtMost(X26,X25,X29)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),X27),X25))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),X26),X28)) ),
inference(variable_rename,[status(thm)],[c_0_1128]) ).
fof(c_0_2039,plain,
! [X63,X64,X65,X66] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X66,tc_bool)),c_Map_Odom(X64,X66,X65)),c_Map_Odom(X63,X66,X65)) != c_Orderings_Obot__class_Obot(tc_fun(X66,tc_bool))
| c_Map_Omap__add(X64,X63,X66,X65) = c_Map_Omap__add(X63,X64,X66,X65) ),
inference(variable_rename,[status(thm)],[c_0_1129]) ).
fof(c_0_2040,plain,
! [X4] :
( ~ class_Orderings_Olinorder(X4)
| c_Lattices_Olower__semilattice(c_COMBC(c_lessequals(X4),X4,X4,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(X4),X4,X4,tc_bool),c_Orderings_Oord__class_Omax(X4),X4) ),
inference(variable_rename,[status(thm)],[c_0_1130]) ).
fof(c_0_2041,plain,
! [X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_Lattices_Olower__semilattice(c_COMBC(c_lessequals(X4),X4,X4,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(X4),X4,X4,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X4),X4) ),
inference(variable_rename,[status(thm)],[c_0_1131]) ).
fof(c_0_2042,plain,
! [X10,X11] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X11)
| c_Complete__Lattice_OSup__class_OSup(X10,X11) = c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X11),c_Orderings_Obot__class_Obot(X11),X10,X11,X11)
| ~ c_Finite__Set_Ofinite(X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1132]) ).
fof(c_0_2043,plain,
! [X24,X25,X26,X27] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X27)
| hBOOL(hAPP(hAPP(c_lessequals(X27),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X24)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X25),X24))) ),
inference(variable_rename,[status(thm)],[c_0_1133]) ).
fof(c_0_2044,plain,
! [X24,X25,X26,X27] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X27)
| hBOOL(hAPP(hAPP(c_lessequals(X27),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X24),X26)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X24),X25))) ),
inference(variable_rename,[status(thm)],[c_0_1134]) ).
fof(c_0_2045,plain,
! [X24,X25,X26,X27] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X24)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X25),X24))) ),
inference(variable_rename,[status(thm)],[c_0_1135]) ).
fof(c_0_2046,plain,
! [X24,X25,X26,X27] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X24),X26)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X24),X25))) ),
inference(variable_rename,[status(thm)],[c_0_1136]) ).
fof(c_0_2047,plain,
! [X13,X14,X15] :
( X14 = hAPP(hAPP(c_Set_Oinsert(X15),X13),c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)))
| X14 = c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X15,tc_bool)),X14),hAPP(hAPP(c_Set_Oinsert(X15),X13),c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool))))) ),
inference(variable_rename,[status(thm)],[c_0_1137]) ).
fof(c_0_2048,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X17,tc_bool)),X16),X15))
| ~ hBOOL(hAPP(hAPP(c_in(X17),X14),X15))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X17,tc_bool)),X16),hAPP(hAPP(c_Set_Oinsert(X17),X14),X15))) ),
inference(variable_rename,[status(thm)],[c_0_1138]) ).
fof(c_0_2049,plain,
! [X14,X15,X16] :
( ~ class_Orderings_Olinorder(X16)
| hBOOL(hAPP(hAPP(c_lessequals(X16),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X16),X16),X14)),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X16),X16),X15)))
| ~ c_Finite__Set_Ofinite(X14,X16)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X16,tc_bool)),X15),X14))
| X15 = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1139]) ).
fof(c_0_2050,plain,
! [X39,X40,X41,X42,X43] :
( ~ class_Ring__and__Field_Ofield(X42)
| c_Finite__Set_Osetprod(X39,c_HOL_Ominus__class_Ominus(X41,hAPP(hAPP(c_Set_Oinsert(X43),X40),c_Orderings_Obot__class_Obot(tc_fun(X43,tc_bool))),tc_fun(X43,tc_bool)),X43,X42) = c_Finite__Set_Osetprod(X39,X41,X43,X42)
| hBOOL(hAPP(hAPP(c_in(X43),X40),X41))
| hAPP(X39,X40) = c_HOL_Ozero__class_Ozero(X42)
| ~ c_Finite__Set_Ofinite(X41,X43) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1140])])]) ).
fof(c_0_2051,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_Orderings_Oorder(X29)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X29,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X28,X27,X29)),c_SetInterval_Oord__class_OatLeastAtMost(X26,X25,X29)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),X26),X25))
| hBOOL(hAPP(hAPP(c_lessequals(X29),X28),X27)) ),
inference(variable_rename,[status(thm)],[c_0_1141]) ).
fof(c_0_2052,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_in(X17),X14),X15))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X17,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X17),X14),X16)),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1142]) ).
fof(c_0_2053,plain,
! [X81,X82,X83,X84] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X84,tc_bool)),X83),X81))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X84,tc_bool)),X82),X81))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X84,tc_bool)),X83),X82)) ),
inference(variable_rename,[status(thm)],[c_0_1143]) ).
fof(c_0_2054,plain,
! [X81,X82,X83,X84] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),X83),X81))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),X82),X81))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),X83),X82)) ),
inference(variable_rename,[status(thm)],[c_0_1144]) ).
fof(c_0_2055,plain,
! [X81,X82,X83,X84] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X84,tc_bool)),X83),X81))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),X82),X81))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X84,tc_bool)),X83),X82)) ),
inference(variable_rename,[status(thm)],[c_0_1145]) ).
fof(c_0_2056,plain,
! [X81,X82,X83,X84] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X84,tc_bool)),X83),X81))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X84,tc_bool)),X82),X81))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),X83),X82)) ),
inference(variable_rename,[status(thm)],[c_0_1146]) ).
fof(c_0_2057,plain,
! [X39,X40,X41,X42,X43] :
( ~ class_OrderedGroup_Oab__group__add(X42)
| c_Finite__Set_Osetsum(X39,c_HOL_Ominus__class_Ominus(X41,hAPP(hAPP(c_Set_Oinsert(X43),X40),c_Orderings_Obot__class_Obot(tc_fun(X43,tc_bool))),tc_fun(X43,tc_bool)),X43,X42) = c_Finite__Set_Osetsum(X39,X41,X43,X42)
| hBOOL(hAPP(hAPP(c_in(X43),X40),X41))
| ~ c_Finite__Set_Ofinite(X41,X43) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1147])])]) ).
fof(c_0_2058,plain,
! [X37,X38,X39] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OBODY(X39)),X38),X37))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Option_Othe(hAPP(c_Com_Obody,X39),tc_Com_Ocom)),X38),X37)) ),
inference(variable_rename,[status(thm)],[c_0_1148]) ).
fof(c_0_2059,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X17,tc_bool)),X16),X15))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X17,tc_bool)),X16),hAPP(hAPP(c_Set_Oinsert(X17),X14),X15)))
| hBOOL(hAPP(hAPP(c_in(X17),X14),X16)) ),
inference(variable_rename,[status(thm)],[c_0_1149]) ).
fof(c_0_2060,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X17,tc_bool)),X16),X15))
| hBOOL(hAPP(hAPP(c_in(X17),X14),X16))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X17,tc_bool)),X16),hAPP(hAPP(c_Set_Oinsert(X17),X14),X15))) ),
inference(variable_rename,[status(thm)],[c_0_1150]) ).
fof(c_0_2061,plain,
! [X24,X25,X26,X27] :
( hBOOL(hAPP(hAPP(c_in(X27),X24),X25))
| ~ hBOOL(hAPP(hAPP(c_in(X27),X24),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X27,tc_bool)),X26),X25))) ),
inference(variable_rename,[status(thm)],[c_0_1151]) ).
fof(c_0_2062,plain,
! [X24,X25,X26,X27] :
( hBOOL(hAPP(hAPP(c_in(X27),X24),X26))
| ~ hBOOL(hAPP(hAPP(c_in(X27),X24),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X27,tc_bool)),X26),X25))) ),
inference(variable_rename,[status(thm)],[c_0_1152]) ).
fof(c_0_2063,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X17,tc_bool)),X16),hAPP(hAPP(c_Set_Oinsert(X17),X14),X15)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X17,tc_bool)),X16),X15))
| hBOOL(hAPP(hAPP(c_in(X17),X14),X16))
| hBOOL(hAPP(hAPP(c_in(X17),X14),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1153]) ).
fof(c_0_2064,plain,
! [X39,X40,X41,X42] :
( c_Finite__Set_Osetsum(X39,c_HOL_Ominus__class_Ominus(X41,hAPP(hAPP(c_Set_Oinsert(X42),X40),c_Orderings_Obot__class_Obot(tc_fun(X42,tc_bool))),tc_fun(X42,tc_bool)),X42,tc_nat) = c_Finite__Set_Osetsum(X39,X41,X42,tc_nat)
| hBOOL(hAPP(hAPP(c_in(X42),X40),X41)) ),
inference(variable_rename,[status(thm)],[c_0_1154]) ).
fof(c_0_2065,plain,
! [X14,X15,X16] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X16,tc_bool)),X15),X14))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(X15,X16)),c_Finite__Set_Ocard(X14,X16)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X16,tc_bool)),X15),X14))
| ~ c_Finite__Set_Ofinite(X14,X16) ),
inference(variable_rename,[status(thm)],[c_0_1155]) ).
fof(c_0_2066,plain,
! [X96,X97,X98,X99,X100] :
( ~ class_Ring__and__Field_Oidom(X100)
| ~ class_Int_Onumber__ring(X100)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X100),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X100),X99),X97)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X100),X98),X96)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X100),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X100),X99),X96)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X100),X98),X97))
| X97 = X96
| X99 = X98 ),
inference(variable_rename,[status(thm)],[c_0_1156]) ).
fof(c_0_2067,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_Ring__and__Field_Oidom(X29)
| ~ class_Int_Onumber__ring(X29)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X29),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X29),X28),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X29),X27),X25)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X29),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X29),X28),X25)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X29),X27),X26))
| X26 = X25
| X28 = X27 ),
inference(variable_rename,[status(thm)],[c_0_1157]) ).
fof(c_0_2068,plain,
! [X39,X40,X41,X42,X43] :
( hBOOL(hAPP(c_Set_Ovimage(X40,X41,X43,X42),X39))
| ~ hBOOL(hAPP(X41,hAPP(X40,X39))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1158])])]) ).
fof(c_0_2069,plain,
! [X81,X82,X83,X84] :
( c_HOL_Ominus__class_Ominus(X82,c_HOL_Ominus__class_Ominus(X81,X83,tc_fun(X84,tc_bool)),tc_fun(X84,tc_bool)) = X83
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),X82),X81))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X84,tc_bool)),X83),X82)) ),
inference(variable_rename,[status(thm)],[c_0_1159]) ).
fof(c_0_2070,plain,
! [X58,X59,X60,X61] :
( ~ class_HOL_Oord(X60)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X61,X60)),X59),X58))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X61,X60)),X58),X59))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X61,X60)),X59),X58)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1160])])]) ).
fof(c_0_2071,plain,
! [X51,X52,X53] :
( c_Orderings_Olinorder(c_COMBC(X51,X53,X53,tc_bool),c_COMBC(X52,X53,X53,tc_bool),X53)
| ~ c_Orderings_Olinorder(X51,X52,X53) ),
inference(variable_rename,[status(thm)],[c_0_1161]) ).
fof(c_0_2072,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X17,tc_bool)),X16),hAPP(hAPP(c_Set_Oinsert(X17),X14),X15)))
| ~ hBOOL(hAPP(hAPP(c_in(X17),X14),X15))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X17,tc_bool)),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1162]) ).
fof(c_0_2073,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X27)
| hBOOL(hAPP(hAPP(c_lessequals(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X25)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X27),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),c_HOL_Ozero__class_Ozero(X27)),X24)) ),
inference(variable_rename,[status(thm)],[c_0_1163]) ).
fof(c_0_2074,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Omult__mono(X27)
| hBOOL(hAPP(hAPP(c_lessequals(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X26),X24)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X25),X24)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X27),c_HOL_Ozero__class_Ozero(X27)),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X27),X26),X25)) ),
inference(variable_rename,[status(thm)],[c_0_1164]) ).
fof(c_0_2075,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Omult__mono(X27)
| hBOOL(hAPP(hAPP(c_lessequals(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X25)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X27),c_HOL_Ozero__class_Ozero(X27)),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X27),X26),X25)) ),
inference(variable_rename,[status(thm)],[c_0_1165]) ).
fof(c_0_2076,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Omult__mono1(X27)
| hBOOL(hAPP(hAPP(c_lessequals(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X25)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X27),c_HOL_Ozero__class_Ozero(X27)),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X27),X26),X25)) ),
inference(variable_rename,[status(thm)],[c_0_1166]) ).
fof(c_0_2077,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X25)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),c_HOL_Ozero__class_Ozero(X27)),X24)) ),
inference(variable_rename,[status(thm)],[c_0_1167]) ).
fof(c_0_2078,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X25)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),c_HOL_Ozero__class_Ozero(X27)),X24))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X26),X25)) ),
inference(variable_rename,[status(thm)],[c_0_1168]) ).
fof(c_0_2079,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X25)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),c_HOL_Ozero__class_Ozero(X27)),X24)) ),
inference(variable_rename,[status(thm)],[c_0_1169]) ).
fof(c_0_2080,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X26),X24)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X25),X24)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),c_HOL_Ozero__class_Ozero(X27)),X24))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X26),X25)) ),
inference(variable_rename,[status(thm)],[c_0_1170]) ).
fof(c_0_2081,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X26),X24)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X25),X24)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),c_HOL_Ozero__class_Ozero(X27)),X24)) ),
inference(variable_rename,[status(thm)],[c_0_1171]) ).
fof(c_0_2082,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X25)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),c_HOL_Ozero__class_Ozero(X27)),X24))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X26),X25)) ),
inference(variable_rename,[status(thm)],[c_0_1172]) ).
fof(c_0_2083,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X22)
| hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),X20))
| hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),X21))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X21),X20)),c_HOL_Ozero__class_Ozero(X22))) ),
inference(variable_rename,[status(thm)],[c_0_1173]) ).
fof(c_0_2084,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X22)
| hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),X20))
| hBOOL(hAPP(hAPP(c_lessequals(X22),X20),c_HOL_Ozero__class_Ozero(X22)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X21),X20)),c_HOL_Ozero__class_Ozero(X22))) ),
inference(variable_rename,[status(thm)],[c_0_1174]) ).
fof(c_0_2085,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X22)
| hBOOL(hAPP(hAPP(c_lessequals(X22),X21),c_HOL_Ozero__class_Ozero(X22)))
| hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),X21))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X21),X20)),c_HOL_Ozero__class_Ozero(X22))) ),
inference(variable_rename,[status(thm)],[c_0_1175]) ).
fof(c_0_2086,plain,
! [X59,X60,X61,X62,X63] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X62)
| c_Finite__Set_Osetsum(X59,hAPP(hAPP(c_Set_Oinsert(X63),X60),X61),X63,X62) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X62),hAPP(X59,X60)),c_Finite__Set_Osetsum(X59,X61,X63,X62))
| hBOOL(hAPP(hAPP(c_in(X63),X60),X61))
| ~ c_Finite__Set_Ofinite(X61,X63) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1176])])]) ).
fof(c_0_2087,plain,
! [X39,X40,X41,X42,X43] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X42)
| c_Finite__Set_Osetprod(X39,hAPP(hAPP(c_Set_Oinsert(X43),X40),X41),X43,X42) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X42),hAPP(X39,X40)),c_Finite__Set_Osetprod(X39,X41,X43,X42))
| hBOOL(hAPP(hAPP(c_in(X43),X40),X41))
| ~ c_Finite__Set_Ofinite(X41,X43) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1177])])]) ).
fof(c_0_2088,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X27)
| hBOOL(hAPP(hAPP(c_lessequals(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X25)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X27),X25),X26))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X24),c_HOL_Ozero__class_Ozero(X27))) ),
inference(variable_rename,[status(thm)],[c_0_1178]) ).
fof(c_0_2089,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Opordered__ring(X27)
| hBOOL(hAPP(hAPP(c_lessequals(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X26),X24)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X25),X24)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X27),X24),c_HOL_Ozero__class_Ozero(X27)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X27),X25),X26)) ),
inference(variable_rename,[status(thm)],[c_0_1179]) ).
fof(c_0_2090,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Opordered__ring(X27)
| hBOOL(hAPP(hAPP(c_lessequals(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X25)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X27),X24),c_HOL_Ozero__class_Ozero(X27)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X27),X25),X26)) ),
inference(variable_rename,[status(thm)],[c_0_1180]) ).
fof(c_0_2091,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X25)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X25),X26))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X24),c_HOL_Ozero__class_Ozero(X27))) ),
inference(variable_rename,[status(thm)],[c_0_1181]) ).
fof(c_0_2092,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X25)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X24),c_HOL_Ozero__class_Ozero(X27)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X25),X26)) ),
inference(variable_rename,[status(thm)],[c_0_1182]) ).
fof(c_0_2093,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X24),X25)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X25),X26))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X24),c_HOL_Ozero__class_Ozero(X27))) ),
inference(variable_rename,[status(thm)],[c_0_1183]) ).
fof(c_0_2094,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X26),X24)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X25),X24)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X24),c_HOL_Ozero__class_Ozero(X27)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X25),X26)) ),
inference(variable_rename,[status(thm)],[c_0_1184]) ).
fof(c_0_2095,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X26),X24)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X25),X24)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X25),X26))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X24),c_HOL_Ozero__class_Ozero(X27))) ),
inference(variable_rename,[status(thm)],[c_0_1185]) ).
fof(c_0_2096,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X22)
| hBOOL(hAPP(hAPP(c_lessequals(X22),X21),c_HOL_Ozero__class_Ozero(X22)))
| hBOOL(hAPP(hAPP(c_lessequals(X22),X20),c_HOL_Ozero__class_Ozero(X22)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X21),X20)),c_HOL_Ozero__class_Ozero(X22))) ),
inference(variable_rename,[status(thm)],[c_0_1186]) ).
fof(c_0_2097,plain,
! [X14,X15,X16] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X16)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X16,tc_bool)),X15),X14) != c_Orderings_Obot__class_Obot(tc_fun(X16,tc_bool))
| X14 = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_bool))
| ~ c_Finite__Set_Ofinite(X14,X16)
| X15 = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_bool))
| ~ c_Finite__Set_Ofinite(X15,X16)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X16),X16),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X16,tc_bool)),X15),X14)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X16),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X16),X16),X15)),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X16),X16),X14)) ),
inference(variable_rename,[status(thm)],[c_0_1187]) ).
fof(c_0_2098,plain,
! [X14,X15,X16] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X16)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X16,tc_bool)),X15),X14) != c_Orderings_Obot__class_Obot(tc_fun(X16,tc_bool))
| X14 = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_bool))
| ~ c_Finite__Set_Ofinite(X14,X16)
| X15 = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_bool))
| ~ c_Finite__Set_Ofinite(X15,X16)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X16),X16),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X16,tc_bool)),X15),X14)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X16),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X16),X16),X15)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X16),X16),X14)) ),
inference(variable_rename,[status(thm)],[c_0_1188]) ).
fof(c_0_2099,plain,
! [X4] :
( ~ class_Orderings_Olinorder(X4)
| c_Orderings_Olinorder(c_COMBC(c_lessequals(X4),X4,X4,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(X4),X4,X4,tc_bool),X4) ),
inference(variable_rename,[status(thm)],[c_0_1189]) ).
fof(c_0_2100,plain,
! [X52,X53,X54,X55,X56,X57,X58] :
( hBOOL(hAPP(hAPP(X54,X53),X52))
| ~ hBOOL(hAPP(hAPP(c_in(X58),X52),X57))
| ~ hBOOL(hAPP(hAPP(X54,X53),hAPP(c_Finite__Set_Ofold1(X56,X58),X57)))
| X57 = c_Orderings_Obot__class_Obot(tc_fun(X58,tc_bool))
| ~ c_Finite__Set_Ofinite(X57,X58)
| ~ c_Lattices_Olower__semilattice(X54,X55,X56,X58) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1190])])]) ).
fof(c_0_2101,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X29)
| hBOOL(hAPP(hAPP(c_lessequals(X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X29),X28),X26)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X29),X27),X25)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),X28),X27)) ),
inference(variable_rename,[status(thm)],[c_0_1191]) ).
fof(c_0_2102,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X29)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X29),X28),X26)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X29),X27),X25)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X29),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X29),X28),X27)) ),
inference(variable_rename,[status(thm)],[c_0_1192]) ).
fof(c_0_2103,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X29)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X29),X28),X26)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X29),X27),X25)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X29),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),X28),X27)) ),
inference(variable_rename,[status(thm)],[c_0_1193]) ).
fof(c_0_2104,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X29)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X29),X28),X26)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X29),X27),X25)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X29),X28),X27)) ),
inference(variable_rename,[status(thm)],[c_0_1194]) ).
fof(c_0_2105,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Olinorder(X15)
| hAPP(c_Finite__Set_Olinorder__class_OMax(X15),X14) = X13
| ~ hBOOL(hAPP(hAPP(c_in(X15),X13),X14))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X15),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(X14,X13,X15)),X13))
| ~ c_Finite__Set_Ofinite(X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_1195]) ).
fof(c_0_2106,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X17,tc_bool)),X16),hAPP(hAPP(c_Set_Oinsert(X17),X14),X15)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X17,tc_bool)),X16),X15))
| hBOOL(hAPP(hAPP(c_in(X17),X14),X16)) ),
inference(variable_rename,[status(thm)],[c_0_1196]) ).
fof(c_0_2107,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X17,tc_bool)),X16),hAPP(hAPP(c_Set_Oinsert(X17),X14),X15)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X17,tc_bool)),X16),X15))
| hBOOL(hAPP(hAPP(c_in(X17),X14),X16)) ),
inference(variable_rename,[status(thm)],[c_0_1197]) ).
fof(c_0_2108,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_Orderings_Oorder(X29)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X29,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X28,X27,X29)),c_SetInterval_Oord__class_OatLeastAtMost(X26,X25,X29)))
| hBOOL(hAPP(hAPP(c_lessequals(X29),X28),X27)) ),
inference(variable_rename,[status(thm)],[c_0_1198]) ).
fof(c_0_2109,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hBOOL(hAPP(hAPP(c_lessequals(X74),X72),X71))
| hBOOL(hAPP(hAPP(c_lessequals(X74),X73),X71))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X73),X72)),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1199]) ).
fof(c_0_2110,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X72),X71))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X73),X71))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X73),X72)),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1200]) ).
fof(c_0_2111,plain,
! [X43,X44,X45,X46] :
( hAPP(X43,X44) = hAPP(c_Option_Ooption_OSome(X45),c_Map_Osko__Map__XdomD__1__1(X44,X43,X46,X45))
| ~ hBOOL(hAPP(hAPP(c_in(X46),X44),c_Map_Odom(X43,X46,X45))) ),
inference(variable_rename,[status(thm)],[c_0_1201]) ).
fof(c_0_2112,plain,
! [X63,X64,X65,X66,X67] :
( c_Map_Omap__le(X65,X63,X67,X66)
| ~ c_Map_Omap__le(X64,X63,X67,X66)
| ~ c_Map_Omap__le(X65,X64,X67,X66) ),
inference(variable_rename,[status(thm)],[c_0_1202]) ).
fof(c_0_2113,plain,
! [X45,X46,X47,X48,X49] :
( hAPP(c_Map_Omap__add(X47,X46,X49,X48),X45) = hAPP(X46,X45)
| ~ hBOOL(hAPP(hAPP(c_in(X49),X45),c_Map_Odom(X46,X49,X48))) ),
inference(variable_rename,[status(thm)],[c_0_1203]) ).
fof(c_0_2114,plain,
! [X24,X25,X26,X27] :
( hBOOL(hAPP(hAPP(c_in(X27),X24),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X27,tc_bool)),X26),X25)))
| ~ hBOOL(hAPP(hAPP(c_in(X27),X24),X25))
| ~ hBOOL(hAPP(hAPP(c_in(X27),X24),X26)) ),
inference(variable_rename,[status(thm)],[c_0_1204]) ).
fof(c_0_2115,plain,
! [X24,X25,X26,X27] :
( hBOOL(hAPP(hAPP(c_in(X27),X24),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X27,tc_bool)),X26),X25)))
| ~ hBOOL(hAPP(hAPP(c_in(X27),X24),X25))
| ~ hBOOL(hAPP(hAPP(c_in(X27),X24),X26)) ),
inference(variable_rename,[status(thm)],[c_0_1205]) ).
fof(c_0_2116,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(X15,X14))
| hBOOL(hAPP(X16,X14))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X17,tc_bool)),X16),X15),X14)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1206])])]) ).
fof(c_0_2117,plain,
! [X58,X59,X60,X61] :
( ~ class_HOL_Oord(X60)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X61,X60)),X58),X59))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X61,X60)),X59),X58)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1207])])]) ).
fof(c_0_2118,plain,
! [X38,X39,X40,X41] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X41,tc_bool)),X40),X39) != c_Orderings_Obot__class_Obot(tc_fun(X41,tc_bool))
| X39 = c_Orderings_Obot__class_Obot(tc_fun(X41,tc_bool))
| ~ c_Finite__Set_Ofinite(X39,X41)
| X40 = c_Orderings_Obot__class_Obot(tc_fun(X41,tc_bool))
| ~ c_Finite__Set_Ofinite(X40,X41)
| ~ c_OrderedGroup_Oab__semigroup__mult(X38,X41)
| hAPP(c_Finite__Set_Ofold1(X38,X41),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X41,tc_bool)),X40),X39)) = hAPP(hAPP(X38,hAPP(c_Finite__Set_Ofold1(X38,X41),X40)),hAPP(c_Finite__Set_Ofold1(X38,X41),X39)) ),
inference(variable_rename,[status(thm)],[c_0_1208]) ).
fof(c_0_2119,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X29)
| hBOOL(hAPP(hAPP(c_lessequals(X29),X28),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X29),X27),X25)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),X26),X25))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X29),X28),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X29),X27),X26))) ),
inference(variable_rename,[status(thm)],[c_0_1209]) ).
fof(c_0_2120,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(X15,X14))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X17,tc_bool)),X16),X15),X14)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1210])])]) ).
fof(c_0_2121,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(X16,X14))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X17,tc_bool)),X16),X15),X14)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1211])])]) ).
fof(c_0_2122,plain,
! [X52,X53,X54,X55,X56,X57] :
( hBOOL(hAPP(hAPP(X52,hAPP(c_Finite__Set_Ofold1(X54,X57),X56)),X55))
| ~ hBOOL(hAPP(hAPP(c_in(X57),X55),X56))
| ~ c_Finite__Set_Ofinite(X56,X57)
| ~ c_Lattices_Olower__semilattice(X52,X53,X54,X57) ),
inference(variable_rename,[status(thm)],[c_0_1212]) ).
fof(c_0_2123,plain,
! [X20,X21,X22] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X22)
| hBOOL(hAPP(hAPP(c_lessequals(X22),X21),X20))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ominus__class_Ominus(X21,X20,X22)),c_HOL_Ozero__class_Ozero(X22))) ),
inference(variable_rename,[status(thm)],[c_0_1213]) ).
fof(c_0_2124,plain,
! [X20,X21,X22] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X22)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),X21),X20))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),c_HOL_Ominus__class_Ominus(X21,X20,X22)),c_HOL_Ozero__class_Ozero(X22))) ),
inference(variable_rename,[status(thm)],[c_0_1214]) ).
fof(c_0_2125,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X10)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X10),X9),c_HOL_Ozero__class_Ozero(X10)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X10),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),X9),X9)),c_HOL_Ozero__class_Ozero(X10))) ),
inference(variable_rename,[status(thm)],[c_0_1215]) ).
fof(c_0_2126,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oordered__idom(X10)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X10),X9),c_HOL_Ozero__class_Ozero(X10)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X10),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),X9),X9)),c_HOL_Ozero__class_Ozero(X10))) ),
inference(variable_rename,[status(thm)],[c_0_1216]) ).
fof(c_0_2127,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X10)
| hBOOL(hAPP(hAPP(c_lessequals(X10),X9),c_HOL_Ozero__class_Ozero(X10)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X10),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),X9),X9)),c_HOL_Ozero__class_Ozero(X10))) ),
inference(variable_rename,[status(thm)],[c_0_1217]) ).
fof(c_0_2128,plain,
! [X20,X21,X22,X23] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X23,tc_bool)),X22),hAPP(hAPP(c_Set_Oinsert(X23),X20),X21)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X23,tc_bool)),X22),X21)) ),
inference(variable_rename,[status(thm)],[c_0_1218]) ).
fof(c_0_2129,plain,
! [X87,X88,X89,X90,X91] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X91)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X91),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X91),X90),X89)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X91),X88),X87)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X91),X88),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X91),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X91),X90),X89)),X87)) ),
inference(variable_rename,[status(thm)],[c_0_1219]) ).
fof(c_0_2130,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X22)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X20),X21)),c_HOL_Ozero__class_Ozero(X22)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),X20),c_HOL_Ozero__class_Ozero(X22)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),c_HOL_Ozero__class_Ozero(X22)),X21)) ),
inference(variable_rename,[status(thm)],[c_0_1220]) ).
fof(c_0_2131,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X22)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X21),X20)),c_HOL_Ozero__class_Ozero(X22)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),X20),c_HOL_Ozero__class_Ozero(X22)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),c_HOL_Ozero__class_Ozero(X22)),X21)) ),
inference(variable_rename,[status(thm)],[c_0_1221]) ).
fof(c_0_2132,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X22)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X21),X20)),c_HOL_Ozero__class_Ozero(X22)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),c_HOL_Ozero__class_Ozero(X22)),X20))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),X21),c_HOL_Ozero__class_Ozero(X22))) ),
inference(variable_rename,[status(thm)],[c_0_1222]) ).
fof(c_0_2133,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X22)
| hBOOL(hAPP(hAPP(c_lessequals(X22),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X21),X20)),c_HOL_Ozero__class_Ozero(X22)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),X20),c_HOL_Ozero__class_Ozero(X22)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),X21)) ),
inference(variable_rename,[status(thm)],[c_0_1223]) ).
fof(c_0_2134,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X22)
| hBOOL(hAPP(hAPP(c_lessequals(X22),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X21),X20)),c_HOL_Ozero__class_Ozero(X22)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),X20))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),X21),c_HOL_Ozero__class_Ozero(X22))) ),
inference(variable_rename,[status(thm)],[c_0_1224]) ).
fof(c_0_2135,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X22)
| hBOOL(hAPP(hAPP(c_lessequals(X22),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X21),X20)),c_HOL_Ozero__class_Ozero(X22)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),X20),c_HOL_Ozero__class_Ozero(X22)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),X21)) ),
inference(variable_rename,[status(thm)],[c_0_1225]) ).
fof(c_0_2136,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X22)
| hBOOL(hAPP(hAPP(c_lessequals(X22),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X21),X20)),c_HOL_Ozero__class_Ozero(X22)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),X20))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),X21),c_HOL_Ozero__class_Ozero(X22))) ),
inference(variable_rename,[status(thm)],[c_0_1226]) ).
fof(c_0_2137,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X22)
| hBOOL(hAPP(hAPP(c_lessequals(X22),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X21),X20)),c_HOL_Ozero__class_Ozero(X22)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),X20),c_HOL_Ozero__class_Ozero(X22)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),X21)) ),
inference(variable_rename,[status(thm)],[c_0_1227]) ).
fof(c_0_2138,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X22)
| hBOOL(hAPP(hAPP(c_lessequals(X22),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X21),X20)),c_HOL_Ozero__class_Ozero(X22)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),X20))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),X21),c_HOL_Ozero__class_Ozero(X22))) ),
inference(variable_rename,[status(thm)],[c_0_1228]) ).
fof(c_0_2139,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X22)
| hBOOL(hAPP(hAPP(c_lessequals(X22),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X20),X21)),c_HOL_Ozero__class_Ozero(X22)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),X20),c_HOL_Ozero__class_Ozero(X22)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),X21)) ),
inference(variable_rename,[status(thm)],[c_0_1229]) ).
fof(c_0_2140,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hBOOL(hAPP(hAPP(c_lessequals(X74),X72),X71))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X73),X72)),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1230]) ).
fof(c_0_2141,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hBOOL(hAPP(hAPP(c_lessequals(X74),X73),X71))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X73),X72)),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1231]) ).
fof(c_0_2142,plain,
! [X20,X21,X22,X23] :
( ~ class_Orderings_Olinorder(X23)
| hBOOL(hAPP(hAPP(c_lessequals(X23),X21),X20))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),hAPP(hAPP(c_Orderings_Oord__class_Omax(X23),X22),X21)),X20)) ),
inference(variable_rename,[status(thm)],[c_0_1232]) ).
fof(c_0_2143,plain,
! [X20,X21,X22,X23] :
( ~ class_Orderings_Olinorder(X23)
| hBOOL(hAPP(hAPP(c_lessequals(X23),X22),X20))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),hAPP(hAPP(c_Orderings_Oord__class_Omax(X23),X22),X21)),X20)) ),
inference(variable_rename,[status(thm)],[c_0_1233]) ).
fof(c_0_2144,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X73),X71))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X73),X72)),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1234]) ).
fof(c_0_2145,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X72),X71))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X73),X72)),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1235]) ).
fof(c_0_2146,plain,
! [X71,X72,X73,X74] :
( ~ class_Lattices_Oupper__semilattice(X74)
| hBOOL(hAPP(hAPP(c_lessequals(X74),X72),X71))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),X73),X72)),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1236]) ).
fof(c_0_2147,plain,
! [X71,X72,X73,X74] :
( ~ class_Lattices_Oupper__semilattice(X74)
| hBOOL(hAPP(hAPP(c_lessequals(X74),X73),X71))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),X73),X72)),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1237]) ).
fof(c_0_2148,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Oupper__semilattice(X23)
| hBOOL(hAPP(hAPP(c_lessequals(X23),X21),X20))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X23),X22),X21)),X20)) ),
inference(variable_rename,[status(thm)],[c_0_1238]) ).
fof(c_0_2149,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Oupper__semilattice(X23)
| hBOOL(hAPP(hAPP(c_lessequals(X23),X22),X20))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X23),X22),X21)),X20)) ),
inference(variable_rename,[status(thm)],[c_0_1239]) ).
fof(c_0_2150,plain,
! [X47,X48,X49,X50,X51] :
( hAPP(X49,X47) = hAPP(X48,X47)
| ~ hBOOL(hAPP(hAPP(c_in(X51),X47),c_Map_Odom(X49,X51,X50)))
| ~ c_Map_Omap__le(X49,X48,X51,X50) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1240])])]) ).
fof(c_0_2151,plain,
! [X15,X16,X17] :
( X15 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(hAPP(c_Set_Oinsert(X17),X16),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_bool))),X17)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X17),X16),c_Orderings_Obot__class_Obot(tc_fun(X17,tc_bool))),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1241]) ).
fof(c_0_2152,plain,
! [X14,X15,X16] :
( X15 = X14
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X16,tc_bool)),X14),X15))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X16,tc_bool)),X15),X14)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1242])])]) ).
fof(c_0_2153,plain,
! [X14,X15,X16] :
( X15 = X14
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X16,tc_bool)),X14),X15))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X16,tc_bool)),X15),X14)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1243])])]) ).
fof(c_0_2154,plain,
! [X52,X53,X54,X55,X56,X57,X58] :
( hBOOL(hAPP(hAPP(X54,hAPP(hAPP(X55,X57),X56)),X52))
| ~ hBOOL(hAPP(hAPP(X54,X56),X52))
| ~ c_Lattices_Olower__semilattice(X53,X54,X55,X58) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1244])])]) ).
fof(c_0_2155,plain,
! [X52,X53,X54,X55,X56,X57,X58] :
( hBOOL(hAPP(hAPP(X54,hAPP(hAPP(X55,X57),X56)),X52))
| ~ hBOOL(hAPP(hAPP(X54,X57),X52))
| ~ c_Lattices_Olower__semilattice(X53,X54,X55,X58) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1245])])]) ).
fof(c_0_2156,plain,
! [X52,X53,X54,X55,X56,X57,X58] :
( hBOOL(hAPP(hAPP(X53,hAPP(hAPP(X55,X57),X56)),X52))
| ~ hBOOL(hAPP(hAPP(X53,X57),X52))
| ~ c_Lattices_Olower__semilattice(X53,X54,X55,X58) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1246])])]) ).
fof(c_0_2157,plain,
! [X52,X53,X54,X55,X56,X57,X58] :
( hBOOL(hAPP(hAPP(X53,hAPP(hAPP(X55,X57),X56)),X52))
| ~ hBOOL(hAPP(hAPP(X53,X56),X52))
| ~ c_Lattices_Olower__semilattice(X53,X54,X55,X58) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1247])])]) ).
fof(c_0_2158,plain,
! [X18,X19,X20,X21] :
( ~ class_Orderings_Olinorder(X21)
| hBOOL(hAPP(hAPP(c_lessequals(X21),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X21),X21),X20)),X19))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X21),X18),X19))
| ~ hBOOL(hAPP(hAPP(c_in(X21),X18),X20))
| X20 = c_Orderings_Obot__class_Obot(tc_fun(X21,tc_bool))
| ~ c_Finite__Set_Ofinite(X20,X21) ),
inference(variable_rename,[status(thm)],[c_0_1248]) ).
fof(c_0_2159,plain,
! [X18,X19,X20,X21] :
( ~ class_Orderings_Olinorder(X21)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X21),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X21),X21),X20)),X19))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X21),X18),X19))
| ~ hBOOL(hAPP(hAPP(c_in(X21),X18),X20))
| X20 = c_Orderings_Obot__class_Obot(tc_fun(X21,tc_bool))
| ~ c_Finite__Set_Ofinite(X20,X21) ),
inference(variable_rename,[status(thm)],[c_0_1249]) ).
fof(c_0_2160,plain,
! [X20,X21,X22] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X22)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X21),X20)),c_HOL_Ozero__class_Ozero(X22)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),X20),c_HOL_Ozero__class_Ozero(X22)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),X21),c_HOL_Ozero__class_Ozero(X22))) ),
inference(variable_rename,[status(thm)],[c_0_1250]) ).
fof(c_0_2161,plain,
! [X20,X21,X22] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X22)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X21),X20)),c_HOL_Ozero__class_Ozero(X22)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),X20),c_HOL_Ozero__class_Ozero(X22)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),X21),c_HOL_Ozero__class_Ozero(X22))) ),
inference(variable_rename,[status(thm)],[c_0_1251]) ).
fof(c_0_2162,plain,
! [X20,X21,X22] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X22)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X21),X20)),c_HOL_Ozero__class_Ozero(X22)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),X20),c_HOL_Ozero__class_Ozero(X22)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),X21),c_HOL_Ozero__class_Ozero(X22))) ),
inference(variable_rename,[status(thm)],[c_0_1252]) ).
fof(c_0_2163,plain,
! [X20,X21,X22] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X22)
| hBOOL(hAPP(hAPP(c_lessequals(X22),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X21),X20)),c_HOL_Ozero__class_Ozero(X22)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),X20),c_HOL_Ozero__class_Ozero(X22)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),X21),c_HOL_Ozero__class_Ozero(X22))) ),
inference(variable_rename,[status(thm)],[c_0_1253]) ).
fof(c_0_2164,plain,
! [X36,X37,X38] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Option_Othe(hAPP(c_Com_Obody,X38),tc_Com_Ocom)),X37),X36))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OBODY(X38)),X37),X36)) ),
inference(variable_rename,[status(thm)],[c_0_1254]) ).
fof(c_0_2165,plain,
! [X57,X58,X59,X60,X61,X62] :
( hAPP(c_Map_Omap__add(X59,X58,X61,X62),X60) != hAPP(c_Option_Ooption_OSome(X62),X57)
| hAPP(X59,X60) = hAPP(c_Option_Ooption_OSome(X62),X57)
| hAPP(X58,X60) = hAPP(c_Option_Ooption_OSome(X62),X57) ),
inference(variable_rename,[status(thm)],[c_0_1255]) ).
fof(c_0_2166,plain,
! [X24,X25,X26,X27] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X27)
| hBOOL(hAPP(hAPP(c_lessequals(X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X24)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X25),X24)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X27),X26),X25)) ),
inference(variable_rename,[status(thm)],[c_0_1256]) ).
fof(c_0_2167,plain,
! [X24,X25,X26,X27] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X27)
| hBOOL(hAPP(hAPP(c_lessequals(X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X24),X26)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X24),X25)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X27),X26),X25)) ),
inference(variable_rename,[status(thm)],[c_0_1257]) ).
fof(c_0_2168,plain,
! [X24,X25,X26,X27] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X27)
| hBOOL(hAPP(hAPP(c_lessequals(X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X24)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X25),X24)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X27),X26),X25)) ),
inference(variable_rename,[status(thm)],[c_0_1258]) ).
fof(c_0_2169,plain,
! [X24,X25,X26,X27] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X27)
| hBOOL(hAPP(hAPP(c_lessequals(X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X24),X26)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X24),X25)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X27),X26),X25)) ),
inference(variable_rename,[status(thm)],[c_0_1259]) ).
fof(c_0_2170,plain,
! [X24,X25,X26,X27] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X24)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X25),X24)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X26),X25)) ),
inference(variable_rename,[status(thm)],[c_0_1260]) ).
fof(c_0_2171,plain,
! [X24,X25,X26,X27] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X24)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X25),X24)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X26),X25)) ),
inference(variable_rename,[status(thm)],[c_0_1261]) ).
fof(c_0_2172,plain,
! [X24,X25,X26,X27] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X24),X26)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X24),X25)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X26),X25)) ),
inference(variable_rename,[status(thm)],[c_0_1262]) ).
fof(c_0_2173,plain,
! [X24,X25,X26,X27] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X24),X26)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X24),X25)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X26),X25)) ),
inference(variable_rename,[status(thm)],[c_0_1263]) ).
fof(c_0_2174,plain,
! [X52,X53,X54,X55,X56,X57,X58] :
( hBOOL(hAPP(hAPP(X53,X52),hAPP(hAPP(X55,X57),X56)))
| ~ hBOOL(hAPP(hAPP(X53,X52),X56))
| ~ hBOOL(hAPP(hAPP(X53,X52),X57))
| ~ c_Lattices_Olower__semilattice(X53,X54,X55,X58) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1264])])]) ).
fof(c_0_2175,plain,
! [X71,X72,X73,X74,X75,X76,X77] :
( hBOOL(hAPP(hAPP(X74,X73),hAPP(hAPP(X76,X72),X71)))
| ~ hBOOL(hAPP(hAPP(X74,X73),X71))
| ~ hBOOL(hAPP(hAPP(X74,X73),X72))
| ~ c_Lattices_Olower__semilattice(X74,X75,X76,X77) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1265])])]) ).
fof(c_0_2176,plain,
! [X71,X72,X73,X74,X75,X76,X77] :
( hBOOL(hAPP(hAPP(X74,X73),hAPP(hAPP(X76,X72),X71)))
| ~ hBOOL(hAPP(hAPP(X74,X73),X71))
| ~ hBOOL(hAPP(hAPP(X74,X73),X72))
| ~ c_Lattices_Olower__semilattice(X74,X75,X76,X77) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1266])])]) ).
fof(c_0_2177,plain,
! [X57,X58,X59,X60,X61,X62] :
( hAPP(c_Map_Omap__add(X59,X58,X61,X62),X60) != hAPP(c_Option_Ooption_OSome(X62),X57)
| hAPP(X58,X60) = c_Option_Ooption_ONone(X62)
| hAPP(X58,X60) = hAPP(c_Option_Ooption_OSome(X62),X57) ),
inference(variable_rename,[status(thm)],[c_0_1267]) ).
fof(c_0_2178,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X22)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),c_HOL_Ozero__class_Ozero(X22)),X20))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),c_HOL_Ozero__class_Ozero(X22)),X21))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),c_HOL_Ozero__class_Ozero(X22)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X20),X21))) ),
inference(variable_rename,[status(thm)],[c_0_1268]) ).
fof(c_0_2179,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X22)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),c_HOL_Ozero__class_Ozero(X22)),X20))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),c_HOL_Ozero__class_Ozero(X22)),X21))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),c_HOL_Ozero__class_Ozero(X22)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X21),X20))) ),
inference(variable_rename,[status(thm)],[c_0_1269]) ).
fof(c_0_2180,plain,
! [X20,X21,X22,X23] :
( ~ class_Orderings_Olinorder(X23)
| hBOOL(hAPP(hAPP(c_lessequals(X23),hAPP(hAPP(c_Orderings_Oord__class_Omax(X23),X22),X21)),X20))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X21),X20))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X22),X20)) ),
inference(variable_rename,[status(thm)],[c_0_1270]) ).
fof(c_0_2181,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hBOOL(hAPP(hAPP(c_lessequals(X74),hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X72),X71)),X73))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X71),X73))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X72),X73)) ),
inference(variable_rename,[status(thm)],[c_0_1271]) ).
fof(c_0_2182,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hBOOL(hAPP(hAPP(c_lessequals(X74),hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X73),X72)),X71))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X72),X71))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X73),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1272]) ).
fof(c_0_2183,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X73),X72)),X71))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X72),X71))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X73),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1273]) ).
fof(c_0_2184,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Oupper__semilattice(X23)
| hBOOL(hAPP(hAPP(c_lessequals(X23),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X23),X22),X21)),X20))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X21),X20))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X22),X20)) ),
inference(variable_rename,[status(thm)],[c_0_1274]) ).
fof(c_0_2185,plain,
! [X71,X72,X73,X74] :
( ~ class_Lattices_Oupper__semilattice(X74)
| hBOOL(hAPP(hAPP(c_lessequals(X74),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),X72),X71)),X73))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X71),X73))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X72),X73)) ),
inference(variable_rename,[status(thm)],[c_0_1275]) ).
fof(c_0_2186,plain,
! [X71,X72,X73,X74] :
( ~ class_Lattices_Oupper__semilattice(X74)
| hBOOL(hAPP(hAPP(c_lessequals(X74),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),X73),X72)),X71))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X72),X71))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X73),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1276]) ).
fof(c_0_2187,plain,
! [X17,X18,X19,X20] :
( c_Hoare__Mirabelle_Ohoare__derivs(X19,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X20)),X18),X17),X20)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X19,X17,X20)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X19,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X20)),X18),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X20),tc_bool))),X20) ),
inference(variable_rename,[status(thm)],[c_0_1277]) ).
fof(c_0_2188,plain,
! [X81,X82,X83,X84] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X84,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X84),X81),X83)),X82) = hAPP(hAPP(c_Set_Oinsert(X84),X81),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X84,tc_bool)),X83),X82))
| ~ hBOOL(hAPP(hAPP(c_in(X84),X81),X82)) ),
inference(variable_rename,[status(thm)],[c_0_1278]) ).
fof(c_0_2189,plain,
! [X83,X84,X85] :
( ~ class_Orderings_Olinorder(X85)
| hBOOL(hAPP(hAPP(c_lessequals(X85),hAPP(c_Finite__Set_Olinorder__class_OMax(X85),X84)),hAPP(c_Finite__Set_Olinorder__class_OMax(X85),X83)))
| ~ c_Finite__Set_Ofinite(X83,X85)
| X84 = c_Orderings_Obot__class_Obot(tc_fun(X85,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X85,tc_bool)),X84),X83)) ),
inference(variable_rename,[status(thm)],[c_0_1279]) ).
fof(c_0_2190,plain,
! [X83,X84,X85] :
( ~ class_Orderings_Olinorder(X85)
| hBOOL(hAPP(hAPP(c_lessequals(X85),hAPP(c_Finite__Set_Olinorder__class_OMin(X85),X83)),hAPP(c_Finite__Set_Olinorder__class_OMin(X85),X84)))
| ~ c_Finite__Set_Ofinite(X83,X85)
| X84 = c_Orderings_Obot__class_Obot(tc_fun(X85,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X85,tc_bool)),X84),X83)) ),
inference(variable_rename,[status(thm)],[c_0_1280]) ).
fof(c_0_2191,plain,
! [X71,X72,X73,X74,X75,X76,X77] :
( hBOOL(hAPP(hAPP(X74,X73),X71))
| ~ hBOOL(hAPP(hAPP(X74,X73),hAPP(hAPP(X76,X72),X71)))
| ~ c_Lattices_Olower__semilattice(X74,X75,X76,X77) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1281])])]) ).
fof(c_0_2192,plain,
! [X71,X72,X73,X74,X75,X76,X77] :
( hBOOL(hAPP(hAPP(X74,X73),X72))
| ~ hBOOL(hAPP(hAPP(X74,X73),hAPP(hAPP(X76,X72),X71)))
| ~ c_Lattices_Olower__semilattice(X74,X75,X76,X77) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1282])])]) ).
fof(c_0_2193,plain,
! [X52,X53,X54,X55,X56,X57,X58] :
( hBOOL(hAPP(hAPP(X53,X52),X57))
| ~ hBOOL(hAPP(hAPP(X53,X52),hAPP(hAPP(X55,X57),X56)))
| ~ c_Lattices_Olower__semilattice(X53,X54,X55,X58) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1283])])]) ).
fof(c_0_2194,plain,
! [X52,X53,X54,X55,X56,X57,X58] :
( hBOOL(hAPP(hAPP(X53,X52),X56))
| ~ hBOOL(hAPP(hAPP(X53,X52),hAPP(hAPP(X55,X57),X56)))
| ~ c_Lattices_Olower__semilattice(X53,X54,X55,X58) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1284])])]) ).
fof(c_0_2195,plain,
! [X24,X25,X26,X27] :
( hBOOL(hAPP(hAPP(c_in(X27),X24),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X27,tc_bool)),X26),X25)))
| ~ hBOOL(hAPP(hAPP(c_in(X27),X24),X25)) ),
inference(variable_rename,[status(thm)],[c_0_1285]) ).
fof(c_0_2196,plain,
! [X24,X25,X26,X27] :
( hBOOL(hAPP(hAPP(c_in(X27),X24),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X27,tc_bool)),X26),X25)))
| ~ hBOOL(hAPP(hAPP(c_in(X27),X24),X26)) ),
inference(variable_rename,[status(thm)],[c_0_1286]) ).
fof(c_0_2197,plain,
! [X45,X46,X47,X48,X49] :
( hAPP(c_Map_Omap__add(X47,X46,X49,X48),X45) = hAPP(X47,X45)
| hBOOL(hAPP(hAPP(c_in(X49),X45),c_Map_Odom(X46,X49,X48))) ),
inference(variable_rename,[status(thm)],[c_0_1287]) ).
fof(c_0_2198,plain,
! [X45,X46,X47,X48,X49] :
( hAPP(c_Map_Omap__add(X47,X46,X49,X48),X45) = hAPP(X46,X45)
| hBOOL(hAPP(hAPP(c_in(X49),X45),c_Map_Odom(X47,X49,X48))) ),
inference(variable_rename,[status(thm)],[c_0_1288]) ).
fof(c_0_2199,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X10),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X10),X9),X9)),c_HOL_Ozero__class_Ozero(X10))) ),
inference(variable_rename,[status(thm)],[c_0_1289]) ).
fof(c_0_2200,plain,
! [X18,X19,X20,X21] :
( ~ class_Orderings_Olinorder(X21)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X21),X19),X18))
| ~ hBOOL(hAPP(hAPP(c_in(X21),X18),X20))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X21),X19),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X21),X21),X20)))
| X20 = c_Orderings_Obot__class_Obot(tc_fun(X21,tc_bool))
| ~ c_Finite__Set_Ofinite(X20,X21) ),
inference(variable_rename,[status(thm)],[c_0_1290]) ).
fof(c_0_2201,plain,
! [X18,X19,X20,X21] :
( ~ class_Lattices_Olower__semilattice(X21)
| hBOOL(hAPP(hAPP(c_lessequals(X21),X19),X18))
| ~ hBOOL(hAPP(hAPP(c_in(X21),X18),X20))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X21),X19),hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X21),X21),X20)))
| X20 = c_Orderings_Obot__class_Obot(tc_fun(X21,tc_bool))
| ~ c_Finite__Set_Ofinite(X20,X21) ),
inference(variable_rename,[status(thm)],[c_0_1291]) ).
fof(c_0_2202,plain,
! [X57,X58,X59,X60,X61] :
( hAPP(c_Map_Omap__add(X58,X57,X60,X61),X59) != c_Option_Ooption_ONone(X61)
| hAPP(X57,X59) = c_Option_Ooption_ONone(X61) ),
inference(variable_rename,[status(thm)],[c_0_1292]) ).
fof(c_0_2203,plain,
! [X57,X58,X59,X60,X61] :
( hAPP(c_Map_Omap__add(X58,X57,X60,X61),X59) != c_Option_Ooption_ONone(X61)
| hAPP(X58,X59) = c_Option_Ooption_ONone(X61) ),
inference(variable_rename,[status(thm)],[c_0_1293]) ).
fof(c_0_2204,plain,
! [X20,X21,X22] :
( X20 = X21
| ~ hBOOL(hAPP(hAPP(c_in(X22),X20),hAPP(hAPP(c_Set_Oinsert(X22),X21),c_Orderings_Obot__class_Obot(tc_fun(X22,tc_bool))))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1294])])]) ).
fof(c_0_2205,plain,
! [X25,X26,X27,X28,X29] :
( hAPP(hAPP(c_Set_Oinsert(X29),X28),hAPP(hAPP(c_Set_Oinsert(X29),X27),c_Orderings_Obot__class_Obot(tc_fun(X29,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X29),X26),hAPP(hAPP(c_Set_Oinsert(X29),X25),c_Orderings_Obot__class_Obot(tc_fun(X29,tc_bool))))
| X27 = X26
| X27 = X25 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1295])])]) ).
fof(c_0_2206,plain,
! [X25,X26,X27,X28,X29] :
( hAPP(hAPP(c_Set_Oinsert(X29),X28),hAPP(hAPP(c_Set_Oinsert(X29),X27),c_Orderings_Obot__class_Obot(tc_fun(X29,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X29),X26),hAPP(hAPP(c_Set_Oinsert(X29),X25),c_Orderings_Obot__class_Obot(tc_fun(X29,tc_bool))))
| X28 = X25
| X27 = X25 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1296])])]) ).
fof(c_0_2207,plain,
! [X25,X26,X27,X28,X29] :
( hAPP(hAPP(c_Set_Oinsert(X29),X28),hAPP(hAPP(c_Set_Oinsert(X29),X27),c_Orderings_Obot__class_Obot(tc_fun(X29,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X29),X26),hAPP(hAPP(c_Set_Oinsert(X29),X25),c_Orderings_Obot__class_Obot(tc_fun(X29,tc_bool))))
| X27 = X26
| X28 = X26 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1297])])]) ).
fof(c_0_2208,plain,
! [X25,X26,X27,X28,X29] :
( hAPP(hAPP(c_Set_Oinsert(X29),X28),hAPP(hAPP(c_Set_Oinsert(X29),X27),c_Orderings_Obot__class_Obot(tc_fun(X29,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X29),X26),hAPP(hAPP(c_Set_Oinsert(X29),X25),c_Orderings_Obot__class_Obot(tc_fun(X29,tc_bool))))
| X28 = X25
| X28 = X26 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1298])])]) ).
fof(c_0_2209,plain,
! [X58,X59,X60,X61] :
( ~ class_HOL_Oord(X60)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X61,X60)),X59),X58))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X61,X60)),X59),X58)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1299])])]) ).
fof(c_0_2210,plain,
! [X24,X25,X26,X27] :
( ~ hBOOL(hAPP(hAPP(c_in(X27),X24),X25))
| ~ hBOOL(hAPP(hAPP(c_in(X27),X24),c_HOL_Ominus__class_Ominus(X26,X25,tc_fun(X27,tc_bool)))) ),
inference(variable_rename,[status(thm)],[c_0_1300]) ).
fof(c_0_2211,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| hBOOL(hAPP(hAPP(c_lessequals(X17),X16),X15))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X17,tc_bool)),c_SetInterval_Oord__class_OlessThan(X16,X17)),c_SetInterval_Oord__class_OlessThan(X15,X17))) ),
inference(variable_rename,[status(thm)],[c_0_1301]) ).
fof(c_0_2212,plain,
! [X14,X15,X16] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X16)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X16),X16),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X16,tc_bool)),X15),X14)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X16),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X16),X16),X15)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X16),X16),X14))
| X14 = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_bool))
| ~ c_Finite__Set_Ofinite(X14,X16)
| X15 = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_bool))
| ~ c_Finite__Set_Ofinite(X15,X16) ),
inference(variable_rename,[status(thm)],[c_0_1302]) ).
fof(c_0_2213,plain,
! [X10,X11,X12] :
( hAPP(hAPP(c_Set_Oinsert(X12),X10),c_HOL_Ominus__class_Ominus(X11,hAPP(hAPP(c_Set_Oinsert(X12),X10),c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool))),tc_fun(X12,tc_bool))) = X11
| ~ hBOOL(hAPP(hAPP(c_in(X12),X10),X11)) ),
inference(variable_rename,[status(thm)],[c_0_1303]) ).
fof(c_0_2214,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X22)
| hBOOL(hAPP(hAPP(c_lessequals(X22),X21),c_HOL_Ozero__class_Ozero(X22)))
| hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),X21))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X21),X20))) ),
inference(variable_rename,[status(thm)],[c_0_1304]) ).
fof(c_0_2215,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X22)
| hBOOL(hAPP(hAPP(c_lessequals(X22),X20),c_HOL_Ozero__class_Ozero(X22)))
| hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),X21))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X21),X20))) ),
inference(variable_rename,[status(thm)],[c_0_1305]) ).
fof(c_0_2216,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X22)
| hBOOL(hAPP(hAPP(c_lessequals(X22),X21),c_HOL_Ozero__class_Ozero(X22)))
| hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),X20))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X21),X20))) ),
inference(variable_rename,[status(thm)],[c_0_1306]) ).
fof(c_0_2217,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X22)
| hBOOL(hAPP(hAPP(c_lessequals(X22),X20),c_HOL_Ozero__class_Ozero(X22)))
| hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),X20))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X21),X20))) ),
inference(variable_rename,[status(thm)],[c_0_1307]) ).
fof(c_0_2218,plain,
! [X52,X53,X54,X55,X56,X57] :
( hBOOL(hAPP(hAPP(X54,hAPP(hAPP(X56,X53),X52)),X52))
| ~ c_Lattices_Olower__semilattice(X54,X55,X56,X57) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1308])])]) ).
fof(c_0_2219,plain,
! [X52,X53,X54,X55,X56,X57] :
( hBOOL(hAPP(hAPP(X54,hAPP(hAPP(X56,X53),X52)),X53))
| ~ c_Lattices_Olower__semilattice(X54,X55,X56,X57) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1309])])]) ).
fof(c_0_2220,plain,
! [X58,X59,X60,X61] :
( X59 = X58
| ~ c_Map_Omap__le(X58,X59,X61,X60)
| ~ c_Map_Omap__le(X59,X58,X61,X60) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1310])])]) ).
fof(c_0_2221,plain,
! [X31,X32,X33,X34,X35,X36,X37] :
( c_Hoare__Mirabelle_Otriple_Otriple(X34,X36,X32,X37) != c_Hoare__Mirabelle_Otriple_Otriple(X33,X35,X31,X37)
| X32 = X31 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1311])])]) ).
fof(c_0_2222,plain,
! [X31,X32,X33,X34,X35,X36,X37] :
( c_Hoare__Mirabelle_Otriple_Otriple(X34,X36,X32,X37) != c_Hoare__Mirabelle_Otriple_Otriple(X33,X35,X31,X37)
| X36 = X35 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1312])])]) ).
fof(c_0_2223,plain,
! [X31,X32,X33,X34,X35,X36,X37] :
( c_Hoare__Mirabelle_Otriple_Otriple(X34,X36,X32,X37) != c_Hoare__Mirabelle_Otriple_Otriple(X33,X35,X31,X37)
| X34 = X33 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1313])])]) ).
fof(c_0_2224,plain,
! [X58,X59,X60,X61,X62] :
( ~ class_HOL_Oord(X61)
| hBOOL(hAPP(hAPP(c_lessequals(X61),hAPP(X60,X58)),hAPP(X59,X58)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X62,X61)),X60),X59)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1314])])]) ).
fof(c_0_2225,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X22)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),c_HOL_Ozero__class_Ozero(X22)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X21),X20)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),c_HOL_Ozero__class_Ozero(X22)),X20))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),c_HOL_Ozero__class_Ozero(X22)),X21)) ),
inference(variable_rename,[status(thm)],[c_0_1315]) ).
fof(c_0_2226,plain,
! [X20,X21,X22] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X22)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),c_HOL_Ozero__class_Ozero(X22)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X21),X20)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),c_HOL_Ozero__class_Ozero(X22)),X20))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),c_HOL_Ozero__class_Ozero(X22)),X21)) ),
inference(variable_rename,[status(thm)],[c_0_1316]) ).
fof(c_0_2227,plain,
! [X20,X21,X22] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X22)
| hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X21),X20)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),X20))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),X21)) ),
inference(variable_rename,[status(thm)],[c_0_1317]) ).
fof(c_0_2228,plain,
! [X20,X21,X22] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X22)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),c_HOL_Ozero__class_Ozero(X22)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X21),X20)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),c_HOL_Ozero__class_Ozero(X22)),X20))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),X21)) ),
inference(variable_rename,[status(thm)],[c_0_1318]) ).
fof(c_0_2229,plain,
! [X20,X21,X22] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X22)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),c_HOL_Ozero__class_Ozero(X22)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X21),X20)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),X20))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),c_HOL_Ozero__class_Ozero(X22)),X21)) ),
inference(variable_rename,[status(thm)],[c_0_1319]) ).
fof(c_0_2230,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X22)
| hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X21),X20)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),X20))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),X21)) ),
inference(variable_rename,[status(thm)],[c_0_1320]) ).
fof(c_0_2231,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X22)
| hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X21),X20)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),X20))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),X21)) ),
inference(variable_rename,[status(thm)],[c_0_1321]) ).
fof(c_0_2232,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Opordered__ring(X22)
| hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X21),X20)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),X20))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),X21)) ),
inference(variable_rename,[status(thm)],[c_0_1322]) ).
fof(c_0_2233,plain,
! [X24,X25,X26,X27] :
( hBOOL(hAPP(hAPP(c_in(X27),X24),X26))
| ~ hBOOL(hAPP(hAPP(c_in(X27),X24),c_HOL_Ominus__class_Ominus(X26,X25,tc_fun(X27,tc_bool)))) ),
inference(variable_rename,[status(thm)],[c_0_1323]) ).
fof(c_0_2234,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Olinorder(X15)
| hAPP(c_Finite__Set_Olinorder__class_OMin(X15),X14) = X13
| ~ hBOOL(hAPP(hAPP(c_in(X15),X13),X14))
| hBOOL(hAPP(hAPP(c_in(X15),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(X14,X13,X15)),X14))
| ~ c_Finite__Set_Ofinite(X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_1324]) ).
fof(c_0_2235,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Olinorder(X15)
| hAPP(c_Finite__Set_Olinorder__class_OMax(X15),X14) = X13
| ~ hBOOL(hAPP(hAPP(c_in(X15),X13),X14))
| hBOOL(hAPP(hAPP(c_in(X15),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(X14,X13,X15)),X14))
| ~ c_Finite__Set_Ofinite(X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_1325]) ).
fof(c_0_2236,plain,
! [X14,X15,X16] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X16,tc_bool)),X15),c_HOL_Ominus__class_Ominus(X14,X15,tc_fun(X16,tc_bool))) = X14
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X16,tc_bool)),X15),X14)) ),
inference(variable_rename,[status(thm)],[c_0_1326]) ).
fof(c_0_2237,plain,
! [X14,X15,X16,X17] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X17,tc_bool)),X16),hAPP(hAPP(c_Set_Oinsert(X17),X14),X15)) = hAPP(hAPP(c_Set_Oinsert(X17),X14),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X17,tc_bool)),X16),X15))
| ~ hBOOL(hAPP(hAPP(c_in(X17),X14),X16)) ),
inference(variable_rename,[status(thm)],[c_0_1327]) ).
fof(c_0_2238,plain,
! [X14,X15,X16,X17] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X16,X15,tc_fun(X17,tc_bool)),X17)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X16,hAPP(hAPP(c_Set_Oinsert(X17),X14),X15),tc_fun(X17,tc_bool)),X17) ),
inference(variable_rename,[status(thm)],[c_0_1328]) ).
fof(c_0_2239,plain,
! [X14,X15,X16] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X16,tc_bool)),X15),X14))
| X15 = X14
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X16,tc_bool)),X15),X14)) ),
inference(variable_rename,[status(thm)],[c_0_1329]) ).
fof(c_0_2240,plain,
! [X14,X15,X16] :
( X15 = X14
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X16,tc_bool)),X15),X14))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X16,tc_bool)),X15),X14)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1330])])]) ).
fof(c_0_2241,plain,
! [X14,X15,X16] :
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X16,tc_bool)),X15),X14))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X16,tc_bool)),X15),X14)) ),
inference(variable_rename,[status(thm)],[c_0_1331]) ).
fof(c_0_2242,plain,
! [X25,X26,X27,X28] :
( ~ class_Ring__and__Field_Oidom(X28)
| ~ class_Int_Onumber__ring(X28)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X28),X25),X27)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X28),X25),X26)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X28),X25),X26)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X28),X25),X27)) ),
inference(variable_rename,[status(thm)],[c_0_1332]) ).
fof(c_0_2243,plain,
! [X71,X72,X73,X74] :
( ~ class_Ring__and__Field_Oidom(X74)
| ~ class_Int_Onumber__ring(X74)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X74),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X74),X73),X72)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X74),X73),X71)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X74),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X74),X73),X71)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X74),X73),X72)) ),
inference(variable_rename,[status(thm)],[c_0_1333]) ).
fof(c_0_2244,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_Orderings_Olinorder(X29)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X29,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X28,X27,X29)),c_SetInterval_Oord__class_OatLeastAtMost(X26,X25,X29)) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Orderings_Oord__class_Omax(X29),X28),X26),hAPP(hAPP(c_Orderings_Oord__class_Omin(X29),X27),X25),X29) ),
inference(variable_rename,[status(thm)],[c_0_1334]) ).
fof(c_0_2245,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_in(X17),X14),X15))
| ~ hBOOL(hAPP(hAPP(c_in(X17),X14),X16))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X17,tc_bool)),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1335]) ).
fof(c_0_2246,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_in(X17),X14),X15))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X17,tc_bool)),X16),X15))
| ~ hBOOL(hAPP(hAPP(c_in(X17),X14),X16)) ),
inference(variable_rename,[status(thm)],[c_0_1336]) ).
fof(c_0_2247,plain,
! [X24,X25,X26,X27] :
( hBOOL(hAPP(hAPP(c_in(X27),X24),X25))
| ~ hBOOL(hAPP(hAPP(c_in(X27),X24),X26))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X27,tc_bool)),X26),X25)) ),
inference(variable_rename,[status(thm)],[c_0_1337]) ).
fof(c_0_2248,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(c_in(X17),X14),X15))
| ~ hBOOL(hAPP(hAPP(c_in(X17),X14),X16))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X17,tc_bool)),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1338]) ).
fof(c_0_2249,plain,
! [X24,X25,X26,X27] :
( hBOOL(hAPP(hAPP(c_in(X27),X24),X25))
| ~ hBOOL(hAPP(hAPP(c_in(X27),X24),X26))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X27,tc_bool)),X26),X25)) ),
inference(variable_rename,[status(thm)],[c_0_1339]) ).
fof(c_0_2250,plain,
! [X14,X15,X16] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(X15,X16)),c_Finite__Set_Ocard(X14,X16)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X16,tc_bool)),X15),X14))
| ~ c_Finite__Set_Ofinite(X14,X16) ),
inference(variable_rename,[status(thm)],[c_0_1340]) ).
fof(c_0_2251,plain,
! [X87,X88,X89,X90,X91] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X91)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X91),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X91),X90),X89)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X91),X88),X87)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X91),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X91),X90),X88)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X91),X89),X87)) ),
inference(variable_rename,[status(thm)],[c_0_1341]) ).
fof(c_0_2252,plain,
! [X87,X88,X89,X90,X91] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X91)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X91),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X91),X90),X89)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X91),X88),X87)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X91),X90),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X91),X89),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X91),X88),X87))) ),
inference(variable_rename,[status(thm)],[c_0_1342]) ).
fof(c_0_2253,plain,
! [X25,X26,X27,X28,X29] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X29)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X29),X28),X27)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X29),X26),X25)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X29),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X29),X28),X26)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X29),X27),X25)) ),
inference(variable_rename,[status(thm)],[c_0_1343]) ).
fof(c_0_2254,plain,
! [X38,X39,X40,X41] :
( hAPP(c_Finite__Set_Ofold1(X38,X41),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X41,tc_bool)),X40),X39)) = hAPP(hAPP(X38,hAPP(c_Finite__Set_Ofold1(X38,X41),X40)),hAPP(c_Finite__Set_Ofold1(X38,X41),X39))
| X39 = c_Orderings_Obot__class_Obot(tc_fun(X41,tc_bool))
| ~ c_Finite__Set_Ofinite(X39,X41)
| X40 = c_Orderings_Obot__class_Obot(tc_fun(X41,tc_bool))
| ~ c_Finite__Set_Ofinite(X40,X41)
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X38,X41) ),
inference(variable_rename,[status(thm)],[c_0_1344]) ).
fof(c_0_2255,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Olinorder(X15)
| hAPP(c_Finite__Set_Olinorder__class_OMin(X15),X14) = X13
| ~ hBOOL(hAPP(hAPP(c_in(X15),X13),X14))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X15),X13),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(X14,X13,X15)))
| ~ c_Finite__Set_Ofinite(X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_1345]) ).
fof(c_0_2256,plain,
! [X13,X14,X15] :
( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X14,hAPP(hAPP(c_Set_Oinsert(X15),X13),c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool))),tc_fun(X15,tc_bool)),X15) = c_Finite__Set_Ocard(X14,X15)
| hBOOL(hAPP(hAPP(c_in(X15),X13),X14))
| ~ c_Finite__Set_Ofinite(X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_1346]) ).
fof(c_0_2257,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X10)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X10),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),X9),X9)),c_HOL_Ozero__class_Ozero(X10)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X10),X9),c_HOL_Ozero__class_Ozero(X10))) ),
inference(variable_rename,[status(thm)],[c_0_1347]) ).
fof(c_0_2258,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oordered__idom(X10)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X10),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),X9),X9)),c_HOL_Ozero__class_Ozero(X10)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X10),X9),c_HOL_Ozero__class_Ozero(X10))) ),
inference(variable_rename,[status(thm)],[c_0_1348]) ).
fof(c_0_2259,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X10)
| hBOOL(hAPP(hAPP(c_lessequals(X10),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),X9),X9)),c_HOL_Ozero__class_Ozero(X10)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X10),X9),c_HOL_Ozero__class_Ozero(X10))) ),
inference(variable_rename,[status(thm)],[c_0_1349]) ).
fof(c_0_2260,plain,
! [X20,X21,X22] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X22)
| hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ominus__class_Ominus(X21,X20,X22)),c_HOL_Ozero__class_Ozero(X22)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),X21),X20)) ),
inference(variable_rename,[status(thm)],[c_0_1350]) ).
fof(c_0_2261,plain,
! [X20,X21,X22] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X22)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),c_HOL_Ominus__class_Ominus(X21,X20,X22)),c_HOL_Ozero__class_Ozero(X22)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),X21),X20)) ),
inference(variable_rename,[status(thm)],[c_0_1351]) ).
fof(c_0_2262,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X22)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),c_HOL_Ozero__class_Ozero(X22)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X21),X20)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),X20),c_HOL_Ozero__class_Ozero(X22)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),X21),c_HOL_Ozero__class_Ozero(X22))) ),
inference(variable_rename,[status(thm)],[c_0_1352]) ).
fof(c_0_2263,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X22)
| hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X21),X20)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),X20),c_HOL_Ozero__class_Ozero(X22)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),X21),c_HOL_Ozero__class_Ozero(X22))) ),
inference(variable_rename,[status(thm)],[c_0_1353]) ).
fof(c_0_2264,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Opordered__ring(X22)
| hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X21),X20)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),X20),c_HOL_Ozero__class_Ozero(X22)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),X21),c_HOL_Ozero__class_Ozero(X22))) ),
inference(variable_rename,[status(thm)],[c_0_1354]) ).
fof(c_0_2265,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Opordered__ring(X22)
| hBOOL(hAPP(hAPP(c_lessequals(X22),c_HOL_Ozero__class_Ozero(X22)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X21),X20)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),X20),c_HOL_Ozero__class_Ozero(X22)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),X21),c_HOL_Ozero__class_Ozero(X22))) ),
inference(variable_rename,[status(thm)],[c_0_1355]) ).
fof(c_0_2266,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Olower__semilattice(X12)
| hBOOL(hAPP(hAPP(c_lessequals(X12),hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X12),X12),X11)),X10))
| ~ hBOOL(hAPP(hAPP(c_in(X12),X10),X11))
| ~ c_Finite__Set_Ofinite(X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1356]) ).
fof(c_0_2267,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hBOOL(hAPP(hAPP(c_lessequals(X74),X71),X72))
| hBOOL(hAPP(hAPP(c_lessequals(X74),X71),X73))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X71),hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X73),X72))) ),
inference(variable_rename,[status(thm)],[c_0_1357]) ).
fof(c_0_2268,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X71),X72))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X71),X73))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X71),hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X73),X72))) ),
inference(variable_rename,[status(thm)],[c_0_1358]) ).
fof(c_0_2269,plain,
! [X71,X72,X73,X74,X75,X76,X77] :
( hAPP(hAPP(X76,hAPP(hAPP(X76,X73),X72)),X71) = hAPP(hAPP(X76,X73),hAPP(hAPP(X76,X72),X71))
| ~ c_Lattices_Olower__semilattice(X74,X75,X76,X77) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1359])])]) ).
fof(c_0_2270,plain,
! [X24,X25,X26,X27] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X27)
| ~ class_OrderedGroup_Ocomm__monoid__add(X27)
| hBOOL(hAPP(hAPP(c_lessequals(X27),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X24)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X27),X25),X26))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X27),c_HOL_Ozero__class_Ozero(X27)),X24)) ),
inference(variable_rename,[status(thm)],[c_0_1360]) ).
fof(c_0_2271,plain,
! [X24,X25,X26,X27] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X27)
| ~ class_OrderedGroup_Ocomm__monoid__add(X27)
| hBOOL(hAPP(hAPP(c_lessequals(X27),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X24)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X27),X25),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X27),c_HOL_Ozero__class_Ozero(X27)),X26)) ),
inference(variable_rename,[status(thm)],[c_0_1361]) ).
fof(c_0_2272,plain,
! [X24,X25,X26,X27] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X27)
| ~ class_OrderedGroup_Ocomm__monoid__add(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X24)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X27),X25),X24))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),c_HOL_Ozero__class_Ozero(X27)),X26)) ),
inference(variable_rename,[status(thm)],[c_0_1362]) ).
fof(c_0_2273,plain,
! [X24,X25,X26,X27] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X27)
| ~ class_OrderedGroup_Ocomm__monoid__add(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X24)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X25),X24))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X27),c_HOL_Ozero__class_Ozero(X27)),X26)) ),
inference(variable_rename,[status(thm)],[c_0_1363]) ).
fof(c_0_2274,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X17,tc_bool)),X16),X15),X14))
| ~ hBOOL(hAPP(X15,X14))
| ~ hBOOL(hAPP(X16,X14)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1364])])]) ).
fof(c_0_2275,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Oordered__semidom(X27)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X24)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),X25),X24))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X27),c_HOL_Ozero__class_Ozero(X27)),X26)) ),
inference(variable_rename,[status(thm)],[c_0_1365]) ).
fof(c_0_2276,plain,
! [X20,X21,X22,X23] :
( ~ class_Orderings_Olinorder(X23)
| hBOOL(hAPP(hAPP(c_lessequals(X23),hAPP(hAPP(c_Orderings_Oord__class_Omin(X23),X22),X21)),X20))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X22),X20)) ),
inference(variable_rename,[status(thm)],[c_0_1366]) ).
fof(c_0_2277,plain,
! [X20,X21,X22,X23] :
( ~ class_Orderings_Olinorder(X23)
| hBOOL(hAPP(hAPP(c_lessequals(X23),hAPP(hAPP(c_Orderings_Oord__class_Omin(X23),X22),X21)),X20))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X21),X20)) ),
inference(variable_rename,[status(thm)],[c_0_1367]) ).
fof(c_0_2278,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hBOOL(hAPP(hAPP(c_lessequals(X74),hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X73),X72)),X71))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X73),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1368]) ).
fof(c_0_2279,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hBOOL(hAPP(hAPP(c_lessequals(X74),hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X73),X72)),X71))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X72),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1369]) ).
fof(c_0_2280,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Olower__semilattice(X23)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X23),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X23),X22),X21)),X20))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X23),X21),X20)) ),
inference(variable_rename,[status(thm)],[c_0_1370]) ).
fof(c_0_2281,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Olower__semilattice(X23)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X23),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X23),X22),X21)),X20))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X23),X22),X20)) ),
inference(variable_rename,[status(thm)],[c_0_1371]) ).
fof(c_0_2282,plain,
! [X20,X21,X22,X23] :
( ~ class_Orderings_Olinorder(X23)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X23),hAPP(hAPP(c_Orderings_Oord__class_Omin(X23),X22),X21)),X20))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X23),X22),X20)) ),
inference(variable_rename,[status(thm)],[c_0_1372]) ).
fof(c_0_2283,plain,
! [X20,X21,X22,X23] :
( ~ class_Orderings_Olinorder(X23)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X23),hAPP(hAPP(c_Orderings_Oord__class_Omin(X23),X22),X21)),X20))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X23),X21),X20)) ),
inference(variable_rename,[status(thm)],[c_0_1373]) ).
fof(c_0_2284,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X73),X72)),X71))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X73),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1374]) ).
fof(c_0_2285,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X73),X72)),X71))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X72),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1375]) ).
fof(c_0_2286,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Olower__semilattice(X23)
| hBOOL(hAPP(hAPP(c_lessequals(X23),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X23),X22),X21)),X20))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X22),X20)) ),
inference(variable_rename,[status(thm)],[c_0_1376]) ).
fof(c_0_2287,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Olower__semilattice(X23)
| hBOOL(hAPP(hAPP(c_lessequals(X23),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X23),X22),X21)),X20))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X21),X20)) ),
inference(variable_rename,[status(thm)],[c_0_1377]) ).
fof(c_0_2288,plain,
! [X43,X44,X45,X46,X47] :
( hAPP(c_Map_Orestrict__map(X44,X45,X47,X46),X43) = hAPP(X44,X43)
| ~ hBOOL(hAPP(hAPP(c_in(X47),X43),X45)) ),
inference(variable_rename,[status(thm)],[c_0_1378]) ).
fof(c_0_2289,plain,
! [X24,X25,X26,X27] :
( hBOOL(hAPP(hAPP(c_in(X27),X24),c_HOL_Ominus__class_Ominus(X26,X25,tc_fun(X27,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(X27),X24),X25))
| ~ hBOOL(hAPP(hAPP(c_in(X27),X24),X26)) ),
inference(variable_rename,[status(thm)],[c_0_1379]) ).
fof(c_0_2290,plain,
! [X24,X25,X26,X27] :
( hBOOL(hAPP(hAPP(c_in(X27),X24),c_HOL_Ominus__class_Ominus(X26,X25,tc_fun(X27,tc_bool))))
| hBOOL(hAPP(hAPP(c_in(X27),X24),X25))
| ~ hBOOL(hAPP(hAPP(c_in(X27),X24),X26)) ),
inference(variable_rename,[status(thm)],[c_0_1380]) ).
fof(c_0_2291,plain,
! [X17,X18,X19,X20] :
( c_Hoare__Mirabelle_Ohoare__derivs(X19,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X20)),X18),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X20),tc_bool))),X20)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X19,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X20)),X18),X17),X20) ),
inference(variable_rename,[status(thm)],[c_0_1381]) ).
fof(c_0_2292,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X10)
| hBOOL(hAPP(hAPP(c_lessequals(X10),c_HOL_Ozero__class_Ozero(X10)),X9))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X10),c_HOL_Ozero__class_Ozero(X10)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),X9),X9))) ),
inference(variable_rename,[status(thm)],[c_0_1382]) ).
fof(c_0_2293,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X10)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X10),c_HOL_Ozero__class_Ozero(X10)),X9))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X10),c_HOL_Ozero__class_Ozero(X10)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),X9),X9))) ),
inference(variable_rename,[status(thm)],[c_0_1383]) ).
fof(c_0_2294,plain,
! [X20,X21,X22,X23] :
( ~ class_Orderings_Olinorder(X23)
| hBOOL(hAPP(hAPP(c_lessequals(X23),X20),hAPP(hAPP(c_Orderings_Oord__class_Omin(X23),X22),X21)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X20),X21))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X20),X22)) ),
inference(variable_rename,[status(thm)],[c_0_1384]) ).
fof(c_0_2295,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hBOOL(hAPP(hAPP(c_lessequals(X74),X73),hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X72),X71)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X73),X71))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X73),X72)) ),
inference(variable_rename,[status(thm)],[c_0_1385]) ).
fof(c_0_2296,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hBOOL(hAPP(hAPP(c_lessequals(X74),X73),hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X72),X71)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X73),X71))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X73),X72)) ),
inference(variable_rename,[status(thm)],[c_0_1386]) ).
fof(c_0_2297,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X71),hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X73),X72)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X71),X72))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X71),X73)) ),
inference(variable_rename,[status(thm)],[c_0_1387]) ).
fof(c_0_2298,plain,
! [X71,X72,X73,X74] :
( ~ class_Lattices_Olower__semilattice(X74)
| hBOOL(hAPP(hAPP(c_lessequals(X74),X73),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),X72),X71)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X73),X71))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X73),X72)) ),
inference(variable_rename,[status(thm)],[c_0_1388]) ).
fof(c_0_2299,plain,
! [X71,X72,X73,X74] :
( ~ class_Lattices_Olower__semilattice(X74)
| hBOOL(hAPP(hAPP(c_lessequals(X74),X73),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),X72),X71)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X73),X71))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X73),X72)) ),
inference(variable_rename,[status(thm)],[c_0_1389]) ).
fof(c_0_2300,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Olower__semilattice(X23)
| hBOOL(hAPP(hAPP(c_lessequals(X23),X20),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X23),X22),X21)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X20),X21))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X20),X22)) ),
inference(variable_rename,[status(thm)],[c_0_1390]) ).
fof(c_0_2301,plain,
! [X79,X80,X81,X82,X83] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X83,X82)),X81),X79))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X82),X80),X79))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X83),X81),X80)) ),
inference(variable_rename,[status(thm)],[c_0_1391]) ).
fof(c_0_2302,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X17,tc_bool)),X16),X15),X14))
| ~ hBOOL(hAPP(X15,X14)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1392])])]) ).
fof(c_0_2303,plain,
! [X14,X15,X16,X17] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X17,tc_bool)),X16),X15),X14))
| ~ hBOOL(hAPP(X16,X14)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1393])])]) ).
fof(c_0_2304,plain,
! [X10,X11] :
( X10 = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X11,tc_bool)),X10),c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)))) ),
inference(variable_rename,[status(thm)],[c_0_1394]) ).
fof(c_0_2305,plain,
! [X14,X15,X16,X17] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X16,hAPP(hAPP(c_Set_Oinsert(X17),X14),X15),tc_fun(X17,tc_bool)),X17)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X16,X15,tc_fun(X17,tc_bool)),X17) ),
inference(variable_rename,[status(thm)],[c_0_1395]) ).
fof(c_0_2306,plain,
! [X71,X72,X73,X74,X75,X76,X77] :
( hAPP(hAPP(X76,X73),hAPP(hAPP(X76,X72),X71)) = hAPP(hAPP(X76,X72),hAPP(hAPP(X76,X73),X71))
| ~ c_Lattices_Olower__semilattice(X74,X75,X76,X77) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1396])])]) ).
fof(c_0_2307,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X72),X71)),X73) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X72),X73)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X71),X73)) ),
inference(variable_rename,[status(thm)],[c_0_1397]) ).
fof(c_0_2308,plain,
! [X71,X72,X73,X74] :
( ~ class_Lattices_Odistrib__lattice(X74)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),X72),X71)),X73) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),X72),X73)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),X71),X73)) ),
inference(variable_rename,[status(thm)],[c_0_1398]) ).
fof(c_0_2309,plain,
! [X24,X25,X26,X27] :
( ~ class_OrderedGroup_Olordered__ab__group__add__join(X27)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X27),X26),X25)),X24) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X24)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X25),X24)) ),
inference(variable_rename,[status(thm)],[c_0_1399]) ).
fof(c_0_2310,plain,
! [X24,X25,X26,X27] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X27)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X27),X26),X25)),X24) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X24)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X25),X24)) ),
inference(variable_rename,[status(thm)],[c_0_1400]) ).
fof(c_0_2311,plain,
! [X24,X25,X26,X27] :
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X27)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X27),X26),X25)),X24) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X24)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X25),X24)) ),
inference(variable_rename,[status(thm)],[c_0_1401]) ).
fof(c_0_2312,plain,
! [X24,X25,X26,X27] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X27)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X27),X26),X25)),X24) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X24)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X25),X24)) ),
inference(variable_rename,[status(thm)],[c_0_1402]) ).
fof(c_0_2313,plain,
! [X71,X72,X73,X74] :
( ~ class_Lattices_Odistrib__lattice(X74)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),X72),X71)),X73) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),X72),X73)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),X71),X73)) ),
inference(variable_rename,[status(thm)],[c_0_1403]) ).
fof(c_0_2314,plain,
! [X71,X72,X73,X74] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X74)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X74),hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X73),X72)),X71) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X74),X73),X71)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X74),X72),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1404]) ).
fof(c_0_2315,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X72),X71)),X73) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X72),X73)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X71),X73)) ),
inference(variable_rename,[status(thm)],[c_0_1405]) ).
fof(c_0_2316,plain,
! [X71,X72,X73,X74] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X74)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X74),hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X73),X72)),X71) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X74),X73),X71)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X74),X72),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1406]) ).
fof(c_0_2317,plain,
! [X43,X44,X45,X46] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X46)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X46),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X46),X45),X43)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X46),X44),X43)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X46),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X46),X45),X44)),X43) ),
inference(variable_rename,[status(thm)],[c_0_1407]) ).
fof(c_0_2318,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X27)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X25)),X24) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X26),X24)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X25),X24)) ),
inference(variable_rename,[status(thm)],[c_0_1408]) ).
fof(c_0_2319,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Ocomm__semiring(X27)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X25)),X24) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X26),X24)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X25),X24)) ),
inference(variable_rename,[status(thm)],[c_0_1409]) ).
fof(c_0_2320,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X17,tc_bool)),c_SetInterval_Oord__class_OlessThan(X16,X17)),c_SetInterval_Oord__class_OlessThan(X15,X17)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1410]) ).
fof(c_0_2321,plain,
! [X43,X44,X45,X46,X47] :
( hAPP(c_Map_Orestrict__map(X44,X45,X47,X46),X43) = c_Option_Ooption_ONone(X46)
| hBOOL(hAPP(hAPP(c_in(X47),X43),X45)) ),
inference(variable_rename,[status(thm)],[c_0_1411]) ).
fof(c_0_2322,plain,
! [X57,X58,X59,X60,X61,X62] :
( hAPP(X59,X60) != hAPP(c_Option_Ooption_OSome(X62),X57)
| hAPP(X58,X60) != c_Option_Ooption_ONone(X62)
| hAPP(c_Map_Omap__add(X59,X58,X61,X62),X60) = hAPP(c_Option_Ooption_OSome(X62),X57) ),
inference(variable_rename,[status(thm)],[c_0_1412]) ).
fof(c_0_2323,plain,
! [X14,X15,X16,X17] :
( ~ hBOOL(hAPP(hAPP(c_in(X17),X14),X15))
| ~ hBOOL(hAPP(hAPP(c_in(X17),X14),X16))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X17,tc_bool)),X16),X15) != c_Orderings_Obot__class_Obot(tc_fun(X17,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1413]) ).
fof(c_0_2324,plain,
! [X20,X21,X22,X23] :
( ~ class_Orderings_Olinorder(X23)
| hBOOL(hAPP(hAPP(c_lessequals(X23),X20),X22))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X20),hAPP(hAPP(c_Orderings_Oord__class_Omin(X23),X22),X21))) ),
inference(variable_rename,[status(thm)],[c_0_1414]) ).
fof(c_0_2325,plain,
! [X20,X21,X22,X23] :
( ~ class_Orderings_Olinorder(X23)
| hBOOL(hAPP(hAPP(c_lessequals(X23),X20),X21))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X20),hAPP(hAPP(c_Orderings_Oord__class_Omin(X23),X22),X21))) ),
inference(variable_rename,[status(thm)],[c_0_1415]) ).
fof(c_0_2326,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hBOOL(hAPP(hAPP(c_lessequals(X74),X73),X72))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X73),hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X72),X71))) ),
inference(variable_rename,[status(thm)],[c_0_1416]) ).
fof(c_0_2327,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hBOOL(hAPP(hAPP(c_lessequals(X74),X73),X71))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X73),hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X72),X71))) ),
inference(variable_rename,[status(thm)],[c_0_1417]) ).
fof(c_0_2328,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X71),X73))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X71),hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X73),X72))) ),
inference(variable_rename,[status(thm)],[c_0_1418]) ).
fof(c_0_2329,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X71),X72))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X71),hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X73),X72))) ),
inference(variable_rename,[status(thm)],[c_0_1419]) ).
fof(c_0_2330,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Olower__semilattice(X23)
| hBOOL(hAPP(hAPP(c_lessequals(X23),X20),X22))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X20),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X23),X22),X21))) ),
inference(variable_rename,[status(thm)],[c_0_1420]) ).
fof(c_0_2331,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Olower__semilattice(X23)
| hBOOL(hAPP(hAPP(c_lessequals(X23),X20),X21))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X20),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X23),X22),X21))) ),
inference(variable_rename,[status(thm)],[c_0_1421]) ).
fof(c_0_2332,plain,
! [X71,X72,X73,X74] :
( ~ class_Lattices_Olower__semilattice(X74)
| hBOOL(hAPP(hAPP(c_lessequals(X74),X73),X72))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X73),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),X72),X71))) ),
inference(variable_rename,[status(thm)],[c_0_1422]) ).
fof(c_0_2333,plain,
! [X71,X72,X73,X74] :
( ~ class_Lattices_Olower__semilattice(X74)
| hBOOL(hAPP(hAPP(c_lessequals(X74),X73),X71))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X73),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),X72),X71))) ),
inference(variable_rename,[status(thm)],[c_0_1423]) ).
fof(c_0_2334,plain,
! [X14,X15,X16] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X16,tc_bool)),X15),X14) = X14
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X16,tc_bool)),X15),X14)) ),
inference(variable_rename,[status(thm)],[c_0_1424]) ).
fof(c_0_2335,plain,
! [X14,X15,X16] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X16,tc_bool)),X15),X14) = X15
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X16,tc_bool)),X14),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1425]) ).
fof(c_0_2336,plain,
! [X14,X15,X16] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X16,tc_bool)),X15),X14) = X15
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X16,tc_bool)),X15),X14)) ),
inference(variable_rename,[status(thm)],[c_0_1426]) ).
fof(c_0_2337,plain,
! [X14,X15,X16] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X16,tc_bool)),X15),X14) = X14
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X16,tc_bool)),X14),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1427]) ).
fof(c_0_2338,plain,
! [X81,X82,X83,X84] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X84,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X84),X81),X83)),X82) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X84,tc_bool)),X83),X82)
| hBOOL(hAPP(hAPP(c_in(X84),X81),X82)) ),
inference(variable_rename,[status(thm)],[c_0_1428]) ).
fof(c_0_2339,plain,
! [X20,X21,X22,X23] :
( hBOOL(hAPP(hAPP(c_in(X23),X21),X22))
| X21 = X20
| ~ hBOOL(hAPP(hAPP(c_in(X23),X21),hAPP(hAPP(c_Set_Oinsert(X23),X20),X22))) ),
inference(variable_rename,[status(thm)],[c_0_1429]) ).
fof(c_0_2340,plain,
! [X20,X21,X22] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X22)
| c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X22),X21),hAPP(hAPP(c_Set_Oinsert(X22),X20),c_Orderings_Obot__class_Obot(tc_fun(X22,tc_bool)))),X22) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X22),X21),X20) ),
inference(variable_rename,[status(thm)],[c_0_1430]) ).
fof(c_0_2341,plain,
! [X20,X21,X22] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X22)
| c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X22),X21),hAPP(hAPP(c_Set_Oinsert(X22),X20),c_Orderings_Obot__class_Obot(tc_fun(X22,tc_bool)))),X22) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X22),X21),X20) ),
inference(variable_rename,[status(thm)],[c_0_1431]) ).
fof(c_0_2342,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X16),X16)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X15),X15)) != c_HOL_Ozero__class_Ozero(X17)
| X15 = c_HOL_Ozero__class_Ozero(X17) ),
inference(variable_rename,[status(thm)],[c_0_1432]) ).
fof(c_0_2343,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X17)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X16),X16)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X15),X15)) != c_HOL_Ozero__class_Ozero(X17)
| X16 = c_HOL_Ozero__class_Ozero(X17) ),
inference(variable_rename,[status(thm)],[c_0_1433]) ).
fof(c_0_2344,plain,
! [X14,X15,X16] :
( ~ class_Orderings_Olinorder(X16)
| hAPP(c_Finite__Set_Olinorder__class_OMax(X16),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X16,tc_bool)),X15),X14)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X16),hAPP(c_Finite__Set_Olinorder__class_OMax(X16),X15)),hAPP(c_Finite__Set_Olinorder__class_OMax(X16),X14))
| X14 = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_bool))
| ~ c_Finite__Set_Ofinite(X14,X16)
| X15 = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_bool))
| ~ c_Finite__Set_Ofinite(X15,X16) ),
inference(variable_rename,[status(thm)],[c_0_1434]) ).
fof(c_0_2345,plain,
! [X14,X15,X16] :
( ~ class_Orderings_Olinorder(X16)
| hAPP(c_Finite__Set_Olinorder__class_OMin(X16),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X16,tc_bool)),X15),X14)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X16),hAPP(c_Finite__Set_Olinorder__class_OMin(X16),X15)),hAPP(c_Finite__Set_Olinorder__class_OMin(X16),X14))
| X14 = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_bool))
| ~ c_Finite__Set_Ofinite(X14,X16)
| X15 = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_bool))
| ~ c_Finite__Set_Ofinite(X15,X16) ),
inference(variable_rename,[status(thm)],[c_0_1435]) ).
fof(c_0_2346,plain,
! [X57,X58,X59,X60,X61,X62] :
( hAPP(X58,X60) != hAPP(c_Option_Ooption_OSome(X62),X57)
| hAPP(c_Map_Omap__add(X59,X58,X61,X62),X60) = hAPP(c_Option_Ooption_OSome(X62),X57) ),
inference(variable_rename,[status(thm)],[c_0_1436]) ).
fof(c_0_2347,plain,
! [X72,X73,X74,X75,X76,X77] :
( hAPP(X73,X75) != hAPP(c_Option_Ooption_OSome(X77),X72)
| hAPP(c_Map_Omap__add(X74,X73,X76,X77),X75) = hAPP(c_Option_Ooption_OSome(X77),X72) ),
inference(variable_rename,[status(thm)],[c_0_1437]) ).
fof(c_0_2348,plain,
! [X57,X58,X59,X60,X61] :
( hAPP(X58,X59) != c_Option_Ooption_ONone(X61)
| hAPP(X57,X59) != c_Option_Ooption_ONone(X61)
| hAPP(c_Map_Omap__add(X58,X57,X60,X61),X59) = c_Option_Ooption_ONone(X61) ),
inference(variable_rename,[status(thm)],[c_0_1438]) ).
fof(c_0_2349,plain,
! [X13,X14] :
( hBOOL(hAPP(hAPP(c_in(X14),X13),c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool))))
| c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(X14),X13),c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool))),X14) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool)),X14)) ),
inference(variable_rename,[status(thm)],[c_0_1439]) ).
fof(c_0_2350,plain,
! [X52,X53,X54,X55,X56,X57] :
( hAPP(hAPP(X56,X53),X52) = X52
| ~ hBOOL(hAPP(hAPP(X54,X52),X53))
| ~ c_Lattices_Olower__semilattice(X54,X55,X56,X57) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1440])])]) ).
fof(c_0_2351,plain,
! [X52,X53,X54,X55,X56,X57] :
( hAPP(hAPP(X56,X53),X52) = X53
| ~ hBOOL(hAPP(hAPP(X54,X53),X52))
| ~ c_Lattices_Olower__semilattice(X54,X55,X56,X57) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1441])])]) ).
fof(c_0_2352,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X10)
| hBOOL(hAPP(hAPP(c_lessequals(X10),c_HOL_Ozero__class_Ozero(X10)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),X9),X9)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X10),c_HOL_Ozero__class_Ozero(X10)),X9)) ),
inference(variable_rename,[status(thm)],[c_0_1442]) ).
fof(c_0_2353,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X10)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X10),c_HOL_Ozero__class_Ozero(X10)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),X9),X9)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X10),c_HOL_Ozero__class_Ozero(X10)),X9)) ),
inference(variable_rename,[status(thm)],[c_0_1443]) ).
fof(c_0_2354,plain,
! [X52,X53,X54,X55,X56,X57] :
( hAPP(hAPP(X56,X53),hAPP(hAPP(X56,X53),X52)) = hAPP(hAPP(X56,X53),X52)
| ~ c_Lattices_Olower__semilattice(X54,X55,X56,X57) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1444])])]) ).
fof(c_0_2355,plain,
! [X52,X53,X54,X55,X56,X57] :
( hAPP(hAPP(X56,X53),X52) != X53
| ~ c_Lattices_Olower__semilattice(X54,X55,X56,X57)
| hBOOL(hAPP(hAPP(X54,X53),X52)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1445])])]) ).
fof(c_0_2356,plain,
! [X71,X72,X73,X74] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X74)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X73),X72),X71,X74) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),c_HOL_Ominus__class_Ominus(X73,X71,X74)),c_HOL_Ominus__class_Ominus(X72,X71,X74)) ),
inference(variable_rename,[status(thm)],[c_0_1446]) ).
fof(c_0_2357,plain,
! [X71,X72,X73,X74] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X74)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X73),X72),X71,X74) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),c_HOL_Ominus__class_Ominus(X73,X71,X74)),c_HOL_Ominus__class_Ominus(X72,X71,X74)) ),
inference(variable_rename,[status(thm)],[c_0_1447]) ).
fof(c_0_2358,plain,
! [X34,X35,X36,X37] :
( hBOOL(hAPP(X35,X34))
| ~ hBOOL(hAPP(X36,X34))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X37,tc_bool)),X36),X35)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1448])])]) ).
fof(c_0_2359,plain,
! [X34,X35,X36,X37] :
( hBOOL(hAPP(X35,X34))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X37,tc_bool)),X36),X35))
| ~ hBOOL(hAPP(X36,X34)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1449])])]) ).
fof(c_0_2360,plain,
! [X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X4)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X4),c_HOL_Ozero__class_Ozero(X4)),c_HOL_Ozero__class_Ozero(X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X4),c_HOL_Ozero__class_Ozero(X4)),c_HOL_Ozero__class_Ozero(X4)))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_HOL_Ozero__class_Ozero(X4)),c_HOL_Ozero__class_Ozero(X4)) = c_HOL_Ozero__class_Ozero(X4) ),
inference(variable_rename,[status(thm)],[c_0_1450]) ).
fof(c_0_2361,plain,
! [X43,X44,X45,X46] :
( hAPP(X43,X44) != c_Option_Ooption_ONone(X45)
| ~ hBOOL(hAPP(hAPP(c_in(X46),X44),c_Map_Odom(X43,X46,X45))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1451])])]) ).
fof(c_0_2362,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| hBOOL(hAPP(hAPP(c_lessequals(X17),hAPP(hAPP(c_Orderings_Oord__class_Omin(X17),X16),X15)),X16)) ),
inference(variable_rename,[status(thm)],[c_0_1452]) ).
fof(c_0_2363,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| hBOOL(hAPP(hAPP(c_lessequals(X17),hAPP(hAPP(c_Orderings_Oord__class_Omin(X17),X16),X15)),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1453]) ).
fof(c_0_2364,plain,
! [X15,X16,X17] :
( ~ class_Lattices_Olattice(X17)
| hBOOL(hAPP(hAPP(c_lessequals(X17),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X17),X16),X15)),X16)) ),
inference(variable_rename,[status(thm)],[c_0_1454]) ).
fof(c_0_2365,plain,
! [X15,X16,X17] :
( ~ class_Lattices_Olattice(X17)
| hBOOL(hAPP(hAPP(c_lessequals(X17),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X17),X16),X15)),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1455]) ).
fof(c_0_2366,plain,
! [X15,X16,X17] :
( ~ class_Lattices_Olower__semilattice(X17)
| hBOOL(hAPP(hAPP(c_lessequals(X17),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X17),X16),X15)),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1456]) ).
fof(c_0_2367,plain,
! [X15,X16,X17] :
( ~ class_Lattices_Olower__semilattice(X17)
| hBOOL(hAPP(hAPP(c_lessequals(X17),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X17),X16),X15)),X16)) ),
inference(variable_rename,[status(thm)],[c_0_1457]) ).
fof(c_0_2368,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X73),hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X72),X71)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X73),X72)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X73),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1458]) ).
fof(c_0_2369,plain,
! [X71,X72,X73,X74] :
( ~ class_Lattices_Odistrib__lattice(X74)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),X73),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),X72),X71)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),X73),X72)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),X73),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1459]) ).
fof(c_0_2370,plain,
! [X24,X25,X26,X27] :
( ~ class_OrderedGroup_Olordered__ab__group__add__join(X27)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X27),X25),X24)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X25)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X24)) ),
inference(variable_rename,[status(thm)],[c_0_1460]) ).
fof(c_0_2371,plain,
! [X24,X25,X26,X27] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X27)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X27),X25),X24)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X25)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X24)) ),
inference(variable_rename,[status(thm)],[c_0_1461]) ).
fof(c_0_2372,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X27)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X25)),X24) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X24)),X25) ),
inference(variable_rename,[status(thm)],[c_0_1462]) ).
fof(c_0_2373,plain,
! [X24,X25,X26,X27] :
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X27)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X27),X25),X24)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X25)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X24)) ),
inference(variable_rename,[status(thm)],[c_0_1463]) ).
fof(c_0_2374,plain,
! [X24,X25,X26,X27] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X27)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X27),X25),X24)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X25)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X24)) ),
inference(variable_rename,[status(thm)],[c_0_1464]) ).
fof(c_0_2375,plain,
! [X71,X72,X73,X74] :
( ~ class_Lattices_Odistrib__lattice(X74)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),X73),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),X72),X71)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),X73),X72)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),X73),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1465]) ).
fof(c_0_2376,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X73),hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X72),X71)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X73),X72)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X73),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1466]) ).
fof(c_0_2377,plain,
! [X87,X88,X89,X90] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X90)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X90),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X90),X89),X88)),X87) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X90),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X90),X89),X87)),X88) ),
inference(variable_rename,[status(thm)],[c_0_1467]) ).
fof(c_0_2378,plain,
! [X71,X72,X73,X74] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X74)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X74),X73),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X74),X72),X71)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X74),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X74),X73),X72)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X74),X73),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1468]) ).
fof(c_0_2379,plain,
! [X14,X15,X16] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X16,tc_bool)),X15),X14) != X14
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X16,tc_bool)),X15),X14)) ),
inference(variable_rename,[status(thm)],[c_0_1469]) ).
fof(c_0_2380,plain,
! [X15,X16,X17] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X17)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),X16),X15) != c_HOL_Ozero__class_Ozero(X17)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X17),c_HOL_Ozero__class_Ozero(X17)),X15))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X17),c_HOL_Ozero__class_Ozero(X17)),X16))
| X15 = c_HOL_Ozero__class_Ozero(X17) ),
inference(variable_rename,[status(thm)],[c_0_1470]) ).
fof(c_0_2381,plain,
! [X15,X16,X17] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X17)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),X16),X15) != c_HOL_Ozero__class_Ozero(X17)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X17),c_HOL_Ozero__class_Ozero(X17)),X15))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X17),c_HOL_Ozero__class_Ozero(X17)),X16))
| X16 = c_HOL_Ozero__class_Ozero(X17) ),
inference(variable_rename,[status(thm)],[c_0_1471]) ).
fof(c_0_2382,plain,
! [X39,X40,X41] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X39,X40,X41),c_ATP__Linkup_Osko__Finite__Set__Xfinite__nonempty__imp__fold1Set__1__1(X40,X39,X41)))
| X40 = c_Orderings_Obot__class_Obot(tc_fun(X41,tc_bool))
| ~ c_Finite__Set_Ofinite(X40,X41) ),
inference(variable_rename,[status(thm)],[c_0_1472]) ).
fof(c_0_2383,plain,
! [X90,X91,X92,X93,X94] :
( ~ class_Ring__and__Field_Oidom(X94)
| ~ class_Int_Onumber__ring(X94)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X94),X90),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X94),X91),X93)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X94),X90),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X94),X91),X92))
| X93 = X92
| X91 = c_HOL_Ozero__class_Ozero(X94) ),
inference(variable_rename,[status(thm)],[c_0_1473]) ).
fof(c_0_2384,plain,
! [X39,X40,X41,X42,X43] :
( hAPP(X40,X39) != c_Option_Ooption_ONone(X43)
| c_HOL_Ominus__class_Ominus(c_Map_Odom(X40,X42,X43),hAPP(hAPP(c_Set_Oinsert(X42),X39),X41),tc_fun(X42,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Map_Odom(X40,X42,X43),X41,tc_fun(X42,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1474]) ).
fof(c_0_2385,plain,
! [X14,X15,X16,X17] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X17,tc_bool)),X16),hAPP(hAPP(c_Set_Oinsert(X17),X14),X15)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X17,tc_bool)),X16),X15)
| hBOOL(hAPP(hAPP(c_in(X17),X14),X16)) ),
inference(variable_rename,[status(thm)],[c_0_1475]) ).
fof(c_0_2386,plain,
! [X13,X14,X15] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X15),X13),X14),hAPP(hAPP(c_Set_Oinsert(X15),X13),c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool))),tc_fun(X15,tc_bool)) = X14
| hBOOL(hAPP(hAPP(c_in(X15),X13),X14)) ),
inference(variable_rename,[status(thm)],[c_0_1476]) ).
fof(c_0_2387,plain,
! [X14,X15,X16] :
( c_Finite__Set_Ofinite(X15,X16)
| ~ c_Finite__Set_Ofinite(X14,X16)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X16,tc_bool)),X15),X14)) ),
inference(variable_rename,[status(thm)],[c_0_1477]) ).
fof(c_0_2388,plain,
! [X14,X15,X16] :
( c_Finite__Set_Ofinite(X15,X16)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X16,tc_bool)),X15),X14))
| ~ c_Finite__Set_Ofinite(X14,X16) ),
inference(variable_rename,[status(thm)],[c_0_1478]) ).
fof(c_0_2389,plain,
! [X14,X15,X16,X17] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X17),X14),X16),X15,tc_fun(X17,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X17),X14),c_HOL_Ominus__class_Ominus(X16,X15,tc_fun(X17,tc_bool)))
| hBOOL(hAPP(hAPP(c_in(X17),X14),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1479]) ).
fof(c_0_2390,plain,
! [X24,X25,X26,X27] :
( c_Set_Ovimage(c_COMBK(X24,X26,X27),X25,X27,X26) = c_Orderings_Obot__class_Obot(tc_fun(X27,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X26),X24),X25)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1480])])]) ).
fof(c_0_2391,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hBOOL(hAPP(hAPP(c_lessequals(X74),X71),hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X73),X72)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X71),X72)) ),
inference(variable_rename,[status(thm)],[c_0_1481]) ).
fof(c_0_2392,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hBOOL(hAPP(hAPP(c_lessequals(X74),X71),hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X73),X72)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X71),X73)) ),
inference(variable_rename,[status(thm)],[c_0_1482]) ).
fof(c_0_2393,plain,
! [X20,X21,X22,X23] :
( ~ class_Orderings_Olinorder(X23)
| hBOOL(hAPP(hAPP(c_lessequals(X23),X20),hAPP(hAPP(c_Orderings_Oord__class_Omax(X23),X22),X21)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X20),X21)) ),
inference(variable_rename,[status(thm)],[c_0_1483]) ).
fof(c_0_2394,plain,
! [X20,X21,X22,X23] :
( ~ class_Orderings_Olinorder(X23)
| hBOOL(hAPP(hAPP(c_lessequals(X23),X20),hAPP(hAPP(c_Orderings_Oord__class_Omax(X23),X22),X21)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X20),X22)) ),
inference(variable_rename,[status(thm)],[c_0_1484]) ).
fof(c_0_2395,plain,
! [X20,X21,X22,X23] :
( ~ class_Orderings_Olinorder(X23)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X23),X20),hAPP(hAPP(c_Orderings_Oord__class_Omax(X23),X22),X21)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X23),X20),X22)) ),
inference(variable_rename,[status(thm)],[c_0_1485]) ).
fof(c_0_2396,plain,
! [X20,X21,X22,X23] :
( ~ class_Orderings_Olinorder(X23)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X23),X20),hAPP(hAPP(c_Orderings_Oord__class_Omax(X23),X22),X21)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X23),X20),X21)) ),
inference(variable_rename,[status(thm)],[c_0_1486]) ).
fof(c_0_2397,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X71),hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X73),X72)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X71),X73)) ),
inference(variable_rename,[status(thm)],[c_0_1487]) ).
fof(c_0_2398,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X71),hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X73),X72)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X71),X72)) ),
inference(variable_rename,[status(thm)],[c_0_1488]) ).
fof(c_0_2399,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Oupper__semilattice(X23)
| hBOOL(hAPP(hAPP(c_lessequals(X23),X20),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X23),X22),X21)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X20),X21)) ),
inference(variable_rename,[status(thm)],[c_0_1489]) ).
fof(c_0_2400,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Oupper__semilattice(X23)
| hBOOL(hAPP(hAPP(c_lessequals(X23),X20),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X23),X22),X21)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X23),X20),X22)) ),
inference(variable_rename,[status(thm)],[c_0_1490]) ).
fof(c_0_2401,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Oupper__semilattice(X23)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X23),X20),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X23),X22),X21)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X23),X20),X22)) ),
inference(variable_rename,[status(thm)],[c_0_1491]) ).
fof(c_0_2402,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Oupper__semilattice(X23)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X23),X20),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X23),X22),X21)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X23),X20),X21)) ),
inference(variable_rename,[status(thm)],[c_0_1492]) ).
fof(c_0_2403,plain,
! [X59,X60,X61] :
( c_Finite__Set_Ofinite(X60,X61)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X61,tc_bool)),X60),X59),X61) ),
inference(variable_rename,[status(thm)],[c_0_1493]) ).
fof(c_0_2404,plain,
! [X59,X60,X61] :
( c_Finite__Set_Ofinite(X59,X61)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X61,tc_bool)),X60),X59),X61) ),
inference(variable_rename,[status(thm)],[c_0_1494]) ).
fof(c_0_2405,plain,
! [X39,X40,X41,X42,X43] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X42)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X42)
| hAPP(X40,X39) != c_HOL_Ozero__class_Ozero(X42)
| ~ hBOOL(hAPP(hAPP(c_in(X43),X39),X41))
| ~ c_Finite__Set_Ofinite(X41,X43)
| c_Finite__Set_Osetprod(X40,X41,X43,X42) = c_HOL_Ozero__class_Ozero(X42) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1495])])]) ).
fof(c_0_2406,plain,
! [X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),c_HOL_Ozero__class_Ozero(X4)),c_HOL_Ozero__class_Ozero(X4))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),c_HOL_Ozero__class_Ozero(X4)),c_HOL_Ozero__class_Ozero(X4))) = c_HOL_Ozero__class_Ozero(X4) ),
inference(variable_rename,[status(thm)],[c_0_1496]) ).
fof(c_0_2407,plain,
! [X20,X21,X22,X23] :
( hBOOL(hAPP(hAPP(c_in(X23),X21),hAPP(hAPP(c_Set_Oinsert(X23),X20),X22)))
| ~ hBOOL(hAPP(hAPP(c_in(X23),X21),X22)) ),
inference(variable_rename,[status(thm)],[c_0_1497]) ).
fof(c_0_2408,plain,
! [X20,X21,X22,X23] :
( hBOOL(hAPP(hAPP(c_in(X23),X21),hAPP(hAPP(c_Set_Oinsert(X23),X20),X22)))
| ~ hBOOL(hAPP(hAPP(c_in(X23),X21),X22)) ),
inference(variable_rename,[status(thm)],[c_0_1498]) ).
fof(c_0_2409,plain,
! [X39,X40,X41,X42,X43] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X42)
| hAPP(X40,X39) != c_HOL_Ozero__class_Ozero(X42)
| ~ hBOOL(hAPP(hAPP(c_in(X43),X39),X41))
| ~ c_Finite__Set_Ofinite(X41,X43)
| c_Finite__Set_Osetprod(X40,X41,X43,X42) = c_HOL_Ozero__class_Ozero(X42) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1499])])]) ).
fof(c_0_2410,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X15)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X15),X15),hAPP(hAPP(c_Set_Oinsert(X15),X13),X14)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X13),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X15),X15),X14))
| hBOOL(hAPP(hAPP(c_in(X15),X13),X14))
| ~ c_Finite__Set_Ofinite(X14,X15)
| X14 = c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1500]) ).
fof(c_0_2411,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X15)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X15),X15),hAPP(hAPP(c_Set_Oinsert(X15),X13),X14)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X13),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X15),X15),X14))
| hBOOL(hAPP(hAPP(c_in(X15),X13),X14))
| ~ c_Finite__Set_Ofinite(X14,X15)
| X14 = c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1501]) ).
fof(c_0_2412,plain,
! [X52,X53,X54,X55,X56,X57] :
( hAPP(hAPP(X56,X53),X52) = hAPP(hAPP(X56,X52),X53)
| ~ c_Lattices_Olower__semilattice(X54,X55,X56,X57) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1502])])]) ).
fof(c_0_2413,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Olinorder(X15)
| hBOOL(hAPP(hAPP(c_lessequals(X15),hAPP(c_Finite__Set_Olinorder__class_OMin(X15),X14)),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X15),X13),X14))
| ~ c_Finite__Set_Ofinite(X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_1503]) ).
fof(c_0_2414,plain,
! [X70,X71,X72,X73,X74] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X74)
| c_HOL_Ominus__class_Ominus(X73,X71,X74) != c_HOL_Ominus__class_Ominus(X72,X70,X74)
| hBOOL(hAPP(hAPP(c_lessequals(X74),X70),X72))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X71),X73)) ),
inference(variable_rename,[status(thm)],[c_0_1504]) ).
fof(c_0_2415,plain,
! [X70,X71,X72,X73,X74] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X74)
| c_HOL_Ominus__class_Ominus(X73,X71,X74) != c_HOL_Ominus__class_Ominus(X72,X70,X74)
| hBOOL(hAPP(hAPP(c_lessequals(X74),X71),X73))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X70),X72)) ),
inference(variable_rename,[status(thm)],[c_0_1505]) ).
fof(c_0_2416,plain,
! [X70,X71,X72,X73,X74] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X74)
| c_HOL_Ominus__class_Ominus(X73,X71,X74) != c_HOL_Ominus__class_Ominus(X72,X70,X74)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X72),X70))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X73),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1506]) ).
fof(c_0_2417,plain,
! [X70,X71,X72,X73,X74] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X74)
| c_HOL_Ominus__class_Ominus(X73,X71,X74) != c_HOL_Ominus__class_Ominus(X72,X70,X74)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X73),X71))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X72),X70)) ),
inference(variable_rename,[status(thm)],[c_0_1507]) ).
fof(c_0_2418,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Opreorder(X74)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X73),X71))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X72),X71))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X73),X72)) ),
inference(variable_rename,[status(thm)],[c_0_1508]) ).
fof(c_0_2419,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Oorder(X74)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X71),X73))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X71),X72))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X72),X73)) ),
inference(variable_rename,[status(thm)],[c_0_1509]) ).
fof(c_0_2420,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Oorder(X74)
| hBOOL(hAPP(hAPP(c_lessequals(X74),X71),X73))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X71),X72))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X72),X73)) ),
inference(variable_rename,[status(thm)],[c_0_1510]) ).
fof(c_0_2421,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Oorder(X74)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X71),X73))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X71),X72))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X72),X73)) ),
inference(variable_rename,[status(thm)],[c_0_1511]) ).
fof(c_0_2422,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Oorder(X74)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X71),X73))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X71),X72))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X72),X73)) ),
inference(variable_rename,[status(thm)],[c_0_1512]) ).
fof(c_0_2423,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Opreorder(X74)
| hBOOL(hAPP(hAPP(c_lessequals(X74),X73),X71))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X72),X71))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X73),X72)) ),
inference(variable_rename,[status(thm)],[c_0_1513]) ).
fof(c_0_2424,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Opreorder(X74)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X73),X71))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X72),X71))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X73),X72)) ),
inference(variable_rename,[status(thm)],[c_0_1514]) ).
fof(c_0_2425,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Opreorder(X74)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X73),X71))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X74),X72),X71))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X74),X73),X72)) ),
inference(variable_rename,[status(thm)],[c_0_1515]) ).
fof(c_0_2426,plain,
! [X38,X39,X40,X41] :
( hAPP(c_Finite__Set_Ofold1(X39,X41),hAPP(hAPP(c_Set_Oinsert(X41),X38),X40)) = hAPP(hAPP(X39,X38),hAPP(c_Finite__Set_Ofold1(X39,X41),X40))
| hBOOL(hAPP(hAPP(c_in(X41),X38),X40))
| ~ c_Finite__Set_Ofinite(X40,X41)
| X40 = c_Orderings_Obot__class_Obot(tc_fun(X41,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__mult(X39,X41) ),
inference(variable_rename,[status(thm)],[c_0_1516]) ).
fof(c_0_2427,plain,
! [X52,X53,X54,X55,X56] :
( hAPP(hAPP(X55,X52),X52) = X52
| ~ c_Lattices_Olower__semilattice(X53,X54,X55,X56) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1517])])]) ).
fof(c_0_2428,plain,
! [X58,X59,X60] :
( ~ class_Lattices_Olattice(X60)
| hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,X60)),X59),X58),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X60),hAPP(X59,v_x)),hAPP(X58,v_x)) ),
inference(variable_rename,[status(thm)],[c_0_1518]) ).
fof(c_0_2429,plain,
! [X58,X59,X60] :
( ~ class_Lattices_Olattice(X60)
| hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,X60)),X59),X58),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X60),hAPP(X59,v_x)),hAPP(X58,v_x)) ),
inference(variable_rename,[status(thm)],[c_0_1519]) ).
fof(c_0_2430,plain,
! [X14,X15,X16,X17] :
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X17),X14),X16),X15,tc_fun(X17,tc_bool)) = c_HOL_Ominus__class_Ominus(X16,X15,tc_fun(X17,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X17),X14),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1520]) ).
fof(c_0_2431,plain,
! [X57,X58] :
( ~ class_Orderings_Oorder(X58)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X58),X57),c_Orderings_Obot__class_Obot(tc_fun(X58,tc_bool))),c_SetInterval_Oord__class_OlessThan(X57,X58),tc_fun(X58,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X58),X57),c_Orderings_Obot__class_Obot(tc_fun(X58,tc_bool))) ),
inference(variable_rename,[status(thm)],[c_0_1521]) ).
fof(c_0_2432,plain,
! [X20,X21,X22] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X22)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X21),X20) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X22),X21),X20)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X22),X21),X20)) ),
inference(variable_rename,[status(thm)],[c_0_1522]) ).
fof(c_0_2433,plain,
! [X71,X72,X73,X74] :
( ~ class_Lattices_Olattice(X74)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),X73),X72)),X71) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),X73),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),X72),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1523]) ).
fof(c_0_2434,plain,
! [X71,X72,X73,X74] :
( ~ class_Lattices_Olower__semilattice(X74)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),X73),X72)),X71) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),X73),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),X72),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1524]) ).
fof(c_0_2435,plain,
! [X71,X72,X73,X74] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X74)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X74),X73),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X74),X72),X71)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X74),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X74),X73),X72)),X71) ),
inference(variable_rename,[status(thm)],[c_0_1525]) ).
fof(c_0_2436,plain,
! [X24,X25,X26,X27] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X27)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X25)),X24) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X25),X24)) ),
inference(variable_rename,[status(thm)],[c_0_1526]) ).
fof(c_0_2437,plain,
! [X24,X25,X26,X27] :
( ~ class_OrderedGroup_Oab__semigroup__add(X27)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X25)),X24) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X25),X24)) ),
inference(variable_rename,[status(thm)],[c_0_1527]) ).
fof(c_0_2438,plain,
! [X25,X26,X27,X28] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X28)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X26),X25)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X27),X26)),X25) ),
inference(variable_rename,[status(thm)],[c_0_1528]) ).
fof(c_0_2439,plain,
! [X24,X25,X26,X27] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X27)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X25)),X24) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X25),X24)) ),
inference(variable_rename,[status(thm)],[c_0_1529]) ).
fof(c_0_2440,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X73),X72)),X71) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X73),hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X72),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1530]) ).
fof(c_0_2441,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X73),X72)),X71) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X73),hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X72),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1531]) ).
fof(c_0_2442,plain,
! [X24,X25,X26,X27] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X27)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X26),X25)),X24) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X26),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X27),X25),X24)) ),
inference(variable_rename,[status(thm)],[c_0_1532]) ).
fof(c_0_2443,plain,
! [X87,X88,X89,X90] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X90)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X90),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X90),X89),X88)),X87) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X90),X89),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X90),X88),X87)) ),
inference(variable_rename,[status(thm)],[c_0_1533]) ).
fof(c_0_2444,plain,
! [X86,X87,X88,X89] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X89)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X89),X88),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X89),X87),X86)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X89),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X89),X88),X87)),X86) ),
inference(variable_rename,[status(thm)],[c_0_1534]) ).
fof(c_0_2445,plain,
! [X71,X72,X73,X74] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X74)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X74),X73),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X74),X72),X71)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X74),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X74),X73),X72)),X71) ),
inference(variable_rename,[status(thm)],[c_0_1535]) ).
fof(c_0_2446,plain,
! [X71,X72,X73,X74] :
( ~ class_Lattices_Olattice(X74)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),X73),X72)),X71) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),X73),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),X72),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1536]) ).
fof(c_0_2447,plain,
! [X71,X72,X73,X74] :
( ~ class_Lattices_Oupper__semilattice(X74)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),X73),X72)),X71) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),X73),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),X72),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1537]) ).
fof(c_0_2448,plain,
! [X93,X94,X95] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X95)),X93))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X94),X93))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X95),X94)) ),
inference(variable_rename,[status(thm)],[c_0_1538]) ).
fof(c_0_2449,plain,
! [X52,X53,X54,X55] :
( c_OrderedGroup_Oab__semigroup__idem__mult(X54,X55)
| ~ c_Lattices_Olower__semilattice(X52,X53,X54,X55) ),
inference(variable_rename,[status(thm)],[c_0_1539]) ).
fof(c_0_2450,plain,
! [X15,X16,X17,X18] :
( hBOOL(hAPP(X17,X16))
| X15 = X16
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X18),X15),X17),X16)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1540])])]) ).
fof(c_0_2451,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Opreorder(X17)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X17),X16),X15))
| hBOOL(hAPP(hAPP(c_lessequals(X17),X15),X16))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1541]) ).
fof(c_0_2452,plain,
! [X13,X14,X15] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X15)
| hBOOL(hAPP(hAPP(c_lessequals(X15),c_Complete__Lattice_OInf__class_OInf(X14,X15)),X13))
| ~ hBOOL(hAPP(hAPP(c_in(X15),X13),X14)) ),
inference(variable_rename,[status(thm)],[c_0_1542]) ).
fof(c_0_2453,plain,
! [X71,X72,X73,X74,X75] :
( ~ class_OrderedGroup_Oab__group__add(X75)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X75),X73),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X75),X72),X71)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X75),X72),X74)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X75),X73),X71) = X74 ),
inference(variable_rename,[status(thm)],[c_0_1543]) ).
fof(c_0_2454,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Olinorder(X15)
| hBOOL(hAPP(hAPP(c_lessequals(X15),X13),hAPP(c_Finite__Set_Olinorder__class_OMax(X15),X14)))
| ~ hBOOL(hAPP(hAPP(c_in(X15),X13),X14))
| ~ c_Finite__Set_Ofinite(X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_1544]) ).
fof(c_0_2455,plain,
! [X14,X15,X16,X17] :
( hAPP(hAPP(c_Set_Oinsert(X17),X14),X16) != hAPP(hAPP(c_Set_Oinsert(X17),X14),X15)
| hBOOL(hAPP(hAPP(c_in(X17),X14),X15))
| hBOOL(hAPP(hAPP(c_in(X17),X14),X16))
| X16 = X15 ),
inference(variable_rename,[status(thm)],[c_0_1545]) ).
fof(c_0_2456,plain,
! [X19,X20,X21] :
( ~ hBOOL(hAPP(X20,X19))
| ~ hBOOL(hAPP(hAPP(c_in(X21),X19),c_Orderings_Obot__class_Obot(tc_fun(X21,tc_bool)))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1546])])]) ).
fof(c_0_2457,plain,
! [X17,X18,X19,X20] :
( c_Hoare__Mirabelle_Ohoare__derivs(X19,X17,X20)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X19,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X20)),X18),X17),X20) ),
inference(variable_rename,[status(thm)],[c_0_1547]) ).
fof(c_0_2458,plain,
! [X22,X23,X24] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X24)
| c_Finite__Set_Osetsum(c_COMBK(c_HOL_Ozero__class_Ozero(X24),X24,X23),X22,X23,X24) = c_HOL_Ozero__class_Ozero(X24) ),
inference(variable_rename,[status(thm)],[c_0_1548]) ).
fof(c_0_2459,plain,
! [X43,X44,X45,X46,X47] :
( hAPP(X43,X45) != hAPP(c_Option_Ooption_OSome(X47),X44)
| hBOOL(hAPP(hAPP(c_in(X46),X45),c_Map_Odom(X43,X46,X47))) ),
inference(variable_rename,[status(thm)],[c_0_1549]) ).
fof(c_0_2460,plain,
! [X13,X14,X15] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X15)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X15),X15),hAPP(hAPP(c_Set_Oinsert(X15),X13),X14)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X15),X13),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X15),X15),X14))
| ~ c_Finite__Set_Ofinite(X14,X15)
| X14 = c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1550]) ).
fof(c_0_2461,plain,
! [X93,X94,X95] :
( ~ class_HOL_Oord(X95)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X95),X94),X93))
| ~ hBOOL(hAPP(hAPP(c_in(X95),X94),c_SetInterval_Oord__class_OlessThan(X93,X95))) ),
inference(variable_rename,[status(thm)],[c_0_1551]) ).
fof(c_0_2462,plain,
! [X19,X20,X21] :
( hBOOL(hAPP(X20,X19))
| ~ hBOOL(hAPP(hAPP(c_in(X21),X19),c_Orderings_Obot__class_Obot(tc_fun(X21,tc_bool)))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1552])])]) ).
fof(c_0_2463,plain,
! [X14,X15,X16] :
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X16,tc_bool)),X15),X14) != c_Orderings_Obot__class_Obot(tc_fun(X16,tc_bool))
| c_HOL_Ominus__class_Ominus(X15,X14,tc_fun(X16,tc_bool)) = X15 ),
inference(variable_rename,[status(thm)],[c_0_1553]) ).
fof(c_0_2464,plain,
! [X59,X60,X61] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X61,tc_bool)),X60),X59),X61)
| ~ c_Finite__Set_Ofinite(X59,X61)
| ~ c_Finite__Set_Ofinite(X60,X61) ),
inference(variable_rename,[status(thm)],[c_0_1554]) ).
fof(c_0_2465,plain,
! [X59,X60,X61] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X61,tc_bool)),X60),X59),X61)
| ~ c_Finite__Set_Ofinite(X59,X61)
| ~ c_Finite__Set_Ofinite(X60,X61) ),
inference(variable_rename,[status(thm)],[c_0_1555]) ).
fof(c_0_2466,plain,
! [X51,X52,X53,X54,X55] :
( ~ hBOOL(hAPP(hAPP(X54,X52),X51))
| ~ hBOOL(hAPP(hAPP(X54,X51),X52))
| ~ c_Orderings_Olinorder(X53,X54,X55) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1556])])]) ).
fof(c_0_2467,plain,
! [X51,X52,X53,X54,X55] :
( ~ hBOOL(hAPP(hAPP(X54,X52),X51))
| ~ hBOOL(hAPP(hAPP(X53,X51),X52))
| ~ c_Orderings_Olinorder(X53,X54,X55) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1557])])]) ).
fof(c_0_2468,plain,
! [X51,X52,X53,X54,X55] :
( ~ hBOOL(hAPP(hAPP(X53,X52),X51))
| ~ hBOOL(hAPP(hAPP(X54,X51),X52))
| ~ c_Orderings_Olinorder(X53,X54,X55) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1558])])]) ).
fof(c_0_2469,plain,
! [X51,X52,X53,X54] :
( ~ hBOOL(hAPP(hAPP(X52,X51),X51))
| ~ c_Orderings_Olinorder(X52,X53,X54)
| ~ hBOOL(hAPP(hAPP(X53,X51),X51)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1559])])]) ).
fof(c_0_2470,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Oorder(X17)
| X16 = X15
| ~ hBOOL(hAPP(hAPP(c_lessequals(X17),X15),X16))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1560]) ).
fof(c_0_2471,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Oorder(X17)
| X16 = X15
| ~ hBOOL(hAPP(hAPP(c_lessequals(X17),X15),X16))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1561]) ).
fof(c_0_2472,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Oorder(X17)
| X16 = X15
| ~ hBOOL(hAPP(hAPP(c_lessequals(X17),X16),X15))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X17),X15),X16)) ),
inference(variable_rename,[status(thm)],[c_0_1562]) ).
fof(c_0_2473,plain,
! [X13,X14] :
( ~ class_Orderings_Olinorder(X14)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X14),X13),X13))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X14),X13),X13)) ),
inference(variable_rename,[status(thm)],[c_0_1563]) ).
fof(c_0_2474,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X17),X16),X15))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X17),X15),X16)) ),
inference(variable_rename,[status(thm)],[c_0_1564]) ).
fof(c_0_2475,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X17),X16),X15))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X17),X15),X16)) ),
inference(variable_rename,[status(thm)],[c_0_1565]) ).
fof(c_0_2476,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Opreorder(X17)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X17),X15),X16))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1566]) ).
fof(c_0_2477,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| hBOOL(hAPP(hAPP(c_lessequals(X10),c_HOL_Ozero__class_Ozero(X10)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X10),X9),X9))) ),
inference(variable_rename,[status(thm)],[c_0_1567]) ).
fof(c_0_2478,plain,
! [X20,X21,X22] :
( ~ class_Orderings_Oorder(X22)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),X21),X20))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),X20),X21)) ),
inference(variable_rename,[status(thm)],[c_0_1568]) ).
fof(c_0_2479,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X17),X16),X15))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X17),X15),X16)) ),
inference(variable_rename,[status(thm)],[c_0_1569]) ).
fof(c_0_2480,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Opreorder(X17)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X17),X15),X16))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1570]) ).
fof(c_0_2481,plain,
! [X20,X21,X22] :
( ~ class_Orderings_Opreorder(X22)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),X20),X21))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),X21),X20)) ),
inference(variable_rename,[status(thm)],[c_0_1571]) ).
fof(c_0_2482,plain,
! [X43,X44,X45,X46] :
( hBOOL(hAPP(hAPP(c_in(X46),X44),c_Map_Odom(X43,X46,X45)))
| hAPP(X43,X44) = c_Option_Ooption_ONone(X45) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1572])])]) ).
fof(c_0_2483,plain,
! [X24,X25,X26,X27] :
( X24 = X25
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X27),X26),X24))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X27),X26),X25)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1573])])]) ).
fof(c_0_2484,plain,
! [X89,X90,X91] :
( ~ class_Orderings_Oorder(X91)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X91,tc_bool)),c_SetInterval_Oord__class_OlessThan(X90,X91)),c_SetInterval_Oord__class_OatLeastAtMost(X90,X89,X91)) = c_Orderings_Obot__class_Obot(tc_fun(X91,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1574]) ).
fof(c_0_2485,plain,
! [X38,X39,X40,X41,X42] :
( hAPP(hAPP(X38,hAPP(hAPP(X38,X41),X40)),X39) = hAPP(hAPP(X38,X41),hAPP(hAPP(X38,X40),X39))
| ~ c_OrderedGroup_Oab__semigroup__mult(X38,X42) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1575])])]) ).
fof(c_0_2486,plain,
! [X38,X39,X40,X41] :
( hAPP(c_Finite__Set_Ofold1(X39,X41),hAPP(hAPP(c_Set_Oinsert(X41),X38),X40)) = hAPP(hAPP(X39,X38),hAPP(c_Finite__Set_Ofold1(X39,X41),X40))
| ~ c_Finite__Set_Ofinite(X40,X41)
| X40 = c_Orderings_Obot__class_Obot(tc_fun(X41,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X39,X41) ),
inference(variable_rename,[status(thm)],[c_0_1576]) ).
fof(c_0_2487,plain,
! [X93,X94,X95] :
( ~ class_HOL_Oord(X95)
| hBOOL(hAPP(hAPP(c_in(X95),X94),c_SetInterval_Oord__class_OlessThan(X93,X95)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X95),X94),X93)) ),
inference(variable_rename,[status(thm)],[c_0_1577]) ).
fof(c_0_2488,plain,
! [X13,X14,X15] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X15)
| hBOOL(hAPP(hAPP(c_lessequals(X15),X13),c_Complete__Lattice_OSup__class_OSup(X14,X15)))
| ~ hBOOL(hAPP(hAPP(c_in(X15),X13),X14)) ),
inference(variable_rename,[status(thm)],[c_0_1578]) ).
fof(c_0_2489,plain,
! [X51,X52,X53,X54,X55,X56] :
( ~ c_Orderings_Olinorder(X51,X52,X53)
| hAPP(c_Finite__Set_Ofold1(X54,X56),hAPP(hAPP(c_Set_Oinsert(X56),X55),c_Orderings_Obot__class_Obot(tc_fun(X56,tc_bool)))) = X55 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1579])])]) ).
fof(c_0_2490,plain,
! [X20,X21,X22] :
( hAPP(hAPP(c_Set_Oinsert(X22),X21),c_Orderings_Obot__class_Obot(tc_fun(X22,tc_bool))) != hAPP(hAPP(c_Set_Oinsert(X22),X20),c_Orderings_Obot__class_Obot(tc_fun(X22,tc_bool)))
| X21 = X20 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1580])])]) ).
fof(c_0_2491,plain,
! [X59,X60,X61] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X61,tc_bool)),X60),X59),X61)
| ~ c_Finite__Set_Ofinite(X59,X61) ),
inference(variable_rename,[status(thm)],[c_0_1581]) ).
fof(c_0_2492,plain,
! [X59,X60,X61] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X61,tc_bool)),X60),X59),X61)
| ~ c_Finite__Set_Ofinite(X60,X61) ),
inference(variable_rename,[status(thm)],[c_0_1582]) ).
fof(c_0_2493,plain,
! [X71,X72,X73,X74,X75,X76] :
( hAPP(hAPP(X74,X73),hAPP(hAPP(X74,X72),X71)) = hAPP(hAPP(X74,X72),hAPP(hAPP(X74,X73),X71))
| ~ c_Finite__Set_Ofun__left__comm(X74,X76,X75) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1583])])]) ).
fof(c_0_2494,plain,
! [X13,X14,X15] :
( c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(X15),X13),X14),X15) = c_Finite__Set_Ocard(X14,X15)
| ~ hBOOL(hAPP(hAPP(c_in(X15),X13),X14))
| ~ c_Finite__Set_Ofinite(X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_1584]) ).
fof(c_0_2495,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| hBOOL(hAPP(hAPP(c_lessequals(X17),X15),hAPP(hAPP(c_Orderings_Oord__class_Omax(X17),X16),X15))) ),
inference(variable_rename,[status(thm)],[c_0_1585]) ).
fof(c_0_2496,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| hBOOL(hAPP(hAPP(c_lessequals(X17),X16),hAPP(hAPP(c_Orderings_Oord__class_Omax(X17),X16),X15))) ),
inference(variable_rename,[status(thm)],[c_0_1586]) ).
fof(c_0_2497,plain,
! [X15,X16,X17] :
( ~ class_Lattices_Oupper__semilattice(X17)
| hBOOL(hAPP(hAPP(c_lessequals(X17),X16),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X17),X16),X15))) ),
inference(variable_rename,[status(thm)],[c_0_1587]) ).
fof(c_0_2498,plain,
! [X15,X16,X17] :
( ~ class_Lattices_Oupper__semilattice(X17)
| hBOOL(hAPP(hAPP(c_lessequals(X17),X15),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X17),X16),X15))) ),
inference(variable_rename,[status(thm)],[c_0_1588]) ).
fof(c_0_2499,plain,
! [X15,X16,X17] :
( ~ class_Lattices_Olattice(X17)
| hBOOL(hAPP(hAPP(c_lessequals(X17),X15),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X17),X16),X15))) ),
inference(variable_rename,[status(thm)],[c_0_1589]) ).
fof(c_0_2500,plain,
! [X15,X16,X17] :
( ~ class_Lattices_Olattice(X17)
| hBOOL(hAPP(hAPP(c_lessequals(X17),X16),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X17),X16),X15))) ),
inference(variable_rename,[status(thm)],[c_0_1590]) ).
fof(c_0_2501,plain,
! [X10,X11] :
( ~ class_Orderings_Olinorder(X11)
| hBOOL(hAPP(hAPP(c_in(X11),hAPP(c_Finite__Set_Olinorder__class_OMax(X11),X10)),X10))
| X10 = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))
| ~ c_Finite__Set_Ofinite(X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1591]) ).
fof(c_0_2502,plain,
! [X10,X11] :
( ~ class_Orderings_Olinorder(X11)
| hBOOL(hAPP(hAPP(c_in(X11),hAPP(c_Finite__Set_Olinorder__class_OMin(X11),X10)),X10))
| X10 = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))
| ~ c_Finite__Set_Ofinite(X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1592]) ).
fof(c_0_2503,plain,
! [X56,X57] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X57),X56))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X56),c_Suc(X57))) ),
inference(variable_rename,[status(thm)],[c_0_1593]) ).
fof(c_0_2504,plain,
! [X71,X72,X73,X74] :
( ~ class_Lattices_Olattice(X74)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),X73),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),X72),X71)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),X72),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),X73),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1594]) ).
fof(c_0_2505,plain,
! [X71,X72,X73,X74] :
( ~ class_Lattices_Olower__semilattice(X74)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),X73),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),X72),X71)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),X72),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X74),X73),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1595]) ).
fof(c_0_2506,plain,
! [X71,X72,X73,X74] :
( ~ class_OrderedGroup_Oab__group__add(X74)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X74),X73),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X74),X72),X71)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X74),X72),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X74),X73),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1596]) ).
fof(c_0_2507,plain,
! [X24,X25,X26,X27] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X27)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X25),X24)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X25),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X24)) ),
inference(variable_rename,[status(thm)],[c_0_1597]) ).
fof(c_0_2508,plain,
! [X25,X26,X27,X28] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X28)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X27),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X26),X25)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X26),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X28),X27),X25)) ),
inference(variable_rename,[status(thm)],[c_0_1598]) ).
fof(c_0_2509,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X73),hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X72),X71)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X72),hAPP(hAPP(c_Orderings_Oord__class_Omin(X74),X73),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1599]) ).
fof(c_0_2510,plain,
! [X71,X72,X73,X74] :
( ~ class_Orderings_Olinorder(X74)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X73),hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X72),X71)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X72),hAPP(hAPP(c_Orderings_Oord__class_Omax(X74),X73),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1600]) ).
fof(c_0_2511,plain,
! [X86,X87,X88,X89] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X89)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X89),X88),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X89),X87),X86)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X89),X87),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X89),X88),X86)) ),
inference(variable_rename,[status(thm)],[c_0_1601]) ).
fof(c_0_2512,plain,
! [X71,X72,X73,X74] :
( ~ class_Lattices_Olattice(X74)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),X73),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),X72),X71)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),X72),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),X73),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1602]) ).
fof(c_0_2513,plain,
! [X71,X72,X73,X74] :
( ~ class_Lattices_Oupper__semilattice(X74)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),X73),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),X72),X71)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),X72),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X74),X73),X71)) ),
inference(variable_rename,[status(thm)],[c_0_1603]) ).
fof(c_0_2514,plain,
! [X39,X40,X41] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X41)
| c_Finite__Set_Osetsum(X39,c_Orderings_Obot__class_Obot(tc_fun(X40,tc_bool)),X40,X41) = c_HOL_Ozero__class_Ozero(X41) ),
inference(variable_rename,[status(thm)],[c_0_1604]) ).
fof(c_0_2515,plain,
! [X20,X21,X22] :
( ~ class_Orderings_Oorder(X22)
| c_Orderings_Obot__class_Obot(tc_fun(X22,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X21,X20,X22)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),X21),X20)) ),
inference(variable_rename,[status(thm)],[c_0_1605]) ).
fof(c_0_2516,plain,
! [X20,X21,X22] :
( ~ class_Orderings_Oorder(X22)
| c_SetInterval_Oord__class_OatLeastAtMost(X21,X20,X22) != c_Orderings_Obot__class_Obot(tc_fun(X22,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),X21),X20)) ),
inference(variable_rename,[status(thm)],[c_0_1606]) ).
fof(c_0_2517,plain,
! [X56,X57] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X57),X56))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X57)),c_Suc(X56))) ),
inference(variable_rename,[status(thm)],[c_0_1607]) ).
fof(c_0_2518,plain,
! [X51,X52,X53,X54,X55] :
( X52 = X51
| hBOOL(hAPP(hAPP(X54,X52),X51))
| ~ hBOOL(hAPP(hAPP(X53,X52),X51))
| ~ c_Orderings_Olinorder(X53,X54,X55) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1608])])]) ).
fof(c_0_2519,plain,
! [X51,X52,X53,X54,X55] :
( X52 = X51
| ~ hBOOL(hAPP(hAPP(X53,X52),X51))
| hBOOL(hAPP(hAPP(X54,X52),X51))
| ~ c_Orderings_Olinorder(X53,X54,X55) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1609])])]) ).
fof(c_0_2520,plain,
! [X14,X15,X16] :
( c_Finite__Set_Ofinite(X15,X16)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X15,X14,tc_fun(X16,tc_bool)),X16)
| ~ c_Finite__Set_Ofinite(X14,X16) ),
inference(variable_rename,[status(thm)],[c_0_1610]) ).
fof(c_0_2521,plain,
! [X14,X15,X16] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X16,tc_bool)),X15),X14) != c_Orderings_Obot__class_Obot(tc_fun(X16,tc_bool))
| X14 = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1611]) ).
fof(c_0_2522,plain,
! [X14,X15,X16] :
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X16,tc_bool)),X15),X14) != c_Orderings_Obot__class_Obot(tc_fun(X16,tc_bool))
| X15 = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1612]) ).
fof(c_0_2523,plain,
! [X10,X11,X12] :
( ~ class_Lattices_Olattice(X12)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12),X10),hAPP(c_Finite__Set_Olattice__class_OInf__fin(X12),X11)) = X10
| ~ hBOOL(hAPP(hAPP(c_in(X12),X10),X11))
| ~ c_Finite__Set_Ofinite(X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1613]) ).
fof(c_0_2524,plain,
! [X20,X21,X22] :
( ~ class_Orderings_Oorder(X22)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),X20),X21))
| X21 = X20
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),X20),X21)) ),
inference(variable_rename,[status(thm)],[c_0_1614]) ).
fof(c_0_2525,plain,
! [X20,X21,X22] :
( ~ class_Orderings_Oorder(X22)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),X20),X21))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),X20),X21))
| X21 = X20 ),
inference(variable_rename,[status(thm)],[c_0_1615]) ).
fof(c_0_2526,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Oorder(X17)
| X16 = X15
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X17),X16),X15))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1616]) ).
fof(c_0_2527,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Oorder(X17)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X17),X16),X15))
| X16 = X15
| ~ hBOOL(hAPP(hAPP(c_lessequals(X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1617]) ).
fof(c_0_2528,plain,
! [X20,X21,X22] :
( ~ class_Orderings_Oorder(X22)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),X21),X20))
| X21 = X20
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),X21),X20)) ),
inference(variable_rename,[status(thm)],[c_0_1618]) ).
fof(c_0_2529,plain,
! [X20,X21,X22] :
( ~ class_Orderings_Oorder(X22)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),X21),X20))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X22),X21),X20))
| X21 = X20 ),
inference(variable_rename,[status(thm)],[c_0_1619]) ).
fof(c_0_2530,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| X16 = X15
| ~ hBOOL(hAPP(hAPP(c_lessequals(X17),X16),X15))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1620]) ).
fof(c_0_2531,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| X16 = X15
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X17),X16),X15))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1621]) ).
fof(c_0_2532,plain,
! [X15,X16,X17,X18] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X18),X15),X17),X16))
| ~ hBOOL(hAPP(X17,X16)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1622])])]) ).
fof(c_0_2533,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Oorder(X17)
| hBOOL(hAPP(hAPP(c_lessequals(X17),X16),X15))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1623]) ).
fof(c_0_2534,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Opreorder(X17)
| hBOOL(hAPP(hAPP(c_lessequals(X17),X16),X15))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1624]) ).
fof(c_0_2535,plain,
! [X56,X57] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X57),X56))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X57)),X56)) ),
inference(variable_rename,[status(thm)],[c_0_1625]) ).
fof(c_0_2536,plain,
! [X56,X57] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X56)),c_Suc(X57)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X56),X57)) ),
inference(variable_rename,[status(thm)],[c_0_1626]) ).
fof(c_0_2537,plain,
! [X56,X57] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X57)),c_Suc(X56)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X57),X56)) ),
inference(variable_rename,[status(thm)],[c_0_1627]) ).
fof(c_0_2538,plain,
! [X13,X14,X15] :
( c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(X15),X13),X14),X15) = c_Suc(c_Finite__Set_Ocard(X14,X15))
| hBOOL(hAPP(hAPP(c_in(X15),X13),X14))
| ~ c_Finite__Set_Ofinite(X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_1628]) ).
fof(c_0_2539,plain,
! [X20,X21,X22] :
( ~ class_OrderedGroup_Ogroup__add(X22)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),c_HOL_Ominus__class_Ominus(X21,X20,X22)),X20) = X21 ),
inference(variable_rename,[status(thm)],[c_0_1629]) ).
fof(c_0_2540,plain,
! [X56,X57,X58] :
( hBOOL(hAPP(hAPP(X58,X56),X57))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X56),X57))
| X57 = X56
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X57),X56)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1630])])]) ).
fof(c_0_2541,plain,
! [X39,X40,X41,X42] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X42)
| c_Finite__Set_Osetsum(X39,X40,X41,X42) = c_HOL_Ozero__class_Ozero(X42)
| c_Finite__Set_Ofinite(X40,X41) ),
inference(variable_rename,[status(thm)],[c_0_1631]) ).
fof(c_0_2542,plain,
! [X39,X40,X41,X42] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X41)
| c_Finite__Set_Osetsum(X39,X40,X42,X41) = c_HOL_Ozero__class_Ozero(X41)
| c_Finite__Set_Ofinite(X40,X42) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1632])])]) ).
fof(c_0_2543,plain,
! [X56,X57] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X57)),X56))
| c_Suc(X57) = X56
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X57),X56)) ),
inference(variable_rename,[status(thm)],[c_0_1633]) ).
fof(c_0_2544,plain,
! [X22,X23,X24] :
( ~ class_HOL_Ominus(X24)
| hAPP(c_HOL_Ominus__class_Ominus(X23,X22,tc_fun(t_a,X24)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(X23,v_x),hAPP(X22,v_x),X24) ),
inference(variable_rename,[status(thm)],[c_0_1634]) ).
fof(c_0_2545,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Olinorder(X15)
| hAPP(c_Finite__Set_Olinorder__class_OMin(X15),hAPP(hAPP(c_Set_Oinsert(X15),X13),X14)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X15),X13),hAPP(c_Finite__Set_Olinorder__class_OMin(X15),X14))
| X14 = c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool))
| ~ c_Finite__Set_Ofinite(X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_1635]) ).
fof(c_0_2546,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Olinorder(X15)
| hAPP(c_Finite__Set_Olinorder__class_OMax(X15),hAPP(hAPP(c_Set_Oinsert(X15),X13),X14)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X15),X13),hAPP(c_Finite__Set_Olinorder__class_OMax(X15),X14))
| X14 = c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool))
| ~ c_Finite__Set_Ofinite(X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_1636]) ).
fof(c_0_2547,plain,
! [X80,X81,X82] :
( X80 = hAPP(c_Option_Ooption_OSome(X82),X81)
| ~ hBOOL(hAPP(hAPP(c_in(X82),X81),c_Option_Oset(X80,X82))) ),
inference(variable_rename,[status(thm)],[c_0_1637]) ).
fof(c_0_2548,plain,
! [X39,X40,X41,X42,X43] :
( hAPP(X41,X40) != hAPP(c_Option_Ooption_OSome(X43),X39)
| hAPP(hAPP(c_Set_Oinsert(X42),X40),c_Map_Odom(X41,X42,X43)) = c_Map_Odom(X41,X42,X43) ),
inference(variable_rename,[status(thm)],[c_0_1638]) ).
fof(c_0_2549,plain,
! [X56,X57] :
( X57 = X56
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X57),X56))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X57),c_Suc(X56))) ),
inference(variable_rename,[status(thm)],[c_0_1639]) ).
fof(c_0_2550,plain,
! [X56,X57] :
( X57 = X56
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X56),c_Suc(X57)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X56),X57)) ),
inference(variable_rename,[status(thm)],[c_0_1640]) ).
fof(c_0_2551,plain,
! [X56,X57] :
( X56 = X57
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X56),c_Suc(X57)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X56),X57)) ),
inference(variable_rename,[status(thm)],[c_0_1641]) ).
fof(c_0_2552,plain,
! [X38,X39,X40,X41,X42] :
( hAPP(hAPP(X38,X41),hAPP(hAPP(X38,X40),X39)) = hAPP(hAPP(X38,X40),hAPP(hAPP(X38,X41),X39))
| ~ c_OrderedGroup_Oab__semigroup__mult(X38,X42) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1642])])]) ).
fof(c_0_2553,plain,
! [X20,X21,X22] :
( ~ class_Orderings_Oorder(X22)
| c_SetInterval_Oord__class_OatLeastAtMost(X21,X20,X22) = c_Orderings_Obot__class_Obot(tc_fun(X22,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X22),X20),X21)) ),
inference(variable_rename,[status(thm)],[c_0_1643]) ).
fof(c_0_2554,plain,
! [X56,X57] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X57),c_Suc(X56)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X57),X56)) ),
inference(variable_rename,[status(thm)],[c_0_1644]) ).
fof(c_0_2555,plain,
! [X38,X39,X40,X41,X42] :
( hAPP(hAPP(c_Set_Oinsert(X41),X39),X38) != c_Orderings_Obot__class_Obot(tc_fun(X41,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X41),X39),X38))
| ~ c_OrderedGroup_Oab__semigroup__mult(X40,X42) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1645])])]) ).
fof(c_0_2556,plain,
! [X51,X52,X53,X54,X55] :
( X52 = X51
| hBOOL(hAPP(hAPP(X54,X51),X52))
| hBOOL(hAPP(hAPP(X54,X52),X51))
| ~ c_Orderings_Olinorder(X53,X54,X55) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1646])])]) ).
fof(c_0_2557,plain,
! [X51,X52,X53,X54,X55] :
( hBOOL(hAPP(hAPP(X54,X51),X52))
| hBOOL(hAPP(hAPP(X54,X52),X51))
| X52 = X51
| ~ c_Orderings_Olinorder(X53,X54,X55) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1647])])]) ).
fof(c_0_2558,plain,
! [X51,X52,X53,X54,X55] :
( hBOOL(hAPP(hAPP(X54,X51),X52))
| X52 = X51
| hBOOL(hAPP(hAPP(X54,X52),X51))
| ~ c_Orderings_Olinorder(X53,X54,X55) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1648])])]) ).
fof(c_0_2559,plain,
! [X51,X52,X53,X54,X55] :
( X52 = X51
| hBOOL(hAPP(hAPP(X54,X52),X51))
| hBOOL(hAPP(hAPP(X54,X51),X52))
| ~ c_Orderings_Olinorder(X53,X54,X55) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1649])])]) ).
fof(c_0_2560,plain,
! [X51,X52,X53,X54,X55] :
( hBOOL(hAPP(hAPP(X53,X51),X52))
| hBOOL(hAPP(hAPP(X54,X52),X51))
| ~ c_Orderings_Olinorder(X53,X54,X55) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1650])])]) ).
fof(c_0_2561,plain,
! [X51,X52,X53,X54,X55] :
( hBOOL(hAPP(hAPP(X53,X51),X52))
| hBOOL(hAPP(hAPP(X53,X52),X51))
| ~ c_Orderings_Olinorder(X53,X54,X55) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1651])])]) ).
fof(c_0_2562,plain,
! [X51,X52,X53,X54,X55] :
( hBOOL(hAPP(hAPP(X54,X51),X52))
| hBOOL(hAPP(hAPP(X53,X52),X51))
| ~ c_Orderings_Olinorder(X53,X54,X55) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1652])])]) ).
fof(c_0_2563,plain,
! [X51,X52,X53,X54,X55] :
( hBOOL(hAPP(hAPP(X54,X52),X51))
| hBOOL(hAPP(hAPP(X53,X51),X52))
| ~ c_Orderings_Olinorder(X53,X54,X55) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1653])])]) ).
fof(c_0_2564,plain,
! [X51,X52,X53,X54] :
( hBOOL(hAPP(hAPP(X53,X51),X51))
| ~ c_Orderings_Olinorder(X52,X53,X54)
| hBOOL(hAPP(hAPP(X52,X51),X51)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1654])])]) ).
fof(c_0_2565,plain,
! [X9,X10] :
( ~ class_Orderings_Olinorder(X10)
| hAPP(c_Finite__Set_Olinorder__class_OMin(X10),hAPP(hAPP(c_Set_Oinsert(X10),X9),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)))) = X9 ),
inference(variable_rename,[status(thm)],[c_0_1655]) ).
fof(c_0_2566,plain,
! [X9,X10] :
( ~ class_Orderings_Olinorder(X10)
| hAPP(c_Finite__Set_Olinorder__class_OMax(X10),hAPP(hAPP(c_Set_Oinsert(X10),X9),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)))) = X9 ),
inference(variable_rename,[status(thm)],[c_0_1656]) ).
fof(c_0_2567,plain,
! [X18,X19,X20] :
( hAPP(hAPP(c_Set_Oinsert(X20),X19),X18) != c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X20),X19),X18)) ),
inference(variable_rename,[status(thm)],[c_0_1657]) ).
fof(c_0_2568,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X17),X16),X15) = X15
| ~ hBOOL(hAPP(hAPP(c_lessequals(X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1658]) ).
fof(c_0_2569,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X17),X16),X15) = X16
| ~ hBOOL(hAPP(hAPP(c_lessequals(X17),X15),X16)) ),
inference(variable_rename,[status(thm)],[c_0_1659]) ).
fof(c_0_2570,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X17),X16),X15) = X16
| ~ hBOOL(hAPP(hAPP(c_lessequals(X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1660]) ).
fof(c_0_2571,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X17),X16),X15) = X15
| ~ hBOOL(hAPP(hAPP(c_lessequals(X17),X15),X16)) ),
inference(variable_rename,[status(thm)],[c_0_1661]) ).
fof(c_0_2572,plain,
! [X15,X16,X17] :
( ~ class_Lattices_Oupper__semilattice(X17)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X17),X16),X15) = X16
| ~ hBOOL(hAPP(hAPP(c_lessequals(X17),X15),X16)) ),
inference(variable_rename,[status(thm)],[c_0_1662]) ).
fof(c_0_2573,plain,
! [X15,X16,X17] :
( ~ class_Lattices_Oupper__semilattice(X17)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X17),X16),X15) = X15
| ~ hBOOL(hAPP(hAPP(c_lessequals(X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1663]) ).
fof(c_0_2574,plain,
! [X15,X16,X17] :
( ~ class_Lattices_Olower__semilattice(X17)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X17),X16),X15) = X16
| ~ hBOOL(hAPP(hAPP(c_lessequals(X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1664]) ).
fof(c_0_2575,plain,
! [X15,X16,X17] :
( ~ class_Lattices_Olower__semilattice(X17)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X17),X16),X15) = X15
| ~ hBOOL(hAPP(hAPP(c_lessequals(X17),X15),X16)) ),
inference(variable_rename,[status(thm)],[c_0_1665]) ).
fof(c_0_2576,plain,
! [X9,X10] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X10)
| c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X10),X9),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool))),X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_1666]) ).
fof(c_0_2577,plain,
! [X9,X10] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X10)
| c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X10),X9),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool))),X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_1667]) ).
fof(c_0_2578,plain,
! [X32,X33,X34,X35] :
( c_Hoare__Mirabelle_Ohoare__derivs(X34,X32,X35)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X34,X33,X35)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X33,X32,X35) ),
inference(variable_rename,[status(thm)],[c_0_1668]) ).
fof(c_0_2579,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oordered__idom(X17)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X17),X15),X16))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X17),X16),X15))
| X16 = X15 ),
inference(variable_rename,[status(thm)],[c_0_1669]) ).
fof(c_0_2580,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| X16 = X15
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X17),X15),X16))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1670]) ).
fof(c_0_2581,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X17),X15),X16))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X17),X16),X15))
| X16 = X15 ),
inference(variable_rename,[status(thm)],[c_0_1671]) ).
fof(c_0_2582,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X17),X15),X16))
| X16 = X15
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1672]) ).
fof(c_0_2583,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| X16 = X15
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X17),X16),X15))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X17),X15),X16)) ),
inference(variable_rename,[status(thm)],[c_0_1673]) ).
fof(c_0_2584,plain,
! [X10,X11,X12] :
( hAPP(hAPP(c_Set_Oinsert(X12),X10),X11) = X11
| ~ hBOOL(hAPP(hAPP(c_in(X12),X10),X11)) ),
inference(variable_rename,[status(thm)],[c_0_1674]) ).
fof(c_0_2585,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X17),X16),X15))
| hBOOL(hAPP(hAPP(c_lessequals(X17),X15),X16)) ),
inference(variable_rename,[status(thm)],[c_0_1675]) ).
fof(c_0_2586,plain,
! [X13,X14] :
( ~ class_Orderings_Olinorder(X14)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X14),X13),X13))
| hBOOL(hAPP(hAPP(c_lessequals(X14),X13),X13)) ),
inference(variable_rename,[status(thm)],[c_0_1676]) ).
fof(c_0_2587,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| hBOOL(hAPP(hAPP(c_lessequals(X17),X15),X16))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1677]) ).
fof(c_0_2588,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X17),X15),X16))
| hBOOL(hAPP(hAPP(c_lessequals(X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1678]) ).
fof(c_0_2589,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| hBOOL(hAPP(hAPP(c_lessequals(X17),X15),X16))
| hBOOL(hAPP(hAPP(c_lessequals(X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1679]) ).
fof(c_0_2590,plain,
! [X51,X52,X53,X54] :
( ~ hBOOL(hAPP(hAPP(X53,X51),X51))
| ~ c_Orderings_Olinorder(X52,X53,X54) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1680])])]) ).
fof(c_0_2591,plain,
! [X51,X52,X53,X54] :
( ~ c_Orderings_Olinorder(X52,X53,X54)
| ~ hBOOL(hAPP(hAPP(X53,X51),X51)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1681])])]) ).
fof(c_0_2592,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X17),X16),hAPP(hAPP(c_Orderings_Oord__class_Omin(X17),X16),X15)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X17),X16),X15) ),
inference(variable_rename,[status(thm)],[c_0_1682]) ).
fof(c_0_2593,plain,
! [X15,X16,X17] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X17)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X16),X15)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X16),X15) ),
inference(variable_rename,[status(thm)],[c_0_1683]) ).
fof(c_0_2594,plain,
! [X15,X16,X17] :
( ~ class_Lattices_Olattice(X17)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X17),X16),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X17),X16),X15)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X17),X16),X15) ),
inference(variable_rename,[status(thm)],[c_0_1684]) ).
fof(c_0_2595,plain,
! [X15,X16,X17] :
( ~ class_Lattices_Olower__semilattice(X17)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X17),X16),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X17),X16),X15)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X17),X16),X15) ),
inference(variable_rename,[status(thm)],[c_0_1685]) ).
fof(c_0_2596,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X17),X16),hAPP(hAPP(c_Orderings_Oord__class_Omax(X17),X16),X15)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X17),X16),X15) ),
inference(variable_rename,[status(thm)],[c_0_1686]) ).
fof(c_0_2597,plain,
! [X15,X16,X17] :
( ~ class_Lattices_Olattice(X17)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X17),X16),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X17),X16),X15)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X17),X16),X15) ),
inference(variable_rename,[status(thm)],[c_0_1687]) ).
fof(c_0_2598,plain,
! [X15,X16,X17] :
( ~ class_Lattices_Oupper__semilattice(X17)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X17),X16),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X17),X16),X15)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X17),X16),X15) ),
inference(variable_rename,[status(thm)],[c_0_1688]) ).
fof(c_0_2599,plain,
! [X14,X15,X16] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X15,X14,tc_fun(X16,tc_bool)),X16)
| ~ c_Finite__Set_Ofinite(X15,X16)
| ~ c_Finite__Set_Ofinite(X14,X16) ),
inference(variable_rename,[status(thm)],[c_0_1689]) ).
fof(c_0_2600,plain,
! [X10,X11,X12] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X12)
| c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X12),X10),X11),X12) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X12),X10),c_Complete__Lattice_OSup__class_OSup(X11,X12)) ),
inference(variable_rename,[status(thm)],[c_0_1690]) ).
fof(c_0_2601,plain,
! [X10,X11,X12] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X12)
| c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X12),X10),X11),X12) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X12),X10),c_Complete__Lattice_OInf__class_OInf(X11,X12)) ),
inference(variable_rename,[status(thm)],[c_0_1691]) ).
fof(c_0_2602,plain,
! [X13] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X13),X13))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X13),c_Suc(X13))) ),
inference(variable_rename,[status(thm)],[c_0_1692]) ).
fof(c_0_2603,plain,
! [X56,X57] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X56),c_Suc(X57)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X57),X56)) ),
inference(variable_rename,[status(thm)],[c_0_1693]) ).
fof(c_0_2604,plain,
! [X21,X22,X23] :
( hBOOL(hAPP(X22,X21))
| ~ hBOOL(hAPP(hAPP(c_in(X23),X21),X22)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1694])])]) ).
fof(c_0_2605,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X17),X16),X15) != X15
| hBOOL(hAPP(hAPP(c_lessequals(X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1695]) ).
fof(c_0_2606,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X17),X16),X15) != X16
| hBOOL(hAPP(hAPP(c_lessequals(X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1696]) ).
fof(c_0_2607,plain,
! [X15,X16,X17] :
( ~ class_Lattices_Oupper__semilattice(X17)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X17),X16),X15) != X15
| hBOOL(hAPP(hAPP(c_lessequals(X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1697]) ).
fof(c_0_2608,plain,
! [X15,X16,X17] :
( ~ class_Lattices_Olower__semilattice(X17)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X17),X16),X15) != X16
| hBOOL(hAPP(hAPP(c_lessequals(X17),X16),X15)) ),
inference(variable_rename,[status(thm)],[c_0_1698]) ).
fof(c_0_2609,plain,
! [X10,X11,X12] :
( c_Finite__Set_Ofinite(X11,X12)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X12),X10),X11),X12) ),
inference(variable_rename,[status(thm)],[c_0_1699]) ).
fof(c_0_2610,plain,
! [X39,X40,X41] :
( c_Map_Odom(X39,X41,X40) != c_Orderings_Obot__class_Obot(tc_fun(X41,tc_bool))
| X39 = c_COMBK(c_Option_Ooption_ONone(X40),tc_Option_Ooption(X40),X41) ),
inference(variable_rename,[status(thm)],[c_0_1700]) ).
fof(c_0_2611,plain,
! [X20,X21,X22] :
( ~ class_Orderings_Oorder(X22)
| c_Orderings_Obot__class_Obot(tc_fun(X22,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X21,X20,X22)
| hBOOL(hAPP(hAPP(c_lessequals(X22),X21),X20)) ),
inference(variable_rename,[status(thm)],[c_0_1701]) ).
fof(c_0_2612,plain,
! [X20,X21,X22] :
( ~ class_Orderings_Oorder(X22)
| c_SetInterval_Oord__class_OatLeastAtMost(X21,X20,X22) = c_Orderings_Obot__class_Obot(tc_fun(X22,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X22),X21),X20)) ),
inference(variable_rename,[status(thm)],[c_0_1702]) ).
fof(c_0_2613,plain,
! [X56,X57] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X56),X57))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X57),X56))
| X57 = X56 ),
inference(variable_rename,[status(thm)],[c_0_1703]) ).
fof(c_0_2614,plain,
! [X15,X16] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X15),X16))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X16),X15))
| X16 = X15 ),
inference(variable_rename,[status(thm)],[c_0_1704]) ).
fof(c_0_2615,plain,
! [X14,X15,X16] :
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X15,X14,tc_fun(X16,tc_bool)),X16)
| ~ c_Finite__Set_Ofinite(X15,X16) ),
inference(variable_rename,[status(thm)],[c_0_1705]) ).
fof(c_0_2616,plain,
! [X71,X72,X73,X74] :
( ~ class_Ring__and__Field_Oidom(X74)
| ~ class_Int_Onumber__ring(X74)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X74),X73),X72) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X74),X73),X71)
| X72 = X71 ),
inference(variable_rename,[status(thm)],[c_0_1706]) ).
fof(c_0_2617,plain,
! [X70,X71,X72,X73] :
( ~ class_OrderedGroup_Oab__group__add(X73)
| c_HOL_Ominus__class_Ominus(X72,X72,X73) != c_HOL_Ominus__class_Ominus(X71,X70,X73)
| X71 = X70 ),
inference(variable_rename,[status(thm)],[c_0_1707]) ).
fof(c_0_2618,plain,
! [X18,X19,X20,X21] :
( ~ class_OrderedGroup_Oab__group__add(X21)
| c_HOL_Ominus__class_Ominus(X19,X18,X21) != c_HOL_Ominus__class_Ominus(X20,X20,X21)
| X19 = X18 ),
inference(variable_rename,[status(thm)],[c_0_1708]) ).
fof(c_0_2619,plain,
! [X38,X39,X40,X41] :
( hAPP(hAPP(X40,X39),hAPP(hAPP(X40,X39),X38)) = hAPP(hAPP(X40,X39),X38)
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X40,X41) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1709])])]) ).
fof(c_0_2620,plain,
! [X13,X14] :
( ~ class_Orderings_Oorder(X14)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X14),X13),X13)) ),
inference(variable_rename,[status(thm)],[c_0_1710]) ).
fof(c_0_2621,plain,
! [X13,X14] :
( ~ class_Orderings_Olinorder(X14)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X14),X13),X13)) ),
inference(variable_rename,[status(thm)],[c_0_1711]) ).
fof(c_0_2622,plain,
! [X13,X14] :
( ~ class_Orderings_Opreorder(X14)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X14),X13),X13)) ),
inference(variable_rename,[status(thm)],[c_0_1712]) ).
fof(c_0_2623,plain,
! [X24,X25,X26,X27] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X27)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X25) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X24)
| X25 = X24 ),
inference(variable_rename,[status(thm)],[c_0_1713]) ).
fof(c_0_2624,plain,
! [X24,X25,X26,X27] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X27)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X25) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X26),X24)
| X25 = X24 ),
inference(variable_rename,[status(thm)],[c_0_1714]) ).
fof(c_0_2625,plain,
! [X24,X25,X26,X27] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X27)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X25),X26) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X27),X24),X26)
| X25 = X24 ),
inference(variable_rename,[status(thm)],[c_0_1715]) ).
fof(c_0_2626,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_1716])])]) ).
fof(c_0_2627,plain,
! [X9,X10] :
( ~ class_Orderings_Oorder(X10)
| c_SetInterval_Oord__class_OatLeastAtMost(X9,X9,X10) = hAPP(hAPP(c_Set_Oinsert(X10),X9),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool))) ),
inference(variable_rename,[status(thm)],[c_0_1717]) ).
fof(c_0_2628,plain,
! [X20,X21,X22] :
( ~ class_OrderedGroup_Ogroup__add(X22)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X21),X20),X20,X22) = X21 ),
inference(variable_rename,[status(thm)],[c_0_1718]) ).
fof(c_0_2629,plain,
! [X15,X16,X17] :
( ~ class_Lattices_Olattice(X17)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X17),X16),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X17),X16),X15)) = X16 ),
inference(variable_rename,[status(thm)],[c_0_1719]) ).
fof(c_0_2630,plain,
! [X15,X16,X17] :
( ~ class_Lattices_Olattice(X17)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X17),X16),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X17),X16),X15)) = X16 ),
inference(variable_rename,[status(thm)],[c_0_1720]) ).
fof(c_0_2631,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X17),X16),hAPP(hAPP(c_Orderings_Oord__class_Omax(X17),X16),X15)) = X16 ),
inference(variable_rename,[status(thm)],[c_0_1721]) ).
fof(c_0_2632,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X17),X16),hAPP(hAPP(c_Orderings_Oord__class_Omin(X17),X16),X15)) = X16 ),
inference(variable_rename,[status(thm)],[c_0_1722]) ).
fof(c_0_2633,plain,
! [X21,X22,X23] :
( hBOOL(hAPP(hAPP(c_in(X23),X21),X22))
| ~ hBOOL(hAPP(X22,X21)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1723])])]) ).
fof(c_0_2634,plain,
! [X8,X9] :
( X8 = X9
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X9),X8)) ),
inference(variable_rename,[status(thm)],[c_0_1724]) ).
fof(c_0_2635,plain,
! [X17,X18,X19] :
( c_Hoare__Mirabelle_Ohoare__valids(X18,X17,X19)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X18,X17,X19) ),
inference(variable_rename,[status(thm)],[c_0_1725]) ).
fof(c_0_2636,plain,
! [X10,X11,X12] :
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X12),X10),X11),X12)
| ~ c_Finite__Set_Ofinite(X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1726]) ).
fof(c_0_2637,plain,
! [X13,X14] :
( ~ class_Orderings_Obot(X14)
| hBOOL(hAPP(hAPP(c_lessequals(X14),c_Orderings_Obot__class_Obot(X14)),X13)) ),
inference(variable_rename,[status(thm)],[c_0_1727]) ).
fof(c_0_2638,plain,
! [X13,X14] :
( ~ class_Orderings_Oorder(X14)
| hBOOL(hAPP(hAPP(c_lessequals(X14),X13),X13)) ),
inference(variable_rename,[status(thm)],[c_0_1728]) ).
fof(c_0_2639,plain,
! [X13,X14] :
( ~ class_Orderings_Opreorder(X14)
| hBOOL(hAPP(hAPP(c_lessequals(X14),X13),X13)) ),
inference(variable_rename,[status(thm)],[c_0_1729]) ).
fof(c_0_2640,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X17)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),X16),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X17),X15),X16) ),
inference(variable_rename,[status(thm)],[c_0_1730]) ).
fof(c_0_2641,plain,
! [X20,X21,X22] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X22)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X21),X20) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X22),X20),X21) ),
inference(variable_rename,[status(thm)],[c_0_1731]) ).
fof(c_0_2642,plain,
! [X24,X25,X26] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X26)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X26),X25),X24) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X26),X24),X25) ),
inference(variable_rename,[status(thm)],[c_0_1732]) ).
fof(c_0_2643,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X17)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X16),X15) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X17),X15),X16) ),
inference(variable_rename,[status(thm)],[c_0_1733]) ).
fof(c_0_2644,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X22)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X21),X20) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X20),X21) ),
inference(variable_rename,[status(thm)],[c_0_1734]) ).
fof(c_0_2645,plain,
! [X15,X16,X17] :
( ~ class_Lattices_Olower__semilattice(X17)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X17),X16),X15) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X17),X15),X16) ),
inference(variable_rename,[status(thm)],[c_0_1735]) ).
fof(c_0_2646,plain,
! [X15,X16,X17] :
( ~ class_Lattices_Olattice(X17)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X17),X16),X15) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X17),X15),X16) ),
inference(variable_rename,[status(thm)],[c_0_1736]) ).
fof(c_0_2647,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X17),X16),X15) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X17),X15),X16) ),
inference(variable_rename,[status(thm)],[c_0_1737]) ).
fof(c_0_2648,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X17),X16),X15) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X17),X15),X16) ),
inference(variable_rename,[status(thm)],[c_0_1738]) ).
fof(c_0_2649,plain,
! [X15,X16,X17] :
( ~ class_Lattices_Olattice(X17)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X17),X16),X15) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X17),X15),X16) ),
inference(variable_rename,[status(thm)],[c_0_1739]) ).
fof(c_0_2650,plain,
! [X15,X16,X17] :
( ~ class_Lattices_Oupper__semilattice(X17)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X17),X16),X15) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X17),X15),X16) ),
inference(variable_rename,[status(thm)],[c_0_1740]) ).
fof(c_0_2651,plain,
! [X15,X16,X17] :
( ~ class_Ring__and__Field_Oidom(X17)
| ~ class_Int_Onumber__ring(X17)
| c_HOL_Ominus__class_Ominus(X16,X15,X17) != c_HOL_Ozero__class_Ozero(X17)
| X16 = X15 ),
inference(variable_rename,[status(thm)],[c_0_1741]) ).
fof(c_0_2652,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X22)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X21),X20) != c_HOL_Ozero__class_Ozero(X22)
| X20 = c_HOL_Ozero__class_Ozero(X22)
| X21 = c_HOL_Ozero__class_Ozero(X22) ),
inference(variable_rename,[status(thm)],[c_0_1742]) ).
fof(c_0_2653,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X22)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X21),X20) != c_HOL_Ozero__class_Ozero(X22)
| X20 = c_HOL_Ozero__class_Ozero(X22)
| X21 = c_HOL_Ozero__class_Ozero(X22) ),
inference(variable_rename,[status(thm)],[c_0_1743]) ).
fof(c_0_2654,plain,
! [X20,X21,X22] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X22)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X22),X21),X20) != c_HOL_Ozero__class_Ozero(X22)
| X21 = c_HOL_Ozero__class_Ozero(X22)
| X20 = c_HOL_Ozero__class_Ozero(X22) ),
inference(variable_rename,[status(thm)],[c_0_1744]) ).
fof(c_0_2655,plain,
! [X13,X14,X15] :
( ~ class_Ring__and__Field_Oidom(X15)
| ~ class_Int_Onumber__ring(X15)
| X13 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X15),X13),X14)
| X14 = c_HOL_Ozero__class_Ozero(X15) ),
inference(variable_rename,[status(thm)],[c_0_1745]) ).
fof(c_0_2656,plain,
! [X38,X39,X40,X41] :
( hAPP(hAPP(X38,X40),X39) = hAPP(hAPP(X38,X39),X40)
| ~ c_OrderedGroup_Oab__semigroup__mult(X38,X41) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1746])])]) ).
fof(c_0_2657,plain,
! [X20,X21,X22] :
( ~ class_OrderedGroup_Ogroup__add(X22)
| c_HOL_Ominus__class_Ominus(X21,X20,X22) != c_HOL_Ozero__class_Ozero(X22)
| X21 = X20 ),
inference(variable_rename,[status(thm)],[c_0_1747]) ).
fof(c_0_2658,plain,
! [X20,X21,X22] :
( ~ class_OrderedGroup_Oab__group__add(X22)
| c_HOL_Ominus__class_Ominus(X21,X20,X22) != c_HOL_Ozero__class_Ozero(X22)
| X21 = X20 ),
inference(variable_rename,[status(thm)],[c_0_1748]) ).
fof(c_0_2659,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X10)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),X9),X9) != c_HOL_Ozero__class_Ozero(X10)
| X9 = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_1749]) ).
fof(c_0_2660,plain,
! [X14,X15,X16] :
( ~ class_Lattices_Obounded__lattice(X16)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X16),X15),X14) != c_Orderings_Obot__class_Obot(X16)
| X14 = c_Orderings_Obot__class_Obot(X16) ),
inference(variable_rename,[status(thm)],[c_0_1750]) ).
fof(c_0_2661,plain,
! [X14,X15,X16] :
( ~ class_Lattices_Obounded__lattice(X16)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X16),X15),X14) != c_Orderings_Obot__class_Obot(X16)
| X15 = c_Orderings_Obot__class_Obot(X16) ),
inference(variable_rename,[status(thm)],[c_0_1751]) ).
fof(c_0_2662,plain,
! [X10,X11] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X11)
| hAPP(c_Finite__Set_Olattice__class_OInf__fin(X11),X10) = c_Complete__Lattice_OInf__class_OInf(X10,X11)
| X10 = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))
| ~ c_Finite__Set_Ofinite(X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1752]) ).
fof(c_0_2663,plain,
! [X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_HOL_Ozero__class_Ozero(X4)),c_HOL_Ozero__class_Ozero(X4)) = c_HOL_Ozero__class_Ozero(X4) ),
inference(variable_rename,[status(thm)],[c_0_1753]) ).
fof(c_0_2664,plain,
! [X38,X39] :
( c_Finite__Set_Ofun__left__comm(X38,X39,X39)
| ~ c_OrderedGroup_Oab__semigroup__mult(X38,X39) ),
inference(variable_rename,[status(thm)],[c_0_1754]) ).
fof(c_0_2665,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_1755]) ).
fof(c_0_2666,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X10)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X10),c_HOL_Ozero__class_Ozero(X10)),X9) = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_1756]) ).
fof(c_0_2667,plain,
! [X20,X21] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X21)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X21),c_HOL_Ozero__class_Ozero(X21)),X20) = c_HOL_Ozero__class_Ozero(X21) ),
inference(variable_rename,[status(thm)],[c_0_1757]) ).
fof(c_0_2668,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Omult__zero(X10)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X10),c_HOL_Ozero__class_Ozero(X10)),X9) = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_1758]) ).
fof(c_0_2669,plain,
! [X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X14)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X14),c_HOL_Ozero__class_Ozero(X14)),X13) = c_HOL_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[c_0_1759]) ).
fof(c_0_2670,plain,
! [X13,X14] :
( ~ class_Lattices_Obounded__lattice(X14)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X14),c_Orderings_Obot__class_Obot(X14)),X13) = c_Orderings_Obot__class_Obot(X14) ),
inference(variable_rename,[status(thm)],[c_0_1760]) ).
fof(c_0_2671,plain,
! [X22] :
( ~ class_Orderings_Obot(X22)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X22)),v_x) = c_Orderings_Obot__class_Obot(X22) ),
inference(variable_rename,[status(thm)],[c_0_1761]) ).
fof(c_0_2672,plain,
! [X13,X14] :
( ~ class_Ring__and__Field_Oidom(X14)
| ~ class_Int_Onumber__ring(X14)
| X13 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),X13),c_HOL_Ozero__class_Ozero(X14)) ),
inference(variable_rename,[status(thm)],[c_0_1762]) ).
fof(c_0_2673,plain,
! [X13,X14] :
( ~ class_Ring__and__Field_Oidom(X14)
| ~ class_Int_Onumber__ring(X14)
| c_HOL_Ominus__class_Ominus(X13,X13,X14) = c_HOL_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[c_0_1763]) ).
fof(c_0_2674,plain,
! [X13,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X14)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X14),c_HOL_Ozero__class_Ozero(X14)),X13) = X13 ),
inference(variable_rename,[status(thm)],[c_0_1764]) ).
fof(c_0_2675,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X10)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),c_HOL_Ozero__class_Ozero(X10)),X9) = X9 ),
inference(variable_rename,[status(thm)],[c_0_1765]) ).
fof(c_0_2676,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Omonoid__add(X10)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),c_HOL_Ozero__class_Ozero(X10)),X9) = X9 ),
inference(variable_rename,[status(thm)],[c_0_1766]) ).
fof(c_0_2677,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X10)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),c_HOL_Ozero__class_Ozero(X10)),X9) = X9 ),
inference(variable_rename,[status(thm)],[c_0_1767]) ).
fof(c_0_2678,plain,
! [X13,X14] :
( ~ class_Lattices_Obounded__lattice(X14)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X14),c_Orderings_Obot__class_Obot(X14)),X13) = X13 ),
inference(variable_rename,[status(thm)],[c_0_1768]) ).
fof(c_0_2679,plain,
! [X80,X81] :
( c_Option_Oset(X80,X81) != c_Orderings_Obot__class_Obot(tc_fun(X81,tc_bool))
| X80 = c_Option_Ooption_ONone(X81) ),
inference(variable_rename,[status(thm)],[c_0_1769]) ).
fof(c_0_2680,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X10)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X10),X9),c_HOL_Ozero__class_Ozero(X10)) = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_1770]) ).
fof(c_0_2681,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X10)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X10),X9),c_HOL_Ozero__class_Ozero(X10)) = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_1771]) ).
fof(c_0_2682,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Omult__zero(X10)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X10),X9),c_HOL_Ozero__class_Ozero(X10)) = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_1772]) ).
fof(c_0_2683,plain,
! [X13,X14] :
( ~ class_Lattices_Obounded__lattice(X14)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X14),X13),c_Orderings_Obot__class_Obot(X14)) = c_Orderings_Obot__class_Obot(X14) ),
inference(variable_rename,[status(thm)],[c_0_1773]) ).
fof(c_0_2684,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Ogroup__add(X10)
| c_HOL_Ominus__class_Ominus(X9,c_HOL_Ozero__class_Ozero(X10),X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_1774]) ).
fof(c_0_2685,plain,
! [X4] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X4)
| c_Finite__Set_Ofun__left__comm(c_HOL_Otimes__class_Otimes(X4),X4,X4) ),
inference(variable_rename,[status(thm)],[c_0_1775]) ).
fof(c_0_2686,plain,
! [X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_Finite__Set_Ofun__left__comm(c_HOL_Oplus__class_Oplus(X4),X4,X4) ),
inference(variable_rename,[status(thm)],[c_0_1776]) ).
fof(c_0_2687,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X10)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),X9),c_HOL_Ozero__class_Ozero(X10)) = X9 ),
inference(variable_rename,[status(thm)],[c_0_1777]) ).
fof(c_0_2688,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Omonoid__add(X10)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),X9),c_HOL_Ozero__class_Ozero(X10)) = X9 ),
inference(variable_rename,[status(thm)],[c_0_1778]) ).
fof(c_0_2689,plain,
! [X9,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X10)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),X9),c_HOL_Ozero__class_Ozero(X10)) = X9 ),
inference(variable_rename,[status(thm)],[c_0_1779]) ).
fof(c_0_2690,plain,
! [X13,X14] :
( ~ class_Lattices_Obounded__lattice(X14)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X14),X13),c_Orderings_Obot__class_Obot(X14)) = X13 ),
inference(variable_rename,[status(thm)],[c_0_1780]) ).
fof(c_0_2691,plain,
! [X9,X10] :
( ~ class_OrderedGroup_Ogroup__add(X10)
| c_HOL_Ominus__class_Ominus(X9,X9,X10) = c_HOL_Ozero__class_Ozero(X10) ),
inference(variable_rename,[status(thm)],[c_0_1781]) ).
fof(c_0_2692,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Ogroup__add(X14)
| c_HOL_Ominus__class_Ominus(X13,X13,X14) = c_HOL_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[c_0_1782]) ).
fof(c_0_2693,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Oab__group__add(X14)
| c_HOL_Ominus__class_Ominus(X13,X13,X14) = c_HOL_Ozero__class_Ozero(X14) ),
inference(variable_rename,[status(thm)],[c_0_1783]) ).
fof(c_0_2694,plain,
! [X60,X61,X62] :
( hAPP(c_Option_Ooption_OSome(X62),X61) != hAPP(c_Option_Ooption_OSome(X62),X60)
| X61 = X60 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1784])])]) ).
fof(c_0_2695,plain,
! [X38,X39,X40] :
( hAPP(hAPP(X39,X38),X38) = X38
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X39,X40) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1785])])]) ).
fof(c_0_2696,plain,
! [X13,X14] :
( ~ class_Orderings_Olinorder(X14)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X14),X13),X13) = X13 ),
inference(variable_rename,[status(thm)],[c_0_1786]) ).
fof(c_0_2697,plain,
! [X13,X14] :
( ~ class_Orderings_Olinorder(X14)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X14),X13),X13) = X13 ),
inference(variable_rename,[status(thm)],[c_0_1787]) ).
fof(c_0_2698,plain,
! [X13,X14] :
( ~ class_Lattices_Olower__semilattice(X14)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X14),X13),X13) = X13 ),
inference(variable_rename,[status(thm)],[c_0_1788]) ).
fof(c_0_2699,plain,
! [X13,X14] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X14)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X14),X13),X13) = X13 ),
inference(variable_rename,[status(thm)],[c_0_1789]) ).
fof(c_0_2700,plain,
! [X13,X14] :
( ~ class_Lattices_Oupper__semilattice(X14)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X14),X13),X13) = X13 ),
inference(variable_rename,[status(thm)],[c_0_1790]) ).
fof(c_0_2701,plain,
! [X15,X16,X17] :
( ~ class_Orderings_Olinorder(X17)
| c_SetInterval_Oord__class_OlessThan(X16,X17) != c_SetInterval_Oord__class_OlessThan(X15,X17)
| X16 = X15 ),
inference(variable_rename,[status(thm)],[c_0_1791]) ).
fof(c_0_2702,plain,
! [X68,X69,X70,X71] :
( c_Com_Ocom_OSemi(X71,X69) != c_Com_Ocom_OSemi(X70,X68)
| X69 = X68 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1792])])]) ).
fof(c_0_2703,plain,
! [X68,X69,X70,X71] :
( c_Com_Ocom_OSemi(X71,X69) != c_Com_Ocom_OSemi(X70,X68)
| X71 = X70 ),
inference(variable_rename,[status(thm)],[c_0_1793]) ).
fof(c_0_2704,plain,
! [X6,X7] :
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X6,X7))
| ~ class_Finite__Set_Ofinite_Ofinite(X7)
| ~ class_Finite__Set_Ofinite_Ofinite(X6) ),
inference(variable_rename,[status(thm)],[c_0_1794]) ).
fof(c_0_2705,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_1795]) ).
fof(c_0_2706,plain,
! [X6,X7] :
( class_Lattices_Oupper__semilattice(tc_fun(X6,X7))
| ~ class_Lattices_Olattice(X7) ),
inference(variable_rename,[status(thm)],[c_0_1796]) ).
fof(c_0_2707,plain,
! [X6,X7] :
( class_Lattices_Olower__semilattice(tc_fun(X6,X7))
| ~ class_Lattices_Olattice(X7) ),
inference(variable_rename,[status(thm)],[c_0_1797]) ).
fof(c_0_2708,plain,
! [X6,X7] :
( class_Lattices_Odistrib__lattice(tc_fun(X6,X7))
| ~ class_Lattices_Odistrib__lattice(X7) ),
inference(variable_rename,[status(thm)],[c_0_1798]) ).
fof(c_0_2709,plain,
! [X6,X7] :
( class_Lattices_Obounded__lattice(tc_fun(X6,X7))
| ~ class_Lattices_Obounded__lattice(X7) ),
inference(variable_rename,[status(thm)],[c_0_1799]) ).
fof(c_0_2710,plain,
! [X6,X7] :
( class_Orderings_Opreorder(tc_fun(X6,X7))
| ~ class_Orderings_Opreorder(X7) ),
inference(variable_rename,[status(thm)],[c_0_1800]) ).
fof(c_0_2711,plain,
! [X6,X7] :
( class_Lattices_Olattice(tc_fun(X6,X7))
| ~ class_Lattices_Olattice(X7) ),
inference(variable_rename,[status(thm)],[c_0_1801]) ).
fof(c_0_2712,plain,
! [X6,X7] :
( class_Orderings_Oorder(tc_fun(X6,X7))
| ~ class_Orderings_Oorder(X7) ),
inference(variable_rename,[status(thm)],[c_0_1802]) ).
fof(c_0_2713,plain,
! [X6,X7] :
( class_Orderings_Obot(tc_fun(X6,X7))
| ~ class_Orderings_Obot(X7) ),
inference(variable_rename,[status(thm)],[c_0_1803]) ).
fof(c_0_2714,plain,
! [X6,X7] :
( class_HOL_Ominus(tc_fun(X6,X7))
| ~ class_HOL_Ominus(X7) ),
inference(variable_rename,[status(thm)],[c_0_1804]) ).
fof(c_0_2715,plain,
! [X6,X7] :
( class_HOL_Oord(tc_fun(X6,X7))
| ~ class_HOL_Oord(X7) ),
inference(variable_rename,[status(thm)],[c_0_1805]) ).
fof(c_0_2716,plain,
! [X4] :
( ~ class_Lattices_Olattice(X4)
| c_Finite__Set_Olattice__class_OInf__fin(X4) = c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X4),X4) ),
inference(variable_rename,[status(thm)],[c_0_1806]) ).
fof(c_0_2717,plain,
! [X4] :
( ~ class_Orderings_Olinorder(X4)
| c_Finite__Set_Olinorder__class_OMax(X4) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(X4),X4) ),
inference(variable_rename,[status(thm)],[c_0_1807]) ).
fof(c_0_2718,plain,
! [X4] :
( ~ class_Orderings_Olinorder(X4)
| c_Finite__Set_Olinorder__class_OMin(X4) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X4),X4) ),
inference(variable_rename,[status(thm)],[c_0_1808]) ).
fof(c_0_2719,plain,
! [X4] :
( ~ class_Orderings_Olinorder(X4)
| c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omin(X4),X4) ),
inference(variable_rename,[status(thm)],[c_0_1809]) ).
fof(c_0_2720,plain,
! [X4] :
( ~ class_Orderings_Olinorder(X4)
| c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omax(X4),X4) ),
inference(variable_rename,[status(thm)],[c_0_1810]) ).
fof(c_0_2721,plain,
! [X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Oupper__semilattice__class_Osup(X4),X4) ),
inference(variable_rename,[status(thm)],[c_0_1811]) ).
fof(c_0_2722,plain,
! [X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Olower__semilattice__class_Oinf(X4),X4) ),
inference(variable_rename,[status(thm)],[c_0_1812]) ).
fof(c_0_2723,plain,
! [X4] :
( ~ class_Orderings_Olinorder(X4)
| ~ class_Lattices_Oupper__semilattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X4) = c_Orderings_Oord__class_Omax(X4) ),
inference(variable_rename,[status(thm)],[c_0_1813]) ).
fof(c_0_2724,plain,
! [X4] :
( ~ class_Orderings_Olinorder(X4)
| ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X4) = c_Orderings_Oord__class_Omin(X4) ),
inference(variable_rename,[status(thm)],[c_0_1814]) ).
fof(c_0_2725,plain,
! [X10,X11] :
( ~ class_Finite__Set_Ofinite_Ofinite(X11)
| c_Finite__Set_Ofinite(X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1815]) ).
fof(c_0_2726,plain,
! [X5] :
( class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(X5))
| ~ class_Finite__Set_Ofinite_Ofinite(X5) ),
inference(variable_rename,[status(thm)],[c_0_1816]) ).
fof(c_0_2727,plain,
! [X15,X16] :
( c_Suc(X16) != c_Suc(X15)
| X16 = X15 ),
inference(variable_rename,[status(thm)],[c_0_1817]) ).
fof(c_0_2728,plain,
! [X98,X99] :
( c_Suc(X99) != c_Suc(X98)
| X99 = X98 ),
inference(variable_rename,[status(thm)],[c_0_1818]) ).
fof(c_0_2729,plain,
! [X12,X13] :
( c_Com_Ocom_OBODY(X13) != c_Com_Ocom_OBODY(X12)
| X13 = X12 ),
inference(variable_rename,[status(thm)],[c_0_1819]) ).
cnf(c_0_2730,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_1820]) ).
cnf(c_0_2731,plain,
( hAPP(hAPP(X6,X11),hAPP(X2,X10)) = c_Finite__Set_Ofold(X6,X11,X10,X9,X9)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ c_Finite__Set_Ofinite(X10,X9) ),
inference(split_conjunct,[status(thm)],[c_0_1821]) ).
cnf(c_0_2732,plain,
( hAPP(hAPP(X5,X11),hAPP(X1,X10)) = c_Finite__Set_Ofold(X5,X11,X10,X9,X9)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ c_Finite__Set_Ofinite(X10,X9) ),
inference(split_conjunct,[status(thm)],[c_0_1822]) ).
cnf(c_0_2733,plain,
( hAPP(X2,X10) = c_Finite__Set_Ofold(X6,X7,X10,X9,X9)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ c_Finite__Set_Ofinite(X10,X9) ),
inference(split_conjunct,[status(thm)],[c_0_1823]) ).
cnf(c_0_2734,plain,
( hAPP(X1,X10) = c_Finite__Set_Ofold(X5,X8,X10,X9,X9)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ c_Finite__Set_Ofinite(X10,X9) ),
inference(split_conjunct,[status(thm)],[c_0_1824]) ).
cnf(c_0_2735,plain,
( hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X9),X10),hAPP(hAPP(c_Set_Oinsert(X9),X11),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))))) = 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_1825]) ).
cnf(c_0_2736,plain,
( hAPP(X2,hAPP(hAPP(c_Set_Oinsert(X9),X10),hAPP(hAPP(c_Set_Oinsert(X9),X11),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))))) = 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_1826]) ).
cnf(c_0_2737,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_1827]) ).
cnf(c_0_2738,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_1828]) ).
cnf(c_0_2739,plain,
( hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X9),X10),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)))) = X10
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(split_conjunct,[status(thm)],[c_0_1829]) ).
cnf(c_0_2740,plain,
( hAPP(X2,hAPP(hAPP(c_Set_Oinsert(X9),X10),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)))) = X10
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(split_conjunct,[status(thm)],[c_0_1830]) ).
cnf(c_0_2741,plain,
( hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X9),X10),X11)) = 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_1831]) ).
cnf(c_0_2742,plain,
( hAPP(X2,hAPP(hAPP(c_Set_Oinsert(X9),X10),X11)) = 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_1832]) ).
cnf(c_0_2743,plain,
( X10 = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))
| c_Finite__Set_Olattice_OSup__fin(X6,X10,X9) = hAPP(X2,X10)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ c_Finite__Set_Ofinite(X10,X9) ),
inference(split_conjunct,[status(thm)],[c_0_1833]) ).
cnf(c_0_2744,plain,
( X10 = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))
| c_Finite__Set_Olattice_OInf__fin(X5,X10,X9) = hAPP(X1,X10)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ c_Finite__Set_Ofinite(X10,X9) ),
inference(split_conjunct,[status(thm)],[c_0_1834]) ).
cnf(c_0_2745,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_1835]) ).
cnf(c_0_2746,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_1836]) ).
cnf(c_0_2747,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X4,X3,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X1,X2,X3,X4)),tc_fun(tc_Com_Ostate,tc_bool),t_a),X4,c_COMBK(hAPP(X3,v_sko__Hoare__Mirabelle__Xescape__1(X1,X2,X3,X4)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(split_conjunct,[status(thm)],[c_0_1837]) ).
cnf(c_0_2748,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,c_HOL_Ozero__class_Ozero(X4),X1,X4,X2)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,c_HOL_Ozero__class_Ozero(X4),X3,X4,X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,c_HOL_Ozero__class_Ozero(X4),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X4,X2)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,c_HOL_Ozero__class_Ozero(X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X4,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1838]) ).
cnf(c_0_2749,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X1,X6,X5,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X6,X5,X3,X2,X4))) ),
inference(split_conjunct,[status(thm)],[c_0_1839]) ).
cnf(c_0_2750,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X1,X6,X5,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X1,X6,X5,X3,X2,X4))) ),
inference(split_conjunct,[status(thm)],[c_0_1840]) ).
cnf(c_0_2751,plain,
( c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X5),X1,X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X4,X1,X3)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X5,X1,X3))
| ~ c_Finite__Set_Ofinite(X4,X3)
| ~ c_Finite__Set_Ofinite(X5,X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X5) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1841]) ).
cnf(c_0_2752,plain,
( hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X1,X6,X7,X3,X2,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X7,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X1,X6,X7,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1842]) ).
cnf(c_0_2753,plain,
( hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X6,X7,X3,X2,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X7,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X1,X6,X7,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1843]) ).
cnf(c_0_2754,plain,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,X6,hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X4,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(X5,X3)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,X6,X1,X4,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1844]) ).
cnf(c_0_2755,plain,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(X4),X5,X6,hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X4,X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),hAPP(X5,X3)),c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(X4),X5,X6,X1,X4,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Oab__semigroup__mult(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1845]) ).
cnf(c_0_2756,plain,
( hBOOL(hAPP(hAPP(c_in(X4),X5),X3))
| c_Finite__Set_Ofold__image(X1,X6,X7,hAPP(hAPP(c_Set_Oinsert(X4),X5),X3),X2,X4) = hAPP(hAPP(X1,hAPP(X6,X5)),c_Finite__Set_Ofold__image(X1,X6,X7,X3,X2,X4))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1846]) ).
cnf(c_0_2757,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X1,X1),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X3))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1847]) ).
cnf(c_0_2758,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X1,X1),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X2,X3,X1,X1),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X3))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1848]) ).
cnf(c_0_2759,plain,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X4))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X6,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool))),X2,X2),X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X3,X4,X2,X2),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X6),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1849]) ).
cnf(c_0_2760,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),X6)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X4)),X5)),X6))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1850]) ).
cnf(c_0_2761,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),X6)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X4)),X5)),X6))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1851]) ).
cnf(c_0_2762,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,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool)),X6,X1,X7) ),
inference(split_conjunct,[status(thm)],[c_0_1852]) ).
cnf(c_0_2763,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X6),hAPP(hAPP(X1,X5),X7)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))),tc_fun(X4,tc_bool)),X4,X6),X7))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X5),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1853]) ).
cnf(c_0_2764,plain,
( X7 = X6
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X4,X5,X2,X3),X6))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X4,X5,X2,X3),X7)) ),
inference(split_conjunct,[status(thm)],[c_0_1854]) ).
cnf(c_0_2765,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2)),c_Finite__Set_Ocard(X1,X2)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1855]) ).
cnf(c_0_2766,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X2,X5,X1)),X3)),X4)),X6))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1856]) ).
cnf(c_0_2767,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X2,X5,X1)),X3)),X4)),X6))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1857]) ).
cnf(c_0_2768,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1,X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X4)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X2,X3,X1,X1),X4))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1858]) ).
cnf(c_0_2769,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1,X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X4)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1859]) ).
cnf(c_0_2770,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,hAPP(hAPP(c_Set_Oinsert(X3),X4),X5),X3,X6),hAPP(hAPP(X1,X4),X7)))
| hBOOL(hAPP(hAPP(c_in(X3),X4),X5))
| ~ c_Finite__Set_Ofun__left__comm(X1,X3,X6)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X5,X3,X6),X7)) ),
inference(split_conjunct,[status(thm)],[c_0_1860]) ).
cnf(c_0_2771,plain,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X4))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X6,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),X2,X2),hAPP(hAPP(X1,X6),X5)))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X3,X4,X2,X2),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1861]) ).
cnf(c_0_2772,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1,X6),hAPP(hAPP(X4,X2),X7)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X5,X3,X1,X6),X7)) ),
inference(split_conjunct,[status(thm)],[c_0_1862]) ).
cnf(c_0_2773,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),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))) ),
inference(split_conjunct,[status(thm)],[c_0_1863]) ).
cnf(c_0_2774,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq12__1(X6,X2,X5,X4)),v_sko__Hoare__Mirabelle__Xconseq12__3(X6,X2,X5,X4))) ),
inference(split_conjunct,[status(thm)],[c_0_1864]) ).
cnf(c_0_2775,plain,
( hBOOL(hAPP(hAPP(X1,c_Finite__Set_Ofold(X3,X7,X5,X4,X4)),hAPP(hAPP(X3,X6),X7)))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ c_Finite__Set_Ofinite(X5,X4)
| ~ hBOOL(hAPP(hAPP(c_in(X4),X6),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1865]) ).
cnf(c_0_2776,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)),X6)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X3,X4,X1)),X5)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1866]) ).
cnf(c_0_2777,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)),X6)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X3,X4,X1)),X5)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1867]) ).
cnf(c_0_2778,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X5,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Com_Ocom_OBODY(X3),X4,X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool))),X1)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Com_Ocom_OBODY(X3),X4,X1)),X5),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Option_Othe(hAPP(c_Com_Obody,X3),tc_Com_Ocom),X4,X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool))),X1) ),
inference(split_conjunct,[status(thm)],[c_0_1868]) ).
cnf(c_0_2779,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X2),c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X2),X4,X1,X2,X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1869]) ).
cnf(c_0_2780,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Com_Ocom_OSemi(X4,X6),X7,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X5,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X6,X7,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1870]) ).
cnf(c_0_2781,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X5,X2,X1)),X3)),X6)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1871]) ).
cnf(c_0_2782,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X5,X2,X1)),X3)),X6)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1872]) ).
cnf(c_0_2783,plain,
( c_Finite__Set_Ofold(X1,X4,X5,X2,X3) = X6
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X4,X5,X2,X3),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_1873]) ).
cnf(c_0_2784,plain,
( hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq12__1(X5,X2,X6,X4)),v_sko__Hoare__Mirabelle__Xconseq12__2(X5,X2,X6,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X6,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(split_conjunct,[status(thm)],[c_0_1874]) ).
cnf(c_0_2785,plain,
( hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xconseq12__3(X6,X2,X7,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X7,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xconseq12__2(X6,X2,X7,X4))) ),
inference(split_conjunct,[status(thm)],[c_0_1875]) ).
cnf(c_0_2786,plain,
( hBOOL(hAPP(hAPP(c_in(X4),X2),X3))
| hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X4),X5))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1876]) ).
cnf(c_0_2787,plain,
( X5 = X2
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1877]) ).
cnf(c_0_2788,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Option_Ooption_Ooption__case(X4,X2,hAPP(c_Option_Ooption_OSome(t_b),X3),t_a,t_b))) ),
inference(split_conjunct,[status(thm)],[c_0_1878]) ).
cnf(c_0_2789,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Option_Ooption_Ooption__case(X4,X2,hAPP(c_Option_Ooption_OSome(t_b),X3),t_a,t_b))) ),
inference(split_conjunct,[status(thm)],[c_0_1879]) ).
cnf(c_0_2790,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Option_Ooption_Ooption__case(X2,X3,c_Option_Ooption_ONone(t_b),t_a,t_b))) ),
inference(split_conjunct,[status(thm)],[c_0_1880]) ).
cnf(c_0_2791,plain,
( c_Finite__Set_Ofinite(X3,X4)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_1881]) ).
cnf(c_0_2792,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),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)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1882]) ).
cnf(c_0_2793,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_1883]) ).
cnf(c_0_2794,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Com_Ocom_OBODY(X4),X5,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Option_Othe(hAPP(c_Com_Obody,X4),tc_Com_Ocom),X5,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1884]) ).
cnf(c_0_2795,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X1,X3,tc_Com_Ostate)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X1,X3,tc_Com_Ostate)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))),tc_Com_Ostate) ),
inference(split_conjunct,[status(thm)],[c_0_1885]) ).
cnf(c_0_2796,plain,
( c_Finite__Set_Osetsum(X3,X1,X2,X4) = c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X3,c_HOL_Ozero__class_Ozero(X4),X1,X4,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1886]) ).
cnf(c_0_2797,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xconseq1__1(X5,X2)),v_sko__Hoare__Mirabelle__Xconseq1__2(X5,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1887]) ).
cnf(c_0_2798,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq2__1(X5,X4)),v_sko__Hoare__Mirabelle__Xconseq2__2(X5,X4))) ),
inference(split_conjunct,[status(thm)],[c_0_1888]) ).
cnf(c_0_2799,plain,
( hBOOL(hAPP(hAPP(X4,v_sko__Hoare__Mirabelle__Xconseq2__1(X5,X4)),v_sko__Hoare__Mirabelle__Xconseq2__2(X5,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(split_conjunct,[status(thm)],[c_0_1889]) ).
cnf(c_0_2800,plain,
( hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq1__1(X5,X2)),v_sko__Hoare__Mirabelle__Xconseq1__2(X5,X2)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(split_conjunct,[status(thm)],[c_0_1890]) ).
cnf(c_0_2801,plain,
( c_Map_Orestrict__map(c_Fun_Ofun__upd(X4,X2,X5,X1,tc_Option_Ooption(X6)),X3,X1,X6) = c_Fun_Ofun__upd(c_Map_Orestrict__map(X4,c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool)),X1,X6),X2,X5,X1,tc_Option_Ooption(X6))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1891]) ).
cnf(c_0_2802,plain,
( c_Map_Omap__le(c_Fun_Ofun__upd(X1,X5,c_Option_Ooption_ONone(X4),X3,tc_Option_Ooption(X4)),c_Fun_Ofun__upd(X2,X5,hAPP(c_Option_Ooption_OSome(X4),X6),X3,tc_Option_Ooption(X4)),X3,X4)
| ~ c_Map_Omap__le(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1892]) ).
cnf(c_0_2803,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),X4)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X2),X4,X1,X2,X2)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Lattices_Oupper__semilattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1893]) ).
cnf(c_0_2804,plain,
( c_Map_Omap__le(c_Fun_Ofun__upd(X1,X5,X6,X3,tc_Option_Ooption(X4)),c_Fun_Ofun__upd(X2,X5,X6,X3,tc_Option_Ooption(X4)),X3,X4)
| ~ c_Map_Omap__le(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1894]) ).
cnf(c_0_2805,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1895]) ).
cnf(c_0_2806,plain,
( hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X2,X1,X3,X4)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X2,X1,X3,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X4,X3,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(split_conjunct,[status(thm)],[c_0_1896]) ).
cnf(c_0_2807,plain,
( hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X2,X1,X3,X4)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X2,X1,X3,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X4,X3,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(split_conjunct,[status(thm)],[c_0_1897]) ).
cnf(c_0_2808,plain,
( hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xescape__1(X2,X1,X3,X4)),v_sko__Hoare__Mirabelle__Xescape__2(X2,X1,X3,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X4,X3,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(split_conjunct,[status(thm)],[c_0_1898]) ).
cnf(c_0_2809,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1899]) ).
cnf(c_0_2810,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1900]) ).
cnf(c_0_2811,plain,
( c_Finite__Set_Ofold(X1,X6,X4,X2,X3) = hAPP(hAPP(X1,X5),c_Finite__Set_Ofold(X1,X6,c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X2),X5),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X3))
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| ~ c_Finite__Set_Ofinite(X4,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X5),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1901]) ).
cnf(c_0_2812,plain,
( c_Finite__Set_Ofold(X1,X5,hAPP(hAPP(c_Set_Oinsert(X2),X6),X4),X2,X3) = hAPP(hAPP(X1,X6),c_Finite__Set_Ofold(X1,X5,c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X3))
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| ~ c_Finite__Set_Ofinite(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1902]) ).
cnf(c_0_2813,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2)),c_Finite__Set_Ocard(X1,X2)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1903]) ).
cnf(c_0_2814,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1904]) ).
cnf(c_0_2815,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Finite__Set_Osetsum(X5,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2,X4)),c_Finite__Set_Osetsum(X5,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2,X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Finite__Set_Osetsum(X5,X1,X2,X4)),c_Finite__Set_Osetsum(X5,X3,X2,X4))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1905]) ).
cnf(c_0_2816,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),c_Finite__Set_Osetprod(X5,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2,X4)),c_Finite__Set_Osetprod(X5,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2,X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),c_Finite__Set_Osetprod(X5,X1,X2,X4)),c_Finite__Set_Osetprod(X5,X3,X2,X4))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1906]) ).
cnf(c_0_2817,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Map_Odom(X3,X1,X4)))
| c_Map_Omap__add(c_Fun_Ofun__upd(X5,X2,hAPP(c_Option_Ooption_OSome(X4),X6),X1,tc_Option_Ooption(X4)),X3,X1,X4) = c_Fun_Ofun__upd(c_Map_Omap__add(X5,X3,X1,X4),X2,hAPP(c_Option_Ooption_OSome(X4),X6),X1,tc_Option_Ooption(X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1907]) ).
cnf(c_0_2818,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1908]) ).
cnf(c_0_2819,plain,
( c_Finite__Set_Osetsum(X4,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2,X5) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_Finite__Set_Osetsum(X4,X1,X2,X5)),c_Finite__Set_Osetsum(X4,X3,X2,X5)),c_Finite__Set_Osetsum(X4,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2,X5),X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_OrderedGroup_Oab__group__add(X5) ),
inference(split_conjunct,[status(thm)],[c_0_1909]) ).
cnf(c_0_2820,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),hAPP(c_Finite__Set_Ofold1(X1,X2),X3)),X3))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),hAPP(hAPP(X1,c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1(X1,X2)),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2(X1,X2))),hAPP(hAPP(c_Set_Oinsert(X2),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1(X1,X2)),hAPP(hAPP(c_Set_Oinsert(X2),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2(X1,X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))))) ),
inference(split_conjunct,[status(thm)],[c_0_1910]) ).
cnf(c_0_2821,plain,
( c_Fun_Ofun__upd(c_Map_Orestrict__map(X4,X3,X1,X5),X2,X6,X1,tc_Option_Ooption(X5)) = c_Fun_Ofun__upd(c_Map_Orestrict__map(X4,c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool)),X1,X5),X2,X6,X1,tc_Option_Ooption(X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1911]) ).
cnf(c_0_2822,plain,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3))),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1912]) ).
cnf(c_0_2823,plain,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3))),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1913]) ).
cnf(c_0_2824,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3))),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1914]) ).
cnf(c_0_2825,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1915]) ).
cnf(c_0_2826,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1916]) ).
cnf(c_0_2827,plain,
( c_Finite__Set_Ofold(X3,X6,hAPP(hAPP(c_Set_Oinsert(X4),X7),X5),X4,X4) = hAPP(hAPP(X3,X7),c_Finite__Set_Ofold(X3,X6,X5,X4,X4))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ c_Finite__Set_Ofinite(X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1917]) ).
cnf(c_0_2828,plain,
( X1 = X2
| hAPP(X3,X4) = hAPP(c_Option_Ooption_OSome(X5),X2)
| hAPP(c_Fun_Ofun__upd(X3,X6,hAPP(c_Option_Ooption_OSome(X5),X1),X7,tc_Option_Ooption(X5)),X4) != hAPP(c_Option_Ooption_OSome(X5),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1918]) ).
cnf(c_0_2829,plain,
( X1 = X2
| hAPP(X3,X1) = hAPP(c_Option_Ooption_OSome(X4),X5)
| hAPP(c_Fun_Ofun__upd(X3,X2,hAPP(c_Option_Ooption_OSome(X4),X6),X7,tc_Option_Ooption(X4)),X1) != hAPP(c_Option_Ooption_OSome(X4),X5) ),
inference(split_conjunct,[status(thm)],[c_0_1919]) ).
cnf(c_0_2830,plain,
( X4 = X6
| hAPP(c_Fun_Ofun__upd(X1,X2,hAPP(c_Option_Ooption_OSome(X3),X4),X5,tc_Option_Ooption(X3)),X2) != hAPP(c_Option_Ooption_OSome(X3),X6) ),
inference(split_conjunct,[status(thm)],[c_0_1920]) ).
cnf(c_0_2831,plain,
( hBOOL(hAPP(hAPP(c_in(X2),X5),X4))
| c_Finite__Set_Ofold(X1,X6,hAPP(hAPP(c_Set_Oinsert(X2),X5),X4),X2,X3) = hAPP(hAPP(X1,X5),c_Finite__Set_Ofold(X1,X6,X4,X2,X3))
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| ~ c_Finite__Set_Ofinite(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1921]) ).
cnf(c_0_2832,plain,
( X1 = X2
| c_Fun_Ofun__upd(X3,X4,hAPP(c_Option_Ooption_OSome(X5),X1),X6,tc_Option_Ooption(X5)) != c_Fun_Ofun__upd(X7,X4,hAPP(c_Option_Ooption_OSome(X5),X2),X6,tc_Option_Ooption(X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1922]) ).
cnf(c_0_2833,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)))),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1923]) ).
cnf(c_0_2834,plain,
( hAPP(hAPP(X1,X5),c_Finite__Set_Ofold(X1,X6,X4,X2,X3)) = c_Finite__Set_Ofold(X1,hAPP(hAPP(X1,X5),X6),X4,X2,X3)
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| ~ c_Finite__Set_Ofinite(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1924]) ).
cnf(c_0_2835,plain,
( c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X2),X3,hAPP(hAPP(c_Set_Oinsert(X2),X4),X1),X2,X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X4),c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X2),X3,X1,X2,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1925]) ).
cnf(c_0_2836,plain,
( c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X2),X3,hAPP(hAPP(c_Set_Oinsert(X2),X4),X1),X2,X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X4),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X2),X3,X1,X2,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1926]) ).
cnf(c_0_2837,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),c_Set_Ovimage(X5,X2,X4,X1)),c_Set_Ovimage(X5,X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1927]) ).
cnf(c_0_2838,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X3),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1928]) ).
cnf(c_0_2839,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1929]) ).
cnf(c_0_2840,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1930]) ).
cnf(c_0_2841,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1931]) ).
cnf(c_0_2842,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)))))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1932]) ).
cnf(c_0_2843,plain,
( hAPP(X3,X2) = X5
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Ovimage(X3,hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))),X1,X4))) ),
inference(split_conjunct,[status(thm)],[c_0_1933]) ).
cnf(c_0_2844,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Map_Orestrict__map(c_Fun_Ofun__upd(X4,X2,X5,X1,tc_Option_Ooption(X6)),X3,X1,X6) = c_Map_Orestrict__map(X4,X3,X1,X6) ),
inference(split_conjunct,[status(thm)],[c_0_1934]) ).
cnf(c_0_2845,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1935]) ).
cnf(c_0_2846,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1936]) ).
cnf(c_0_2847,plain,
( hBOOL(hAPP(hAPP(c_in(X2),X5),X4))
| c_Finite__Set_Ofold(X1,X6,hAPP(hAPP(c_Set_Oinsert(X2),X5),X4),X2,X3) = c_Finite__Set_Ofold(X1,hAPP(hAPP(X1,X5),X6),X4,X2,X3)
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| ~ c_Finite__Set_Ofinite(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1937]) ).
cnf(c_0_2848,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4))))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1938]) ).
cnf(c_0_2849,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4))))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1939]) ).
cnf(c_0_2850,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X4,X2,X1)),X3)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),X5)
| ~ class_Ring__and__Field_Oring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1940]) ).
cnf(c_0_2851,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X2,X5,X1)),X3)),X4))
| ~ class_Ring__and__Field_Oring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1941]) ).
cnf(c_0_2852,plain,
( c_Fun_Ofun__upd(c_Map_Orestrict__map(X4,X3,X1,X5),X2,c_Option_Ooption_ONone(X5),X1,tc_Option_Ooption(X5)) = c_Map_Orestrict__map(X4,c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool)),X1,X5)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1942]) ).
cnf(c_0_2853,plain,
( c_Map_Omap__le(c_Map_Omap__add(X1,X5,X3,X4),X2,X3,X4)
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| ~ c_Map_Omap__le(X5,X2,X3,X4)
| ~ c_Map_Omap__le(X1,c_Map_Omap__add(X1,X5,X3,X4),X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1943]) ).
cnf(c_0_2854,plain,
( X1 = c_Option_Ooption_ONone(X2)
| c_Map_Odom(c_Fun_Ofun__upd(X3,X4,X1,X5,tc_Option_Ooption(X2)),X5,X2) = hAPP(hAPP(c_Set_Oinsert(X5),X4),c_Map_Odom(X3,X5,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1944]) ).
cnf(c_0_2855,plain,
( hAPP(c_Fun_Ofun__upd(X1,X2,hAPP(c_Option_Ooption_OSome(X3),X4),X5,tc_Option_Ooption(X3)),X6) = hAPP(c_Option_Ooption_OSome(X3),X7)
| X6 = X2
| hAPP(X1,X6) != hAPP(c_Option_Ooption_OSome(X3),X7) ),
inference(split_conjunct,[status(thm)],[c_0_1945]) ).
cnf(c_0_2856,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_Map_Osko__Map__Xmap__le__def__1__1(X2,X3,X1,X4)),c_Map_Odom(X2,X1,X4)))
| c_Map_Omap__le(X2,X3,X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1946]) ).
cnf(c_0_2857,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1947]) ).
cnf(c_0_2858,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1948]) ).
cnf(c_0_2859,plain,
( X1 = X2
| hAPP(c_Fun_Ofun__upd(X3,X2,X4,X5,X6),X1) = hAPP(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_1949]) ).
cnf(c_0_2860,plain,
( X1 = X2
| hAPP(c_Fun_Ofun__upd(X3,X2,X4,X5,X6),X1) = hAPP(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_1950]) ).
cnf(c_0_2861,plain,
( c_Finite__Set_Osetsum(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_Finite__Set_Osetsum(X1,X3,X2,X5)),c_Finite__Set_Osetsum(X1,X4,X2,X5))
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X4,X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_OrderedGroup_Ocomm__monoid__add(X5) ),
inference(split_conjunct,[status(thm)],[c_0_1951]) ).
cnf(c_0_2862,plain,
( c_Finite__Set_Osetprod(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Finite__Set_Osetprod(X1,X3,X2,X5)),c_Finite__Set_Osetprod(X1,X4,X2,X5))
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X4,X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_OrderedGroup_Ocomm__monoid__mult(X5) ),
inference(split_conjunct,[status(thm)],[c_0_1952]) ).
cnf(c_0_2863,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1953]) ).
cnf(c_0_2864,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1954]) ).
cnf(c_0_2865,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool))),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1955]) ).
cnf(c_0_2866,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_1956]) ).
cnf(c_0_2867,plain,
( c_Finite__Set_Osetsum(X4,X1,X2,X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(X4,X3)),c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X5))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X5) ),
inference(split_conjunct,[status(thm)],[c_0_1957]) ).
cnf(c_0_2868,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X1,tc_bool))),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1958]) ).
cnf(c_0_2869,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)),X2) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1959]) ).
cnf(c_0_2870,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Fun_Ofun__upd(c_Map_Orestrict__map(X4,X3,X1,X5),X2,c_Option_Ooption_ONone(X5),X1,tc_Option_Ooption(X5)) = c_Map_Orestrict__map(X4,X3,X1,X5) ),
inference(split_conjunct,[status(thm)],[c_0_1960]) ).
cnf(c_0_2871,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_1961]) ).
cnf(c_0_2872,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_1962]) ).
cnf(c_0_2873,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X4)),X5) = X6
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X5) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),X6)
| ~ class_Ring__and__Field_Oring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1963]) ).
cnf(c_0_2874,plain,
( X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),c_HOL_Ominus__class_Ominus(X3,X4,X2)),X5)),X6)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X4),X5)),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X5)),X6)
| ~ class_Ring__and__Field_Oring(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1964]) ).
cnf(c_0_2875,plain,
( c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2,X5) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),c_Finite__Set_Osetsum(X4,X3,X2,X5),X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X1))
| ~ class_OrderedGroup_Oab__group__add(X5) ),
inference(split_conjunct,[status(thm)],[c_0_1965]) ).
cnf(c_0_2876,plain,
( hAPP(X1,X2) = X3
| c_Fun_Ofun__upd(X1,X2,X3,X4,X5) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_1966]) ).
cnf(c_0_2877,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1967]) ).
cnf(c_0_2878,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)),X5)
| ~ class_Ring__and__Field_Osemiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1968]) ).
cnf(c_0_2879,plain,
( c_Map_Omap__le(X1,X2,X3,X4)
| hAPP(X1,c_Map_Osko__Map__Xmap__le__def__1__1(X1,X2,X3,X4)) != hAPP(X2,c_Map_Osko__Map__Xmap__le__def__1__1(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1969]) ).
cnf(c_0_2880,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1970]) ).
cnf(c_0_2881,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1971]) ).
cnf(c_0_2882,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_1972]) ).
cnf(c_0_2883,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1973]) ).
cnf(c_0_2884,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1974]) ).
cnf(c_0_2885,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1975]) ).
cnf(c_0_2886,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1976]) ).
cnf(c_0_2887,plain,
( X3 = X4
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1977]) ).
cnf(c_0_2888,plain,
( hBOOL(hAPP(X2,hAPP(X1,X5)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X1,X2,X3,X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1978]) ).
cnf(c_0_2889,plain,
( c_Map_Omap__add(X1,X2,X3,X4) = c_Map_Omap__add(X2,X1,X3,X4)
| ~ c_Map_Omap__le(X1,c_Map_Omap__add(X1,X2,X3,X4),X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1979]) ).
cnf(c_0_2890,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_1980]) ).
cnf(c_0_2891,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_1981]) ).
cnf(c_0_2892,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1982]) ).
cnf(c_0_2893,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1983]) ).
cnf(c_0_2894,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1984]) ).
cnf(c_0_2895,plain,
( c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X5) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),hAPP(X4,X3),X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Ring__and__Field_Oring(X5) ),
inference(split_conjunct,[status(thm)],[c_0_1985]) ).
cnf(c_0_2896,plain,
( c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X5) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),hAPP(X4,X3),X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_OrderedGroup_Oab__group__add(X5) ),
inference(split_conjunct,[status(thm)],[c_0_1986]) ).
cnf(c_0_2897,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1987]) ).
cnf(c_0_2898,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),c_HOL_Ozero__class_Ozero(X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3))))
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1988]) ).
cnf(c_0_2899,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),c_HOL_Ozero__class_Ozero(X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1))))
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1989]) ).
cnf(c_0_2900,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3))))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1990]) ).
cnf(c_0_2901,plain,
( c_Map_Omap__le(X1,c_Map_Omap__add(X1,X2,X3,X4),X3,X4)
| c_Map_Omap__add(X1,X2,X3,X4) != c_Map_Omap__add(X2,X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1991]) ).
cnf(c_0_2902,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X4),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1992]) ).
cnf(c_0_2903,plain,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(X2),X3,X1,X2,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Oab__semigroup__mult(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1993]) ).
cnf(c_0_2904,plain,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = c_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(X2),X3,X1,X2,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1994]) ).
cnf(c_0_2905,plain,
( hBOOL(hAPP(hAPP(c_in(X2),X4),X3))
| hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = c_Finite__Set_Ofold(X1,X4,X3,X2,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1995]) ).
cnf(c_0_2906,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1996]) ).
cnf(c_0_2907,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1997]) ).
cnf(c_0_2908,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1998]) ).
cnf(c_0_2909,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1999]) ).
cnf(c_0_2910,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Opordered__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2000]) ).
cnf(c_0_2911,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Opordered__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2001]) ).
cnf(c_0_2912,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2002]) ).
cnf(c_0_2913,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2003]) ).
cnf(c_0_2914,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2004]) ).
cnf(c_0_2915,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2005]) ).
cnf(c_0_2916,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2006]) ).
cnf(c_0_2917,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2007]) ).
cnf(c_0_2918,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2008]) ).
cnf(c_0_2919,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2009]) ).
cnf(c_0_2920,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2010]) ).
cnf(c_0_2921,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2011]) ).
cnf(c_0_2922,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_2012]) ).
cnf(c_0_2923,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_2013]) ).
cnf(c_0_2924,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_2014]) ).
cnf(c_0_2925,plain,
( c_Map_Omap__le(X2,X5,X3,X4)
| ~ c_Map_Omap__le(c_Map_Omap__add(X1,X2,X3,X4),X5,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2015]) ).
cnf(c_0_2926,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3) = c_Finite__Set_Ofold(c_Set_Oinsert(X2),X3,X1,X2,tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2016]) ).
cnf(c_0_2927,plain,
( hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(X2),X3,X1,X2,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2017]) ).
cnf(c_0_2928,plain,
( hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = c_Finite__Set_Ofold(X1,X4,X3,X2,X2)
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2018]) ).
cnf(c_0_2929,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2019]) ).
cnf(c_0_2930,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2020]) ).
cnf(c_0_2931,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2021]) ).
cnf(c_0_2932,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2022]) ).
cnf(c_0_2933,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2023]) ).
cnf(c_0_2934,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2024]) ).
cnf(c_0_2935,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2025]) ).
cnf(c_0_2936,plain,
( c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2)) = c_Finite__Set_Ocard(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2026]) ).
cnf(c_0_2937,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X4),X2)),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2027]) ).
cnf(c_0_2938,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2028]) ).
cnf(c_0_2939,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2029]) ).
cnf(c_0_2940,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2030]) ).
cnf(c_0_2941,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Map_Odom(X1,X3,X4)),c_Map_Odom(X2,X3,X4)))
| ~ c_Map_Omap__le(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2031]) ).
cnf(c_0_2942,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),c_Complete__Lattice_OInf__class_OInf(X1,X2)) = c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X2),X3,X1,X2,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2032]) ).
cnf(c_0_2943,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),c_Complete__Lattice_OSup__class_OSup(X1,X2)) = c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X2),X3,X1,X2,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2033]) ).
cnf(c_0_2944,plain,
( c_Fun_Ofun__upd(X1,X2,hAPP(c_Option_Ooption_OSome(X3),X4),X5,tc_Option_Ooption(X3)) = X1
| hAPP(X1,X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(split_conjunct,[status(thm)],[c_0_2034]) ).
cnf(c_0_2945,plain,
( c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2) = c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2))
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2035]) ).
cnf(c_0_2946,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X3),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2036]) ).
cnf(c_0_2947,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2037]) ).
cnf(c_0_2948,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2038]) ).
cnf(c_0_2949,plain,
( c_Map_Omap__add(X1,X2,X3,X4) = c_Map_Omap__add(X2,X1,X3,X4)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),c_Map_Odom(X1,X3,X4)),c_Map_Odom(X2,X3,X4)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2039]) ).
cnf(c_0_2950,plain,
( c_Lattices_Olower__semilattice(c_COMBC(c_lessequals(X1),X1,X1,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(X1),X1,X1,tc_bool),c_Orderings_Oord__class_Omax(X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2040]) ).
cnf(c_0_2951,plain,
( c_Lattices_Olower__semilattice(c_COMBC(c_lessequals(X1),X1,X1,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(X1),X1,X1,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2041]) ).
cnf(c_0_2952,plain,
( c_Complete__Lattice_OSup__class_OSup(X1,X2) = c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X2),c_Orderings_Obot__class_Obot(X2),X1,X2,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2042]) ).
cnf(c_0_2953,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2043]) ).
cnf(c_0_2954,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2044]) ).
cnf(c_0_2955,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2045]) ).
cnf(c_0_2956,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2046]) ).
cnf(c_0_2957,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X2 = hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))))) ),
inference(split_conjunct,[status(thm)],[c_0_2047]) ).
cnf(c_0_2958,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2048]) ).
cnf(c_0_2959,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X3)),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1),X3))
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2049]) ).
cnf(c_0_2960,plain,
( hAPP(X3,X4) = c_HOL_Ozero__class_Ozero(X5)
| hBOOL(hAPP(hAPP(c_in(X2),X4),X1))
| c_Finite__Set_Osetprod(X3,c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X5) = c_Finite__Set_Osetprod(X3,X1,X2,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(split_conjunct,[status(thm)],[c_0_2050]) ).
cnf(c_0_2961,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2051]) ).
cnf(c_0_2962,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2052]) ).
cnf(c_0_2963,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2053]) ).
cnf(c_0_2964,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2054]) ).
cnf(c_0_2965,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2055]) ).
cnf(c_0_2966,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2056]) ).
cnf(c_0_2967,plain,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X5) = c_Finite__Set_Osetsum(X4,X1,X2,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Oab__group__add(X5) ),
inference(split_conjunct,[status(thm)],[c_0_2057]) ).
cnf(c_0_2968,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OBODY(X1)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Option_Othe(hAPP(c_Com_Obody,X1),tc_Com_Ocom)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2058]) ).
cnf(c_0_2969,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2059]) ).
cnf(c_0_2970,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2060]) ).
cnf(c_0_2971,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2061]) ).
cnf(c_0_2972,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2062]) ).
cnf(c_0_2973,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2063]) ).
cnf(c_0_2974,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool)),X1,tc_nat) = c_Finite__Set_Osetsum(X4,X3,X1,tc_nat) ),
inference(split_conjunct,[status(thm)],[c_0_2064]) ).
cnf(c_0_2975,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X2,tc_bool)),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(X3,X2)),c_Finite__Set_Ocard(X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2065]) ).
cnf(c_0_2976,plain,
( X1 = X2
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X3))
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(split_conjunct,[status(thm)],[c_0_2066]) ).
cnf(c_0_2977,plain,
( X1 = X2
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X3))
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(split_conjunct,[status(thm)],[c_0_2067]) ).
cnf(c_0_2978,plain,
( hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3))
| ~ hBOOL(hAPP(X1,hAPP(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2068]) ).
cnf(c_0_2979,plain,
( c_HOL_Ominus__class_Ominus(X3,c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2069]) ).
cnf(c_0_2980,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X4),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X3),X4))
| ~ class_HOL_Oord(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2070]) ).
cnf(c_0_2981,plain,
( c_Orderings_Olinorder(c_COMBC(X1,X3,X3,tc_bool),c_COMBC(X2,X3,X3,tc_bool),X3)
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2071]) ).
cnf(c_0_2982,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2072]) ).
cnf(c_0_2983,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2073]) ).
cnf(c_0_2984,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Omult__mono(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2074]) ).
cnf(c_0_2985,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Omult__mono(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2075]) ).
cnf(c_0_2986,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Omult__mono1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2076]) ).
cnf(c_0_2987,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2077]) ).
cnf(c_0_2988,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2078]) ).
cnf(c_0_2989,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2079]) ).
cnf(c_0_2990,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2080]) ).
cnf(c_0_2991,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2081]) ).
cnf(c_0_2992,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2082]) ).
cnf(c_0_2993,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2083]) ).
cnf(c_0_2994,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2084]) ).
cnf(c_0_2995,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2085]) ).
cnf(c_0_2996,plain,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| c_Finite__Set_Osetsum(X4,hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2,X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(X4,X3)),c_Finite__Set_Osetsum(X4,X1,X2,X5))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X5) ),
inference(split_conjunct,[status(thm)],[c_0_2086]) ).
cnf(c_0_2997,plain,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| c_Finite__Set_Osetprod(X4,hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2,X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(X4,X3)),c_Finite__Set_Osetprod(X4,X1,X2,X5))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X5) ),
inference(split_conjunct,[status(thm)],[c_0_2087]) ).
cnf(c_0_2998,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2088]) ).
cnf(c_0_2999,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2089]) ).
cnf(c_0_3000,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2090]) ).
cnf(c_0_3001,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2091]) ).
cnf(c_0_3002,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2092]) ).
cnf(c_0_3003,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2093]) ).
cnf(c_0_3004,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2094]) ).
cnf(c_0_3005,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2095]) ).
cnf(c_0_3006,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2096]) ).
cnf(c_0_3007,plain,
( hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),X2)),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),X3))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(X3,X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2097]) ).
cnf(c_0_3008,plain,
( hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),X2)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),X3))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(X3,X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2098]) ).
cnf(c_0_3009,plain,
( c_Orderings_Olinorder(c_COMBC(c_lessequals(X1),X1,X1,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(X1),X1,X1,tc_bool),X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2099]) ).
cnf(c_0_3010,plain,
( X5 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| hBOOL(hAPP(hAPP(X1,X6),X7))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ c_Finite__Set_Ofinite(X5,X4)
| ~ hBOOL(hAPP(hAPP(X1,X6),hAPP(c_Finite__Set_Ofold1(X3,X4),X5)))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X7),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_2100]) ).
cnf(c_0_3011,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2101]) ).
cnf(c_0_3012,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2102]) ).
cnf(c_0_3013,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2103]) ).
cnf(c_0_3014,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2104]) ).
cnf(c_0_3015,plain,
( hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1) = X3
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(X1,X3,X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2105]) ).
cnf(c_0_3016,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2106]) ).
cnf(c_0_3017,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2107]) ).
cnf(c_0_3018,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2108]) ).
cnf(c_0_3019,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2109]) ).
cnf(c_0_3020,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2110]) ).
cnf(c_0_3021,plain,
( hAPP(X3,X2) = hAPP(c_Option_Ooption_OSome(X4),c_Map_Osko__Map__XdomD__1__1(X2,X3,X1,X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Map_Odom(X3,X1,X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2111]) ).
cnf(c_0_3022,plain,
( c_Map_Omap__le(X1,X5,X3,X4)
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| ~ c_Map_Omap__le(X2,X5,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2112]) ).
cnf(c_0_3023,plain,
( hAPP(c_Map_Omap__add(X5,X3,X1,X4),X2) = hAPP(X3,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Map_Odom(X3,X1,X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2113]) ).
cnf(c_0_3024,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2114]) ).
cnf(c_0_3025,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2115]) ).
cnf(c_0_3026,plain,
( hBOOL(hAPP(X2,X4))
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2116]) ).
cnf(c_0_3027,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X4),X3))
| ~ class_HOL_Oord(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2117]) ).
cnf(c_0_3028,plain,
( hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4)) = hAPP(hAPP(X1,hAPP(c_Finite__Set_Ofold1(X1,X2),X3)),hAPP(c_Finite__Set_Ofold1(X1,X2),X4))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X4,X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2118]) ).
cnf(c_0_3029,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2119]) ).
cnf(c_0_3030,plain,
( hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2120]) ).
cnf(c_0_3031,plain,
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2121]) ).
cnf(c_0_3032,plain,
( hBOOL(hAPP(hAPP(X1,hAPP(c_Finite__Set_Ofold1(X3,X4),X5)),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ c_Finite__Set_Ofinite(X5,X4)
| ~ hBOOL(hAPP(hAPP(c_in(X4),X6),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_2122]) ).
cnf(c_0_3033,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2123]) ).
cnf(c_0_3034,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2124]) ).
cnf(c_0_3035,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2125]) ).
cnf(c_0_3036,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2126]) ).
cnf(c_0_3037,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2127]) ).
cnf(c_0_3038,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2128]) ).
cnf(c_0_3039,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2129]) ).
cnf(c_0_3040,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2130]) ).
cnf(c_0_3041,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2131]) ).
cnf(c_0_3042,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2132]) ).
cnf(c_0_3043,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2133]) ).
cnf(c_0_3044,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2134]) ).
cnf(c_0_3045,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2135]) ).
cnf(c_0_3046,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2136]) ).
cnf(c_0_3047,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2137]) ).
cnf(c_0_3048,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2138]) ).
cnf(c_0_3049,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2139]) ).
cnf(c_0_3050,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2140]) ).
cnf(c_0_3051,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2141]) ).
cnf(c_0_3052,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2142]) ).
cnf(c_0_3053,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2143]) ).
cnf(c_0_3054,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2144]) ).
cnf(c_0_3055,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2145]) ).
cnf(c_0_3056,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2146]) ).
cnf(c_0_3057,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2147]) ).
cnf(c_0_3058,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2148]) ).
cnf(c_0_3059,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2149]) ).
cnf(c_0_3060,plain,
( hAPP(X1,X5) = hAPP(X2,X5)
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),c_Map_Odom(X1,X3,X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2150]) ).
cnf(c_0_3061,plain,
( X3 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2151]) ).
cnf(c_0_3062,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2152]) ).
cnf(c_0_3063,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2153]) ).
cnf(c_0_3064,plain,
( hBOOL(hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X5)),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X2,X5),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_2154]) ).
cnf(c_0_3065,plain,
( hBOOL(hAPP(hAPP(X2,hAPP(hAPP(X3,X5),X7)),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X2,X5),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_2155]) ).
cnf(c_0_3066,plain,
( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(X3,X5),X7)),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_2156]) ).
cnf(c_0_3067,plain,
( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(X3,X7),X5)),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_2157]) ).
cnf(c_0_3068,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X1)),X4))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X3),X4))
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2158]) ).
cnf(c_0_3069,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X1)),X4))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X3),X4))
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2159]) ).
cnf(c_0_3070,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2160]) ).
cnf(c_0_3071,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2161]) ).
cnf(c_0_3072,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2162]) ).
cnf(c_0_3073,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2163]) ).
cnf(c_0_3074,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Option_Othe(hAPP(c_Com_Obody,X1),tc_Com_Ocom)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OBODY(X1)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2164]) ).
cnf(c_0_3075,plain,
( hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(X5,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(c_Map_Omap__add(X5,X1,X6,X3),X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(split_conjunct,[status(thm)],[c_0_2165]) ).
cnf(c_0_3076,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2166]) ).
cnf(c_0_3077,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2167]) ).
cnf(c_0_3078,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2168]) ).
cnf(c_0_3079,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2169]) ).
cnf(c_0_3080,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2170]) ).
cnf(c_0_3081,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2171]) ).
cnf(c_0_3082,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2172]) ).
cnf(c_0_3083,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2173]) ).
cnf(c_0_3084,plain,
( hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7)))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),X6))
| ~ hBOOL(hAPP(hAPP(X1,X5),X7)) ),
inference(split_conjunct,[status(thm)],[c_0_2174]) ).
cnf(c_0_3085,plain,
( hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7)))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),X6))
| ~ hBOOL(hAPP(hAPP(X1,X5),X7)) ),
inference(split_conjunct,[status(thm)],[c_0_2175]) ).
cnf(c_0_3086,plain,
( hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7)))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),X6))
| ~ hBOOL(hAPP(hAPP(X1,X5),X7)) ),
inference(split_conjunct,[status(thm)],[c_0_2176]) ).
cnf(c_0_3087,plain,
( hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X5,X1,X6,X3),X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(split_conjunct,[status(thm)],[c_0_2177]) ).
cnf(c_0_3088,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2178]) ).
cnf(c_0_3089,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2179]) ).
cnf(c_0_3090,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2180]) ).
cnf(c_0_3091,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2181]) ).
cnf(c_0_3092,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2182]) ).
cnf(c_0_3093,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2183]) ).
cnf(c_0_3094,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2184]) ).
cnf(c_0_3095,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2185]) ).
cnf(c_0_3096,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2186]) ).
cnf(c_0_3097,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),X4),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2187]) ).
cnf(c_0_3098,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2188]) ).
cnf(c_0_3099,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X2)),hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2189]) ).
cnf(c_0_3100,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_Finite__Set_Olinorder__class_OMin(X1),X3)),hAPP(c_Finite__Set_Olinorder__class_OMin(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2190]) ).
cnf(c_0_3101,plain,
( hBOOL(hAPP(hAPP(X1,X5),X7))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7))) ),
inference(split_conjunct,[status(thm)],[c_0_2191]) ).
cnf(c_0_3102,plain,
( hBOOL(hAPP(hAPP(X1,X5),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7))) ),
inference(split_conjunct,[status(thm)],[c_0_2192]) ).
cnf(c_0_3103,plain,
( hBOOL(hAPP(hAPP(X1,X5),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7))) ),
inference(split_conjunct,[status(thm)],[c_0_2193]) ).
cnf(c_0_3104,plain,
( hBOOL(hAPP(hAPP(X1,X5),X7))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7))) ),
inference(split_conjunct,[status(thm)],[c_0_2194]) ).
cnf(c_0_3105,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2195]) ).
cnf(c_0_3106,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2196]) ).
cnf(c_0_3107,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Map_Odom(X3,X1,X4)))
| hAPP(c_Map_Omap__add(X5,X3,X1,X4),X2) = hAPP(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2197]) ).
cnf(c_0_3108,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Map_Odom(X3,X1,X4)))
| hAPP(c_Map_Omap__add(X3,X5,X1,X4),X2) = hAPP(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2198]) ).
cnf(c_0_3109,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2199]) ).
cnf(c_0_3110,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X3),X4))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X3),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2200]) ).
cnf(c_0_3111,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X2),X3),X4))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X3),hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),X1))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2201]) ).
cnf(c_0_3112,plain,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X4,X1,X5,X3),X2) != c_Option_Ooption_ONone(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2202]) ).
cnf(c_0_3113,plain,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X1,X4,X5,X3),X2) != c_Option_Ooption_ONone(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2203]) ).
cnf(c_0_3114,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))))) ),
inference(split_conjunct,[status(thm)],[c_0_2204]) ).
cnf(c_0_3115,plain,
( X1 = X2
| X1 = X3
| hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X3),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) ),
inference(split_conjunct,[status(thm)],[c_0_2205]) ).
cnf(c_0_3116,plain,
( X1 = X2
| X3 = X2
| hAPP(hAPP(c_Set_Oinsert(X4),X3),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) ),
inference(split_conjunct,[status(thm)],[c_0_2206]) ).
cnf(c_0_3117,plain,
( X1 = X2
| X3 = X2
| hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X2),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) ),
inference(split_conjunct,[status(thm)],[c_0_2207]) ).
cnf(c_0_3118,plain,
( X1 = X2
| X1 = X3
| hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X2),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) ),
inference(split_conjunct,[status(thm)],[c_0_2208]) ).
cnf(c_0_3119,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))
| ~ class_HOL_Oord(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2209]) ).
cnf(c_0_3120,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_2210]) ).
cnf(c_0_3121,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OlessThan(X2,X1)),c_SetInterval_Oord__class_OlessThan(X3,X1)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2211]) ).
cnf(c_0_3122,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),X1)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),X3))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2212]) ).
cnf(c_0_3123,plain,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))) = X3
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2213]) ).
cnf(c_0_3124,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2214]) ).
cnf(c_0_3125,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2215]) ).
cnf(c_0_3126,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2216]) ).
cnf(c_0_3127,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2217]) ).
cnf(c_0_3128,plain,
( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(X3,X5),X6)),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2218]) ).
cnf(c_0_3129,plain,
( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(X3,X5),X6)),X5))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2219]) ).
cnf(c_0_3130,plain,
( X1 = X2
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| ~ c_Map_Omap__le(X2,X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2220]) ).
cnf(c_0_3131,plain,
( X1 = X2
| c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X1,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X6,X7,X2,X5) ),
inference(split_conjunct,[status(thm)],[c_0_2221]) ).
cnf(c_0_3132,plain,
( X1 = X2
| c_Hoare__Mirabelle_Otriple_Otriple(X3,X1,X4,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X6,X2,X7,X5) ),
inference(split_conjunct,[status(thm)],[c_0_2222]) ).
cnf(c_0_3133,plain,
( X1 = X2
| c_Hoare__Mirabelle_Otriple_Otriple(X1,X3,X4,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X2,X6,X7,X5) ),
inference(split_conjunct,[status(thm)],[c_0_2223]) ).
cnf(c_0_3134,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(X3,X5)),hAPP(X4,X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X3),X4))
| ~ class_HOL_Oord(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2224]) ).
cnf(c_0_3135,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2225]) ).
cnf(c_0_3136,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2226]) ).
cnf(c_0_3137,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2227]) ).
cnf(c_0_3138,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2228]) ).
cnf(c_0_3139,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2229]) ).
cnf(c_0_3140,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2230]) ).
cnf(c_0_3141,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2231]) ).
cnf(c_0_3142,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2232]) ).
cnf(c_0_3143,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_2233]) ).
cnf(c_0_3144,plain,
( hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(X1,X3,X2)),X1))
| hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1) = X3
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2234]) ).
cnf(c_0_3145,plain,
( hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(X1,X3,X2)),X1))
| hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1) = X3
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2235]) ).
cnf(c_0_3146,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X1,tc_bool))) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2236]) ).
cnf(c_0_3147,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2237]) ).
cnf(c_0_3148,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2238]) ).
cnf(c_0_3149,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2239]) ).
cnf(c_0_3150,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2240]) ).
cnf(c_0_3151,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2241]) ).
cnf(c_0_3152,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2242]) ).
cnf(c_0_3153,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2243]) ).
cnf(c_0_3154,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X5),X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2244]) ).
cnf(c_0_3155,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2245]) ).
cnf(c_0_3156,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2246]) ).
cnf(c_0_3157,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2247]) ).
cnf(c_0_3158,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2248]) ).
cnf(c_0_3159,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2249]) ).
cnf(c_0_3160,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(X3,X2)),c_Finite__Set_Ocard(X1,X2)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X2,tc_bool)),X3),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2250]) ).
cnf(c_0_3161,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2251]) ).
cnf(c_0_3162,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2252]) ).
cnf(c_0_3163,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2253]) ).
cnf(c_0_3164,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4)) = hAPP(hAPP(X1,hAPP(c_Finite__Set_Ofold1(X1,X2),X3)),hAPP(c_Finite__Set_Ofold1(X1,X2),X4))
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2254]) ).
cnf(c_0_3165,plain,
( hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1) = X3
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X3),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(X1,X3,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2255]) ).
cnf(c_0_3166,plain,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2) = c_Finite__Set_Ocard(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2256]) ).
cnf(c_0_3167,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2257]) ).
cnf(c_0_3168,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2258]) ).
cnf(c_0_3169,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2259]) ).
cnf(c_0_3170,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2260]) ).
cnf(c_0_3171,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2261]) ).
cnf(c_0_3172,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2262]) ).
cnf(c_0_3173,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2263]) ).
cnf(c_0_3174,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2264]) ).
cnf(c_0_3175,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2265]) ).
cnf(c_0_3176,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X2),X1)),X3))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2266]) ).
cnf(c_0_3177,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2267]) ).
cnf(c_0_3178,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2268]) ).
cnf(c_0_3179,plain,
( hAPP(hAPP(X3,hAPP(hAPP(X3,X5),X6)),X7) = hAPP(hAPP(X3,X5),hAPP(hAPP(X3,X6),X7))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2269]) ).
cnf(c_0_3180,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2270]) ).
cnf(c_0_3181,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2271]) ).
cnf(c_0_3182,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2272]) ).
cnf(c_0_3183,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2273]) ).
cnf(c_0_3184,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X1),X3),X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2274]) ).
cnf(c_0_3185,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2275]) ).
cnf(c_0_3186,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2276]) ).
cnf(c_0_3187,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2277]) ).
cnf(c_0_3188,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2278]) ).
cnf(c_0_3189,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2279]) ).
cnf(c_0_3190,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2280]) ).
cnf(c_0_3191,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2281]) ).
cnf(c_0_3192,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2282]) ).
cnf(c_0_3193,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2283]) ).
cnf(c_0_3194,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2284]) ).
cnf(c_0_3195,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2285]) ).
cnf(c_0_3196,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2286]) ).
cnf(c_0_3197,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2287]) ).
cnf(c_0_3198,plain,
( hAPP(c_Map_Orestrict__map(X4,X3,X1,X5),X2) = hAPP(X4,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2288]) ).
cnf(c_0_3199,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_2289]) ).
cnf(c_0_3200,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_2290]) ).
cnf(c_0_3201,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2291]) ).
cnf(c_0_3202,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2292]) ).
cnf(c_0_3203,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2293]) ).
cnf(c_0_3204,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2294]) ).
cnf(c_0_3205,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2295]) ).
cnf(c_0_3206,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2296]) ).
cnf(c_0_3207,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2297]) ).
cnf(c_0_3208,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2298]) ).
cnf(c_0_3209,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2299]) ).
cnf(c_0_3210,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2300]) ).
cnf(c_0_3211,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X1,X4)),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X4),X3),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_2301]) ).
cnf(c_0_3212,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X1),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2302]) ).
cnf(c_0_3213,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2303]) ).
cnf(c_0_3214,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) ),
inference(split_conjunct,[status(thm)],[c_0_2304]) ).
cnf(c_0_3215,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X3),X4),X2),tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_2305]) ).
cnf(c_0_3216,plain,
( hAPP(hAPP(X3,X5),hAPP(hAPP(X3,X6),X7)) = hAPP(hAPP(X3,X6),hAPP(hAPP(X3,X5),X7))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2306]) ).
cnf(c_0_3217,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2307]) ).
cnf(c_0_3218,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2308]) ).
cnf(c_0_3219,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Olordered__ab__group__add__join(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2309]) ).
cnf(c_0_3220,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2310]) ).
cnf(c_0_3221,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2311]) ).
cnf(c_0_3222,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2312]) ).
cnf(c_0_3223,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2313]) ).
cnf(c_0_3224,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2314]) ).
cnf(c_0_3225,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2315]) ).
cnf(c_0_3226,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2316]) ).
cnf(c_0_3227,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2317]) ).
cnf(c_0_3228,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2318]) ).
cnf(c_0_3229,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2319]) ).
cnf(c_0_3230,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OlessThan(X2,X1)),c_SetInterval_Oord__class_OlessThan(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2320]) ).
cnf(c_0_3231,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hAPP(c_Map_Orestrict__map(X4,X3,X1,X5),X2) = c_Option_Ooption_ONone(X5) ),
inference(split_conjunct,[status(thm)],[c_0_2321]) ).
cnf(c_0_3232,plain,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(c_Option_Ooption_OSome(X4),X6)
| hAPP(X2,X5) != c_Option_Ooption_ONone(X4)
| hAPP(X1,X5) != hAPP(c_Option_Ooption_OSome(X4),X6) ),
inference(split_conjunct,[status(thm)],[c_0_2322]) ).
cnf(c_0_3233,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2323]) ).
cnf(c_0_3234,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2324]) ).
cnf(c_0_3235,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2325]) ).
cnf(c_0_3236,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2326]) ).
cnf(c_0_3237,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2327]) ).
cnf(c_0_3238,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2328]) ).
cnf(c_0_3239,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2329]) ).
cnf(c_0_3240,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2330]) ).
cnf(c_0_3241,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2331]) ).
cnf(c_0_3242,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2332]) ).
cnf(c_0_3243,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2333]) ).
cnf(c_0_3244,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2334]) ).
cnf(c_0_3245,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X2) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2335]) ).
cnf(c_0_3246,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2336]) ).
cnf(c_0_3247,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X2) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2337]) ).
cnf(c_0_3248,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X3) ),
inference(split_conjunct,[status(thm)],[c_0_2338]) ).
cnf(c_0_3249,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_2339]) ).
cnf(c_0_3250,plain,
( c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2340]) ).
cnf(c_0_3251,plain,
( c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2341]) ).
cnf(c_0_3252,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2342]) ).
cnf(c_0_3253,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2343]) ).
cnf(c_0_3254,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(c_Finite__Set_Olinorder__class_OMax(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1)),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X3))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2344]) ).
cnf(c_0_3255,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(c_Finite__Set_Olinorder__class_OMin(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X2),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1)),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X3))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2345]) ).
cnf(c_0_3256,plain,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(c_Option_Ooption_OSome(X4),X6)
| hAPP(X2,X5) != hAPP(c_Option_Ooption_OSome(X4),X6) ),
inference(split_conjunct,[status(thm)],[c_0_2346]) ).
cnf(c_0_3257,plain,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(c_Option_Ooption_OSome(X4),X6)
| hAPP(X2,X5) != hAPP(c_Option_Ooption_OSome(X4),X6) ),
inference(split_conjunct,[status(thm)],[c_0_2347]) ).
cnf(c_0_3258,plain,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = c_Option_Ooption_ONone(X4)
| hAPP(X2,X5) != c_Option_Ooption_ONone(X4)
| hAPP(X1,X5) != c_Option_Ooption_ONone(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2348]) ).
cnf(c_0_3259,plain,
( c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) ),
inference(split_conjunct,[status(thm)],[c_0_2349]) ).
cnf(c_0_3260,plain,
( hAPP(hAPP(X3,X6),X5) = X5
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_2350]) ).
cnf(c_0_3261,plain,
( hAPP(hAPP(X3,X5),X6) = X5
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),X6)) ),
inference(split_conjunct,[status(thm)],[c_0_2351]) ).
cnf(c_0_3262,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2352]) ).
cnf(c_0_3263,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2353]) ).
cnf(c_0_3264,plain,
( hAPP(hAPP(X3,X5),hAPP(hAPP(X3,X5),X6)) = hAPP(hAPP(X3,X5),X6)
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2354]) ).
cnf(c_0_3265,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ c_Lattices_Olower__semilattice(X1,X4,X5,X6)
| hAPP(hAPP(X5,X2),X3) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_2355]) ).
cnf(c_0_3266,plain,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3),X4,X1) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_HOL_Ominus__class_Ominus(X2,X4,X1)),c_HOL_Ominus__class_Ominus(X3,X4,X1))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2356]) ).
cnf(c_0_3267,plain,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3),X4,X1) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_HOL_Ominus__class_Ominus(X2,X4,X1)),c_HOL_Ominus__class_Ominus(X3,X4,X1))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2357]) ).
cnf(c_0_3268,plain,
( hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2358]) ).
cnf(c_0_3269,plain,
( hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2359]) ).
cnf(c_0_3270,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2360]) ).
cnf(c_0_3271,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Map_Odom(X3,X1,X4)))
| hAPP(X3,X2) != c_Option_Ooption_ONone(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2361]) ).
cnf(c_0_3272,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2362]) ).
cnf(c_0_3273,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2363]) ).
cnf(c_0_3274,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X2))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2364]) ).
cnf(c_0_3275,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X3))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2365]) ).
cnf(c_0_3276,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X3))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2366]) ).
cnf(c_0_3277,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X2))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2367]) ).
cnf(c_0_3278,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2368]) ).
cnf(c_0_3279,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2369]) ).
cnf(c_0_3280,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Olordered__ab__group__add__join(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2370]) ).
cnf(c_0_3281,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2371]) ).
cnf(c_0_3282,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2372]) ).
cnf(c_0_3283,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2373]) ).
cnf(c_0_3284,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2374]) ).
cnf(c_0_3285,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2375]) ).
cnf(c_0_3286,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2376]) ).
cnf(c_0_3287,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2377]) ).
cnf(c_0_3288,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2378]) ).
cnf(c_0_3289,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) != X3 ),
inference(split_conjunct,[status(thm)],[c_0_2379]) ).
cnf(c_0_3290,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_HOL_Ozero__class_Ozero(X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_HOL_Ozero__class_Ozero(X2)),X1))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2380]) ).
cnf(c_0_3291,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_HOL_Ozero__class_Ozero(X2)),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_HOL_Ozero__class_Ozero(X2)),X3))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2381]) ).
cnf(c_0_3292,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X1,X2),c_ATP__Linkup_Osko__Finite__Set__Xfinite__nonempty__imp__fold1Set__1__1(X1,X3,X2)))
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2382]) ).
cnf(c_0_3293,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4))
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2383]) ).
cnf(c_0_3294,plain,
( c_HOL_Ominus__class_Ominus(c_Map_Odom(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X2),X4),X5),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Map_Odom(X1,X2,X3),X5,tc_fun(X2,tc_bool))
| hAPP(X1,X4) != c_Option_Ooption_ONone(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2384]) ).
cnf(c_0_3295,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4) ),
inference(split_conjunct,[status(thm)],[c_0_2385]) ).
cnf(c_0_3296,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool)) = X3 ),
inference(split_conjunct,[status(thm)],[c_0_2386]) ).
cnf(c_0_3297,plain,
( c_Finite__Set_Ofinite(X2,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ c_Finite__Set_Ofinite(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2387]) ).
cnf(c_0_3298,plain,
( c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2388]) ).
cnf(c_0_3299,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X1),X2),X4),X3,tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_HOL_Ominus__class_Ominus(X4,X3,tc_fun(X1,tc_bool))) ),
inference(split_conjunct,[status(thm)],[c_0_2389]) ).
cnf(c_0_3300,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_2390]) ).
cnf(c_0_3301,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2391]) ).
cnf(c_0_3302,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2392]) ).
cnf(c_0_3303,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2393]) ).
cnf(c_0_3304,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2394]) ).
cnf(c_0_3305,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2395]) ).
cnf(c_0_3306,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2396]) ).
cnf(c_0_3307,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2397]) ).
cnf(c_0_3308,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2398]) ).
cnf(c_0_3309,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2399]) ).
cnf(c_0_3310,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2400]) ).
cnf(c_0_3311,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2401]) ).
cnf(c_0_3312,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2402]) ).
cnf(c_0_3313,plain,
( c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_2403]) ).
cnf(c_0_3314,plain,
( c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_2404]) ).
cnf(c_0_3315,plain,
( c_Finite__Set_Osetprod(X1,X2,X3,X4) = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2))
| hAPP(X1,X5) != c_HOL_Ozero__class_Ozero(X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| ~ class_Ring__and__Field_Ono__zero__divisors(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2405]) ).
cnf(c_0_3316,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2406]) ).
cnf(c_0_3317,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2407]) ).
cnf(c_0_3318,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2408]) ).
cnf(c_0_3319,plain,
( c_Finite__Set_Osetprod(X1,X2,X3,X4) = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2))
| hAPP(X1,X5) != c_HOL_Ozero__class_Ozero(X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2409]) ).
cnf(c_0_3320,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X2),X2),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2410]) ).
cnf(c_0_3321,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Oab__semigroup__mult(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2411]) ).
cnf(c_0_3322,plain,
( hAPP(hAPP(X3,X5),X6) = hAPP(hAPP(X3,X6),X5)
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2412]) ).
cnf(c_0_3323,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1)),X3))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2413]) ).
cnf(c_0_3324,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(X3,X2,X1) != c_HOL_Ominus__class_Ominus(X5,X4,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2414]) ).
cnf(c_0_3325,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(X5,X4,X1) != c_HOL_Ominus__class_Ominus(X3,X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2415]) ).
cnf(c_0_3326,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2416]) ).
cnf(c_0_3327,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(X4,X5,X1) != c_HOL_Ominus__class_Ominus(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2417]) ).
cnf(c_0_3328,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2418]) ).
cnf(c_0_3329,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2419]) ).
cnf(c_0_3330,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2420]) ).
cnf(c_0_3331,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2421]) ).
cnf(c_0_3332,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2422]) ).
cnf(c_0_3333,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2423]) ).
cnf(c_0_3334,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2424]) ).
cnf(c_0_3335,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2425]) ).
cnf(c_0_3336,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),X4),X3))
| hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = hAPP(hAPP(X1,X4),hAPP(c_Finite__Set_Ofold1(X1,X2),X3))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2426]) ).
cnf(c_0_3337,plain,
( hAPP(hAPP(X3,X5),X5) = X5
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2427]) ).
cnf(c_0_3338,plain,
( hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,X1)),X2),X3),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(X2,v_x)),hAPP(X3,v_x))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2428]) ).
cnf(c_0_3339,plain,
( hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,X1)),X2),X3),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(X2,v_x)),hAPP(X3,v_x))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2429]) ).
cnf(c_0_3340,plain,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X1),X2),X4),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_2430]) ).
cnf(c_0_3341,plain,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_SetInterval_Oord__class_OlessThan(X2,X1),tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2431]) ).
cnf(c_0_3342,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2432]) ).
cnf(c_0_3343,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2433]) ).
cnf(c_0_3344,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2434]) ).
cnf(c_0_3345,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2435]) ).
cnf(c_0_3346,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2436]) ).
cnf(c_0_3347,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2437]) ).
cnf(c_0_3348,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2438]) ).
cnf(c_0_3349,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2439]) ).
cnf(c_0_3350,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2440]) ).
cnf(c_0_3351,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2441]) ).
cnf(c_0_3352,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2442]) ).
cnf(c_0_3353,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2443]) ).
cnf(c_0_3354,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2444]) ).
cnf(c_0_3355,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2445]) ).
cnf(c_0_3356,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2446]) ).
cnf(c_0_3357,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2447]) ).
cnf(c_0_3358,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2448]) ).
cnf(c_0_3359,plain,
( c_OrderedGroup_Oab__semigroup__idem__mult(X3,X4)
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2449]) ).
cnf(c_0_3360,plain,
( X2 = X4
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2450]) ).
cnf(c_0_3361,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2451]) ).
cnf(c_0_3362,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_Complete__Lattice_OInf__class_OInf(X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2452]) ).
cnf(c_0_3363,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X4)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2453]) ).
cnf(c_0_3364,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X2),X3),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2454]) ).
cnf(c_0_3365,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| hAPP(hAPP(c_Set_Oinsert(X3),X4),X1) != hAPP(hAPP(c_Set_Oinsert(X3),X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2455]) ).
cnf(c_0_3366,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_2456]) ).
cnf(c_0_3367,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2457]) ).
cnf(c_0_3368,plain,
( c_Finite__Set_Osetsum(c_COMBK(c_HOL_Ozero__class_Ozero(X1),X1,X2),X3,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2458]) ).
cnf(c_0_3369,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Map_Odom(X3,X1,X4)))
| hAPP(X3,X2) != hAPP(c_Option_Ooption_OSome(X4),X5) ),
inference(split_conjunct,[status(thm)],[c_0_2459]) ).
cnf(c_0_3370,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2460]) ).
cnf(c_0_3371,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord__class_OlessThan(X3,X1)))
| ~ class_HOL_Oord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2461]) ).
cnf(c_0_3372,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_2462]) ).
cnf(c_0_3373,plain,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = X1
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2463]) ).
cnf(c_0_3374,plain,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2464]) ).
cnf(c_0_3375,plain,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2465]) ).
cnf(c_0_3376,plain,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ hBOOL(hAPP(hAPP(X2,X5),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2466]) ).
cnf(c_0_3377,plain,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X5))
| ~ hBOOL(hAPP(hAPP(X2,X5),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2467]) ).
cnf(c_0_3378,plain,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ hBOOL(hAPP(hAPP(X1,X5),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2468]) ).
cnf(c_0_3379,plain,
( ~ hBOOL(hAPP(hAPP(X1,X2),X2))
| ~ c_Orderings_Olinorder(X3,X1,X4)
| ~ hBOOL(hAPP(hAPP(X3,X2),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2469]) ).
cnf(c_0_3380,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2470]) ).
cnf(c_0_3381,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2471]) ).
cnf(c_0_3382,plain,
( X3 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2472]) ).
cnf(c_0_3383,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2473]) ).
cnf(c_0_3384,plain,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2474]) ).
cnf(c_0_3385,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2475]) ).
cnf(c_0_3386,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2476]) ).
cnf(c_0_3387,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2477]) ).
cnf(c_0_3388,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2478]) ).
cnf(c_0_3389,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2479]) ).
cnf(c_0_3390,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2480]) ).
cnf(c_0_3391,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2481]) ).
cnf(c_0_3392,plain,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hBOOL(hAPP(hAPP(c_in(X4),X2),c_Map_Odom(X1,X4,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2482]) ).
cnf(c_0_3393,plain,
( X4 = X3
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2483]) ).
cnf(c_0_3394,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OlessThan(X2,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2484]) ).
cnf(c_0_3395,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X3),X4)),X5) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2485]) ).
cnf(c_0_3396,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = hAPP(hAPP(X1,X4),hAPP(c_Finite__Set_Ofold1(X1,X2),X3))
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2486]) ).
cnf(c_0_3397,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord__class_OlessThan(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_HOL_Oord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2487]) ).
cnf(c_0_3398,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Complete__Lattice_OSup__class_OSup(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2488]) ).
cnf(c_0_3399,plain,
( hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))) = X3
| ~ c_Orderings_Olinorder(X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_2489]) ).
cnf(c_0_3400,plain,
( X1 = X2
| hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) != hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) ),
inference(split_conjunct,[status(thm)],[c_0_2490]) ).
cnf(c_0_3401,plain,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X1),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2491]) ).
cnf(c_0_3402,plain,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2492]) ).
cnf(c_0_3403,plain,
( hAPP(hAPP(X1,X4),hAPP(hAPP(X1,X5),X6)) = hAPP(hAPP(X1,X5),hAPP(hAPP(X1,X4),X6))
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2493]) ).
cnf(c_0_3404,plain,
( c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2) = c_Finite__Set_Ocard(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2494]) ).
cnf(c_0_3405,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2495]) ).
cnf(c_0_3406,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2496]) ).
cnf(c_0_3407,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2497]) ).
cnf(c_0_3408,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2498]) ).
cnf(c_0_3409,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2499]) ).
cnf(c_0_3410,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2500]) ).
cnf(c_0_3411,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1)),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2501]) ).
cnf(c_0_3412,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1)),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2502]) ).
cnf(c_0_3413,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2503]) ).
cnf(c_0_3414,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2504]) ).
cnf(c_0_3415,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2505]) ).
cnf(c_0_3416,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2506]) ).
cnf(c_0_3417,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2507]) ).
cnf(c_0_3418,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2508]) ).
cnf(c_0_3419,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2509]) ).
cnf(c_0_3420,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2510]) ).
cnf(c_0_3421,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2511]) ).
cnf(c_0_3422,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2512]) ).
cnf(c_0_3423,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2513]) ).
cnf(c_0_3424,plain,
( c_Finite__Set_Osetsum(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2514]) ).
cnf(c_0_3425,plain,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2515]) ).
cnf(c_0_3426,plain,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2516]) ).
cnf(c_0_3427,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),c_Suc(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2517]) ).
cnf(c_0_3428,plain,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| X4 = X5
| ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_2518]) ).
cnf(c_0_3429,plain,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| X4 = X5
| ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_2519]) ).
cnf(c_0_3430,plain,
( c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2520]) ).
cnf(c_0_3431,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X1) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2521]) ).
cnf(c_0_3432,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2522]) ).
cnf(c_0_3433,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),hAPP(c_Finite__Set_Olattice__class_OInf__fin(X2),X1)) = X3
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Lattices_Olattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2523]) ).
cnf(c_0_3434,plain,
( X3 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2524]) ).
cnf(c_0_3435,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2525]) ).
cnf(c_0_3436,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2526]) ).
cnf(c_0_3437,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2527]) ).
cnf(c_0_3438,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2528]) ).
cnf(c_0_3439,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2529]) ).
cnf(c_0_3440,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2530]) ).
cnf(c_0_3441,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2531]) ).
cnf(c_0_3442,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X4),X1),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2532]) ).
cnf(c_0_3443,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2533]) ).
cnf(c_0_3444,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2534]) ).
cnf(c_0_3445,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2535]) ).
cnf(c_0_3446,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),c_Suc(X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2536]) ).
cnf(c_0_3447,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),c_Suc(X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2537]) ).
cnf(c_0_3448,plain,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2) = c_Suc(c_Finite__Set_Ocard(X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2538]) ).
cnf(c_0_3449,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X3) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2539]) ).
cnf(c_0_3450,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1))
| hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2540]) ).
cnf(c_0_3451,plain,
( c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Osetsum(X3,X1,X2,X4) = c_HOL_Ozero__class_Ozero(X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2541]) ).
cnf(c_0_3452,plain,
( c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Osetsum(X3,X1,X2,X4) = c_HOL_Ozero__class_Ozero(X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
inference(split_conjunct,[status(thm)],[c_0_2542]) ).
cnf(c_0_3453,plain,
( c_Suc(X1) = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2543]) ).
cnf(c_0_3454,plain,
( hAPP(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(t_a,X3)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(X1,v_x),hAPP(X2,v_x),X3)
| ~ class_HOL_Ominus(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2544]) ).
cnf(c_0_3455,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(c_Finite__Set_Olinorder__class_OMin(X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X2),X3),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2545]) ).
cnf(c_0_3456,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(c_Finite__Set_Olinorder__class_OMax(X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),X3),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2546]) ).
cnf(c_0_3457,plain,
( X3 = hAPP(c_Option_Ooption_OSome(X1),X2)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Option_Oset(X3,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2547]) ).
cnf(c_0_3458,plain,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Map_Odom(X3,X1,X4)) = c_Map_Odom(X3,X1,X4)
| hAPP(X3,X2) != hAPP(c_Option_Ooption_OSome(X4),X5) ),
inference(split_conjunct,[status(thm)],[c_0_2548]) ).
cnf(c_0_3459,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2549]) ).
cnf(c_0_3460,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| X2 = X1
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2550]) ).
cnf(c_0_3461,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_2551]) ).
cnf(c_0_3462,plain,
( hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5)) = hAPP(hAPP(X1,X4),hAPP(hAPP(X1,X3),X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2552]) ).
cnf(c_0_3463,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2553]) ).
cnf(c_0_3464,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2554]) ).
cnf(c_0_3465,plain,
( hBOOL(hAPP(hAPP(c_in(X3),X4),X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hAPP(hAPP(c_Set_Oinsert(X3),X4),X5) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2555]) ).
cnf(c_0_3466,plain,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| hBOOL(hAPP(hAPP(X2,X5),X4))
| X4 = X5
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2556]) ).
cnf(c_0_3467,plain,
( X4 = X5
| hBOOL(hAPP(hAPP(X2,X4),X5))
| hBOOL(hAPP(hAPP(X2,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2557]) ).
cnf(c_0_3468,plain,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| X4 = X5
| hBOOL(hAPP(hAPP(X2,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2558]) ).
cnf(c_0_3469,plain,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| hBOOL(hAPP(hAPP(X2,X5),X4))
| X5 = X4
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2559]) ).
cnf(c_0_3470,plain,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2560]) ).
cnf(c_0_3471,plain,
( hBOOL(hAPP(hAPP(X1,X4),X5))
| hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2561]) ).
cnf(c_0_3472,plain,
( hBOOL(hAPP(hAPP(X1,X4),X5))
| hBOOL(hAPP(hAPP(X2,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2562]) ).
cnf(c_0_3473,plain,
( hBOOL(hAPP(hAPP(X1,X4),X5))
| hBOOL(hAPP(hAPP(X2,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2563]) ).
cnf(c_0_3474,plain,
( hBOOL(hAPP(hAPP(X1,X2),X2))
| hBOOL(hAPP(hAPP(X3,X2),X2))
| ~ c_Orderings_Olinorder(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2564]) ).
cnf(c_0_3475,plain,
( hAPP(c_Finite__Set_Olinorder__class_OMin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2565]) ).
cnf(c_0_3476,plain,
( hAPP(c_Finite__Set_Olinorder__class_OMax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2566]) ).
cnf(c_0_3477,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2567]) ).
cnf(c_0_3478,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2568]) ).
cnf(c_0_3479,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2569]) ).
cnf(c_0_3480,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2570]) ).
cnf(c_0_3481,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X2) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2571]) ).
cnf(c_0_3482,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2572]) ).
cnf(c_0_3483,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2573]) ).
cnf(c_0_3484,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2574]) ).
cnf(c_0_3485,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2575]) ).
cnf(c_0_3486,plain,
( c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2576]) ).
cnf(c_0_3487,plain,
( c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2577]) ).
cnf(c_0_3488,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X4,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2578]) ).
cnf(c_0_3489,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X2),X1))
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2579]) ).
cnf(c_0_3490,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| X2 = X3
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2580]) ).
cnf(c_0_3491,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X2),X1))
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2581]) ).
cnf(c_0_3492,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2582]) ).
cnf(c_0_3493,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2583]) ).
cnf(c_0_3494,plain,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2584]) ).
cnf(c_0_3495,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2585]) ).
cnf(c_0_3496,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2586]) ).
cnf(c_0_3497,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2587]) ).
cnf(c_0_3498,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2588]) ).
cnf(c_0_3499,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2589]) ).
cnf(c_0_3500,plain,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X2,X4),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2590]) ).
cnf(c_0_3501,plain,
( ~ hBOOL(hAPP(hAPP(X1,X2),X2))
| ~ c_Orderings_Olinorder(X3,X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2591]) ).
cnf(c_0_3502,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2592]) ).
cnf(c_0_3503,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2593]) ).
cnf(c_0_3504,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2594]) ).
cnf(c_0_3505,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2595]) ).
cnf(c_0_3506,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2596]) ).
cnf(c_0_3507,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2597]) ).
cnf(c_0_3508,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2598]) ).
cnf(c_0_3509,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2599]) ).
cnf(c_0_3510,plain,
( c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Complete__Lattice_OSup__class_OSup(X3,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2600]) ).
cnf(c_0_3511,plain,
( c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Complete__Lattice_OInf__class_OInf(X3,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2601]) ).
cnf(c_0_3512,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2602]) ).
cnf(c_0_3513,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),c_Suc(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2603]) ).
cnf(c_0_3514,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2604]) ).
cnf(c_0_3515,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) != X3
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2605]) ).
cnf(c_0_3516,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) != X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2606]) ).
cnf(c_0_3517,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) != X3
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2607]) ).
cnf(c_0_3518,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) != X2
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2608]) ).
cnf(c_0_3519,plain,
( c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_2609]) ).
cnf(c_0_3520,plain,
( X1 = c_COMBK(c_Option_Ooption_ONone(X2),tc_Option_Ooption(X2),X3)
| c_Map_Odom(X1,X3,X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2610]) ).
cnf(c_0_3521,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2611]) ).
cnf(c_0_3522,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2612]) ).
cnf(c_0_3523,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2613]) ).
cnf(c_0_3524,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_2614]) ).
cnf(c_0_3525,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2615]) ).
cnf(c_0_3526,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2616]) ).
cnf(c_0_3527,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_2617]) ).
cnf(c_0_3528,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_2618]) ).
cnf(c_0_3529,plain,
( hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X3),X4)) = hAPP(hAPP(X1,X3),X4)
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2619]) ).
cnf(c_0_3530,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2620]) ).
cnf(c_0_3531,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2621]) ).
cnf(c_0_3532,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2622]) ).
cnf(c_0_3533,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2623]) ).
cnf(c_0_3534,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2624]) ).
cnf(c_0_3535,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2625]) ).
cnf(c_0_3536,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2626]) ).
cnf(c_0_3537,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,X2) = hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2627]) ).
cnf(c_0_3538,plain,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X3,X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2628]) ).
cnf(c_0_3539,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2629]) ).
cnf(c_0_3540,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2630]) ).
cnf(c_0_3541,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)) = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2631]) ).
cnf(c_0_3542,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)) = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2632]) ).
cnf(c_0_3543,plain,
( hBOOL(hAPP(hAPP(c_in(X3),X2),X1))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2633]) ).
cnf(c_0_3544,plain,
( X2 = X1
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2634]) ).
cnf(c_0_3545,plain,
( c_Hoare__Mirabelle_Ohoare__valids(X1,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2635]) ).
cnf(c_0_3546,plain,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2636]) ).
cnf(c_0_3547,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_Orderings_Obot__class_Obot(X1)),X2))
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2637]) ).
cnf(c_0_3548,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2638]) ).
cnf(c_0_3549,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2639]) ).
cnf(c_0_3550,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2640]) ).
cnf(c_0_3551,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2641]) ).
cnf(c_0_3552,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2642]) ).
cnf(c_0_3553,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2643]) ).
cnf(c_0_3554,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2644]) ).
cnf(c_0_3555,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2645]) ).
cnf(c_0_3556,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2646]) ).
cnf(c_0_3557,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2647]) ).
cnf(c_0_3558,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2648]) ).
cnf(c_0_3559,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2649]) ).
cnf(c_0_3560,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2650]) ).
cnf(c_0_3561,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2651]) ).
cnf(c_0_3562,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2652]) ).
cnf(c_0_3563,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2653]) ).
cnf(c_0_3564,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2654]) ).
cnf(c_0_3565,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2655]) ).
cnf(c_0_3566,plain,
( hAPP(hAPP(X1,X3),X4) = hAPP(hAPP(X1,X4),X3)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2656]) ).
cnf(c_0_3567,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2657]) ).
cnf(c_0_3568,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2658]) ).
cnf(c_0_3569,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2659]) ).
cnf(c_0_3570,plain,
( X1 = c_Orderings_Obot__class_Obot(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),X1) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2660]) ).
cnf(c_0_3571,plain,
( X1 = c_Orderings_Obot__class_Obot(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X1),X3) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2661]) ).
cnf(c_0_3572,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(c_Finite__Set_Olattice__class_OInf__fin(X2),X1) = c_Complete__Lattice_OInf__class_OInf(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2662]) ).
cnf(c_0_3573,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2663]) ).
cnf(c_0_3574,plain,
( c_Finite__Set_Ofun__left__comm(X1,X2,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2664]) ).
cnf(c_0_3575,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_2665]) ).
cnf(c_0_3576,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2666]) ).
cnf(c_0_3577,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2667]) ).
cnf(c_0_3578,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2668]) ).
cnf(c_0_3579,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2669]) ).
cnf(c_0_3580,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X2) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2670]) ).
cnf(c_0_3581,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2671]) ).
cnf(c_0_3582,plain,
( X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Ozero__class_Ozero(X2))
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2672]) ).
cnf(c_0_3583,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2673]) ).
cnf(c_0_3584,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2674]) ).
cnf(c_0_3585,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2675]) ).
cnf(c_0_3586,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2676]) ).
cnf(c_0_3587,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2677]) ).
cnf(c_0_3588,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2678]) ).
cnf(c_0_3589,plain,
( X1 = c_Option_Ooption_ONone(X2)
| c_Option_Oset(X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_2679]) ).
cnf(c_0_3590,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2680]) ).
cnf(c_0_3591,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2681]) ).
cnf(c_0_3592,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2682]) ).
cnf(c_0_3593,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2683]) ).
cnf(c_0_3594,plain,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2684]) ).
cnf(c_0_3595,plain,
( c_Finite__Set_Ofun__left__comm(c_HOL_Otimes__class_Otimes(X1),X1,X1)
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2685]) ).
cnf(c_0_3596,plain,
( c_Finite__Set_Ofun__left__comm(c_HOL_Oplus__class_Oplus(X1),X1,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2686]) ).
cnf(c_0_3597,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2687]) ).
cnf(c_0_3598,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2688]) ).
cnf(c_0_3599,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2689]) ).
cnf(c_0_3600,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Orderings_Obot__class_Obot(X1)) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2690]) ).
cnf(c_0_3601,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2691]) ).
cnf(c_0_3602,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2692]) ).
cnf(c_0_3603,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2693]) ).
cnf(c_0_3604,plain,
( X1 = X2
| hAPP(c_Option_Ooption_OSome(X3),X1) != hAPP(c_Option_Ooption_OSome(X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2694]) ).
cnf(c_0_3605,plain,
( hAPP(hAPP(X1,X3),X3) = X3
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2695]) ).
cnf(c_0_3606,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X2) = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2696]) ).
cnf(c_0_3607,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X2) = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2697]) ).
cnf(c_0_3608,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X2) = X2
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2698]) ).
cnf(c_0_3609,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2) = X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2699]) ).
cnf(c_0_3610,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X2) = X2
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2700]) ).
cnf(c_0_3611,plain,
( X1 = X2
| c_SetInterval_Oord__class_OlessThan(X1,X3) != c_SetInterval_Oord__class_OlessThan(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_2701]) ).
cnf(c_0_3612,plain,
( X1 = X2
| c_Com_Ocom_OSemi(X3,X1) != c_Com_Ocom_OSemi(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2702]) ).
cnf(c_0_3613,plain,
( X1 = X2
| c_Com_Ocom_OSemi(X1,X3) != c_Com_Ocom_OSemi(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_2703]) ).
cnf(c_0_3614,plain,
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2))
| ~ class_Finite__Set_Ofinite_Ofinite(X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2704]) ).
cnf(c_0_3615,plain,
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2705]) ).
cnf(c_0_3616,plain,
( class_Lattices_Oupper__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2706]) ).
cnf(c_0_3617,plain,
( class_Lattices_Olower__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2707]) ).
cnf(c_0_3618,plain,
( class_Lattices_Odistrib__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2708]) ).
cnf(c_0_3619,plain,
( class_Lattices_Obounded__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2709]) ).
cnf(c_0_3620,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2710]) ).
cnf(c_0_3621,plain,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2711]) ).
cnf(c_0_3622,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2712]) ).
cnf(c_0_3623,plain,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2713]) ).
cnf(c_0_3624,plain,
( class_HOL_Ominus(tc_fun(X2,X1))
| ~ class_HOL_Ominus(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2714]) ).
cnf(c_0_3625,plain,
( class_HOL_Oord(tc_fun(X2,X1))
| ~ class_HOL_Oord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2715]) ).
cnf(c_0_3626,plain,
( c_Finite__Set_Olattice__class_OInf__fin(X1) = c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X1),X1)
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2716]) ).
cnf(c_0_3627,plain,
( c_Finite__Set_Olinorder__class_OMax(X1) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2717]) ).
cnf(c_0_3628,plain,
( c_Finite__Set_Olinorder__class_OMin(X1) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2718]) ).
cnf(c_0_3629,plain,
( c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omin(X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2719]) ).
cnf(c_0_3630,plain,
( c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omax(X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2720]) ).
cnf(c_0_3631,plain,
( c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Oupper__semilattice__class_Osup(X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2721]) ).
cnf(c_0_3632,plain,
( c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Olower__semilattice__class_Oinf(X1),X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2722]) ).
cnf(c_0_3633,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1) = c_Orderings_Oord__class_Omax(X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2723]) ).
cnf(c_0_3634,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1) = c_Orderings_Oord__class_Omin(X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2724]) ).
cnf(c_0_3635,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2725]) ).
cnf(c_0_3636,plain,
( class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(X1))
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2726]) ).
cnf(c_0_3637,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2727]) ).
cnf(c_0_3638,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2728]) ).
cnf(c_0_3639,plain,
( X1 = X2
| c_Com_Ocom_OBODY(X1) != c_Com_Ocom_OBODY(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2729]) ).
cnf(c_0_3640,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_2730,
[final] ).
cnf(c_0_3641,plain,
( hAPP(hAPP(X6,X11),hAPP(X2,X10)) = c_Finite__Set_Ofold(X6,X11,X10,X9,X9)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ c_Finite__Set_Ofinite(X10,X9) ),
c_0_2731,
[final] ).
cnf(c_0_3642,plain,
( hAPP(hAPP(X5,X11),hAPP(X1,X10)) = c_Finite__Set_Ofold(X5,X11,X10,X9,X9)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ c_Finite__Set_Ofinite(X10,X9) ),
c_0_2732,
[final] ).
cnf(c_0_3643,plain,
( hAPP(X2,X10) = c_Finite__Set_Ofold(X6,X7,X10,X9,X9)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ c_Finite__Set_Ofinite(X10,X9) ),
c_0_2733,
[final] ).
cnf(c_0_3644,plain,
( hAPP(X1,X10) = c_Finite__Set_Ofold(X5,X8,X10,X9,X9)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ c_Finite__Set_Ofinite(X10,X9) ),
c_0_2734,
[final] ).
cnf(c_0_3645,plain,
( hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X9),X10),hAPP(hAPP(c_Set_Oinsert(X9),X11),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))))) = hAPP(hAPP(X5,X10),X11)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
c_0_2735,
[final] ).
cnf(c_0_3646,plain,
( hAPP(X2,hAPP(hAPP(c_Set_Oinsert(X9),X10),hAPP(hAPP(c_Set_Oinsert(X9),X11),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))))) = hAPP(hAPP(X6,X10),X11)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
c_0_2736,
[final] ).
cnf(c_0_3647,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_2737,
[final] ).
cnf(c_0_3648,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_2738,
[final] ).
cnf(c_0_3649,plain,
( hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X9),X10),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)))) = X10
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
c_0_2739,
[final] ).
cnf(c_0_3650,plain,
( hAPP(X2,hAPP(hAPP(c_Set_Oinsert(X9),X10),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)))) = X10
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
c_0_2740,
[final] ).
cnf(c_0_3651,plain,
( hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X9),X10),X11)) = hAPP(hAPP(X5,X10),hAPP(X1,X11))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
c_0_2741,
[final] ).
cnf(c_0_3652,plain,
( hAPP(X2,hAPP(hAPP(c_Set_Oinsert(X9),X10),X11)) = hAPP(hAPP(X6,X10),hAPP(X2,X11))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
c_0_2742,
[final] ).
cnf(c_0_3653,plain,
( X10 = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))
| c_Finite__Set_Olattice_OSup__fin(X6,X10,X9) = hAPP(X2,X10)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ c_Finite__Set_Ofinite(X10,X9) ),
c_0_2743,
[final] ).
cnf(c_0_3654,plain,
( X10 = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))
| c_Finite__Set_Olattice_OInf__fin(X5,X10,X9) = hAPP(X1,X10)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ c_Finite__Set_Ofinite(X10,X9) ),
c_0_2744,
[final] ).
cnf(c_0_3655,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_2745,
[final] ).
cnf(c_0_3656,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_2746,
[final] ).
cnf(c_0_3657,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X4,X3,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X1,X2,X3,X4)),tc_fun(tc_Com_Ostate,tc_bool),t_a),X4,c_COMBK(hAPP(X3,v_sko__Hoare__Mirabelle__Xescape__1(X1,X2,X3,X4)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
c_0_2747,
[final] ).
cnf(c_0_3658,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,c_HOL_Ozero__class_Ozero(X4),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X4,X2)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,c_HOL_Ozero__class_Ozero(X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X4,X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,c_HOL_Ozero__class_Ozero(X4),X1,X4,X2)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,c_HOL_Ozero__class_Ozero(X4),X3,X4,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
c_0_2748,
[final] ).
cnf(c_0_3659,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X1,X6,X5,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X6,X5,X3,X2,X4))) ),
c_0_2749,
[final] ).
cnf(c_0_3660,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X1,X6,X5,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X1,X6,X5,X3,X2,X4))) ),
c_0_2750,
[final] ).
cnf(c_0_3661,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X4,X1,X3)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X5,X1,X3)) = c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X5),X1,X3)
| ~ c_Finite__Set_Ofinite(X4,X3)
| ~ c_Finite__Set_Ofinite(X5,X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X5) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_2751,
[final] ).
cnf(c_0_3662,plain,
( hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X1,X6,X7,X3,X2,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X7,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X1,X6,X7,X3))) ),
c_0_2752,
[final] ).
cnf(c_0_3663,plain,
( hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X6,X7,X3,X2,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X7,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X1,X6,X7,X3))) ),
c_0_2753,
[final] ).
cnf(c_0_3664,plain,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,X6,hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X4,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(X5,X3)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,X6,X1,X4,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
c_0_2754,
[final] ).
cnf(c_0_3665,plain,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(X4),X5,X6,hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X4,X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),hAPP(X5,X3)),c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(X4),X5,X6,X1,X4,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Oab__semigroup__mult(X4) ),
c_0_2755,
[final] ).
cnf(c_0_3666,plain,
( hBOOL(hAPP(hAPP(c_in(X4),X5),X3))
| c_Finite__Set_Ofold__image(X1,X6,X7,hAPP(hAPP(c_Set_Oinsert(X4),X5),X3),X2,X4) = hAPP(hAPP(X1,hAPP(X6,X5)),c_Finite__Set_Ofold__image(X1,X6,X7,X3,X2,X4))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X4) ),
c_0_2756,
[final] ).
cnf(c_0_3667,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X1,X1),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X3))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_2757,
[final] ).
cnf(c_0_3668,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X1,X1),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X2,X3,X1,X1),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X3))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
c_0_2758,
[final] ).
cnf(c_0_3669,plain,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X4))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X6,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool))),X2,X2),X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X3,X4,X2,X2),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X6),X4)) ),
c_0_2759,
[final] ).
cnf(c_0_3670,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),X6)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X4)),X5)),X6))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
c_0_2760,
[final] ).
cnf(c_0_3671,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),X6)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X4)),X5)),X6))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
c_0_2761,
[final] ).
cnf(c_0_3672,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,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool)),X6,X1,X7) ),
c_0_2762,
[final] ).
cnf(c_0_3673,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X6),hAPP(hAPP(X1,X5),X7)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))),tc_fun(X4,tc_bool)),X4,X6),X7))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X5),X3)) ),
c_0_2763,
[final] ).
cnf(c_0_3674,plain,
( X7 = X6
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X4,X5,X2,X3),X6))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X4,X5,X2,X3),X7)) ),
c_0_2764,
[final] ).
cnf(c_0_3675,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2)),c_Finite__Set_Ocard(X1,X2)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),X1)) ),
c_0_2765,
[final] ).
cnf(c_0_3676,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X2,X5,X1)),X3)),X4)),X6))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
c_0_2766,
[final] ).
cnf(c_0_3677,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X2,X5,X1)),X3)),X4)),X6))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
c_0_2767,
[final] ).
cnf(c_0_3678,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1,X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X4)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X2,X3,X1,X1),X4))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
c_0_2768,
[final] ).
cnf(c_0_3679,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1,X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X4)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_2769,
[final] ).
cnf(c_0_3680,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,hAPP(hAPP(c_Set_Oinsert(X3),X4),X5),X3,X6),hAPP(hAPP(X1,X4),X7)))
| hBOOL(hAPP(hAPP(c_in(X3),X4),X5))
| ~ c_Finite__Set_Ofun__left__comm(X1,X3,X6)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X5,X3,X6),X7)) ),
c_0_2770,
[final] ).
cnf(c_0_3681,plain,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X4))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X6,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),X2,X2),hAPP(hAPP(X1,X6),X5)))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X3,X4,X2,X2),X5)) ),
c_0_2771,
[final] ).
cnf(c_0_3682,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1,X6),hAPP(hAPP(X4,X2),X7)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X5,X3,X1,X6),X7)) ),
c_0_2772,
[final] ).
cnf(c_0_3683,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),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))) ),
c_0_2773,
[final] ).
cnf(c_0_3684,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq12__1(X6,X2,X5,X4)),v_sko__Hoare__Mirabelle__Xconseq12__3(X6,X2,X5,X4))) ),
c_0_2774,
[final] ).
cnf(c_0_3685,plain,
( hBOOL(hAPP(hAPP(X1,c_Finite__Set_Ofold(X3,X7,X5,X4,X4)),hAPP(hAPP(X3,X6),X7)))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ c_Finite__Set_Ofinite(X5,X4)
| ~ hBOOL(hAPP(hAPP(c_in(X4),X6),X5)) ),
c_0_2775,
[final] ).
cnf(c_0_3686,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)),X6)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X3,X4,X1)),X5)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
c_0_2776,
[final] ).
cnf(c_0_3687,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)),X6)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X3,X4,X1)),X5)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
c_0_2777,
[final] ).
cnf(c_0_3688,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X5,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Com_Ocom_OBODY(X3),X4,X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool))),X1)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Com_Ocom_OBODY(X3),X4,X1)),X5),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Option_Othe(hAPP(c_Com_Obody,X3),tc_Com_Ocom),X4,X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool))),X1) ),
c_0_2778,
[final] ).
cnf(c_0_3689,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X2),c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X2),X4,X1,X2,X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Lattices_Olower__semilattice(X2) ),
c_0_2779,
[final] ).
cnf(c_0_3690,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Com_Ocom_OSemi(X4,X6),X7,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X5,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X6,X7,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
c_0_2780,
[final] ).
cnf(c_0_3691,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X5,X2,X1)),X3)),X6)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
c_0_2781,
[final] ).
cnf(c_0_3692,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X5,X2,X1)),X3)),X6)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
c_0_2782,
[final] ).
cnf(c_0_3693,plain,
( c_Finite__Set_Ofold(X1,X4,X5,X2,X3) = X6
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X4,X5,X2,X3),X6)) ),
c_0_2783,
[final] ).
cnf(c_0_3694,plain,
( hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq12__1(X5,X2,X6,X4)),v_sko__Hoare__Mirabelle__Xconseq12__2(X5,X2,X6,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X6,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
c_0_2784,
[final] ).
cnf(c_0_3695,plain,
( hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xconseq12__3(X6,X2,X7,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X7,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xconseq12__2(X6,X2,X7,X4))) ),
c_0_2785,
[final] ).
cnf(c_0_3696,plain,
( hBOOL(hAPP(hAPP(c_in(X4),X2),X3))
| hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X4),X5))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X4),X5)) ),
c_0_2786,
[final] ).
cnf(c_0_3697,plain,
( X5 = X2
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X4),X5)) ),
c_0_2787,
[final] ).
cnf(c_0_3698,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Option_Ooption_Ooption__case(X4,X2,hAPP(c_Option_Ooption_OSome(t_b),X3),t_a,t_b))) ),
c_0_2788,
[final] ).
cnf(c_0_3699,plain,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Option_Ooption_Ooption__case(X4,X2,hAPP(c_Option_Ooption_OSome(t_b),X3),t_a,t_b))) ),
c_0_2789,
[final] ).
cnf(c_0_3700,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Option_Ooption_Ooption__case(X2,X3,c_Option_Ooption_ONone(t_b),t_a,t_b))) ),
c_0_2790,
[final] ).
cnf(c_0_3701,plain,
( c_Finite__Set_Ofinite(X3,X4)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),X6)) ),
c_0_2791,
[final] ).
cnf(c_0_3702,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),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)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
c_0_2792,
[final] ).
cnf(c_0_3703,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_2793,
[final] ).
cnf(c_0_3704,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Com_Ocom_OBODY(X4),X5,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Option_Othe(hAPP(c_Com_Obody,X4),tc_Com_Ocom),X5,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
c_0_2794,
[final] ).
cnf(c_0_3705,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X1,X3,tc_Com_Ostate)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X1,X3,tc_Com_Ostate)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))),tc_Com_Ostate) ),
c_0_2795,
[final] ).
cnf(c_0_3706,plain,
( c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X3,c_HOL_Ozero__class_Ozero(X4),X1,X4,X2) = c_Finite__Set_Osetsum(X3,X1,X2,X4)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
c_0_2796,
[final] ).
cnf(c_0_3707,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xconseq1__1(X5,X2)),v_sko__Hoare__Mirabelle__Xconseq1__2(X5,X2))) ),
c_0_2797,
[final] ).
cnf(c_0_3708,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq2__1(X5,X4)),v_sko__Hoare__Mirabelle__Xconseq2__2(X5,X4))) ),
c_0_2798,
[final] ).
cnf(c_0_3709,plain,
( hBOOL(hAPP(hAPP(X4,v_sko__Hoare__Mirabelle__Xconseq2__1(X5,X4)),v_sko__Hoare__Mirabelle__Xconseq2__2(X5,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
c_0_2799,
[final] ).
cnf(c_0_3710,plain,
( hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq1__1(X5,X2)),v_sko__Hoare__Mirabelle__Xconseq1__2(X5,X2)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
c_0_2800,
[final] ).
cnf(c_0_3711,plain,
( c_Fun_Ofun__upd(c_Map_Orestrict__map(X4,c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool)),X1,X6),X2,X5,X1,tc_Option_Ooption(X6)) = c_Map_Orestrict__map(c_Fun_Ofun__upd(X4,X2,X5,X1,tc_Option_Ooption(X6)),X3,X1,X6)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_2801,
[final] ).
cnf(c_0_3712,plain,
( c_Map_Omap__le(c_Fun_Ofun__upd(X1,X5,c_Option_Ooption_ONone(X4),X3,tc_Option_Ooption(X4)),c_Fun_Ofun__upd(X2,X5,hAPP(c_Option_Ooption_OSome(X4),X6),X3,tc_Option_Ooption(X4)),X3,X4)
| ~ c_Map_Omap__le(X1,X2,X3,X4) ),
c_0_2802,
[final] ).
cnf(c_0_3713,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),X4)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X2),X4,X1,X2,X2)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Lattices_Oupper__semilattice(X2) ),
c_0_2803,
[final] ).
cnf(c_0_3714,plain,
( c_Map_Omap__le(c_Fun_Ofun__upd(X1,X5,X6,X3,tc_Option_Ooption(X4)),c_Fun_Ofun__upd(X2,X5,X6,X3,tc_Option_Ooption(X4)),X3,X4)
| ~ c_Map_Omap__le(X1,X2,X3,X4) ),
c_0_2804,
[final] ).
cnf(c_0_3715,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
c_0_2805,
[final] ).
cnf(c_0_3716,plain,
( hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X2,X1,X3,X4)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X2,X1,X3,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X4,X3,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
c_0_2806,
[final] ).
cnf(c_0_3717,plain,
( hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X2,X1,X3,X4)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X2,X1,X3,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X4,X3,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
c_0_2807,
[final] ).
cnf(c_0_3718,plain,
( hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xescape__1(X2,X1,X3,X4)),v_sko__Hoare__Mirabelle__Xescape__2(X2,X1,X3,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X4,X3,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
c_0_2808,
[final] ).
cnf(c_0_3719,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2)) ),
c_0_2809,
[final] ).
cnf(c_0_3720,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3)) ),
c_0_2810,
[final] ).
cnf(c_0_3721,plain,
( hAPP(hAPP(X1,X5),c_Finite__Set_Ofold(X1,X6,c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X2),X5),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X3)) = c_Finite__Set_Ofold(X1,X6,X4,X2,X3)
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| ~ c_Finite__Set_Ofinite(X4,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X5),X4)) ),
c_0_2811,
[final] ).
cnf(c_0_3722,plain,
( hAPP(hAPP(X1,X6),c_Finite__Set_Ofold(X1,X5,c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X3)) = c_Finite__Set_Ofold(X1,X5,hAPP(hAPP(c_Set_Oinsert(X2),X6),X4),X2,X3)
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| ~ c_Finite__Set_Ofinite(X4,X2) ),
c_0_2812,
[final] ).
cnf(c_0_3723,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2)),c_Finite__Set_Ocard(X1,X2)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1)) ),
c_0_2813,
[final] ).
cnf(c_0_3724,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
c_0_2814,
[final] ).
cnf(c_0_3725,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Finite__Set_Osetsum(X5,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2,X4)),c_Finite__Set_Osetsum(X5,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2,X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Finite__Set_Osetsum(X5,X1,X2,X4)),c_Finite__Set_Osetsum(X5,X3,X2,X4))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
c_0_2815,
[final] ).
cnf(c_0_3726,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),c_Finite__Set_Osetprod(X5,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2,X4)),c_Finite__Set_Osetprod(X5,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2,X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),c_Finite__Set_Osetprod(X5,X1,X2,X4)),c_Finite__Set_Osetprod(X5,X3,X2,X4))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X4) ),
c_0_2816,
[final] ).
cnf(c_0_3727,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Map_Odom(X3,X1,X4)))
| c_Fun_Ofun__upd(c_Map_Omap__add(X5,X3,X1,X4),X2,hAPP(c_Option_Ooption_OSome(X4),X6),X1,tc_Option_Ooption(X4)) = c_Map_Omap__add(c_Fun_Ofun__upd(X5,X2,hAPP(c_Option_Ooption_OSome(X4),X6),X1,tc_Option_Ooption(X4)),X3,X1,X4) ),
c_0_2817,
[final] ).
cnf(c_0_3728,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
c_0_2818,
[final] ).
cnf(c_0_3729,plain,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_Finite__Set_Osetsum(X4,X1,X2,X5)),c_Finite__Set_Osetsum(X4,X3,X2,X5)),c_Finite__Set_Osetsum(X4,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2,X5),X5) = c_Finite__Set_Osetsum(X4,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_OrderedGroup_Oab__group__add(X5) ),
c_0_2819,
[final] ).
cnf(c_0_3730,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),hAPP(c_Finite__Set_Ofold1(X1,X2),X3)),X3))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),hAPP(hAPP(X1,c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1(X1,X2)),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2(X1,X2))),hAPP(hAPP(c_Set_Oinsert(X2),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1(X1,X2)),hAPP(hAPP(c_Set_Oinsert(X2),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2(X1,X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))))) ),
c_0_2820,
[final] ).
cnf(c_0_3731,plain,
( c_Fun_Ofun__upd(c_Map_Orestrict__map(X4,c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool)),X1,X5),X2,X6,X1,tc_Option_Ooption(X5)) = c_Fun_Ofun__upd(c_Map_Orestrict__map(X4,X3,X1,X5),X2,X6,X1,tc_Option_Ooption(X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_2821,
[final] ).
cnf(c_0_3732,plain,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3))),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_2822,
[final] ).
cnf(c_0_3733,plain,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3))),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_2823,
[final] ).
cnf(c_0_3734,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3))),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_2824,
[final] ).
cnf(c_0_3735,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X2)) ),
c_0_2825,
[final] ).
cnf(c_0_3736,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X2)) ),
c_0_2826,
[final] ).
cnf(c_0_3737,plain,
( c_Finite__Set_Ofold(X3,X6,hAPP(hAPP(c_Set_Oinsert(X4),X7),X5),X4,X4) = hAPP(hAPP(X3,X7),c_Finite__Set_Ofold(X3,X6,X5,X4,X4))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ c_Finite__Set_Ofinite(X5,X4) ),
c_0_2827,
[final] ).
cnf(c_0_3738,plain,
( X1 = X2
| hAPP(X3,X4) = hAPP(c_Option_Ooption_OSome(X5),X2)
| hAPP(c_Fun_Ofun__upd(X3,X6,hAPP(c_Option_Ooption_OSome(X5),X1),X7,tc_Option_Ooption(X5)),X4) != hAPP(c_Option_Ooption_OSome(X5),X2) ),
c_0_2828,
[final] ).
cnf(c_0_3739,plain,
( X1 = X2
| hAPP(X3,X1) = hAPP(c_Option_Ooption_OSome(X4),X5)
| hAPP(c_Fun_Ofun__upd(X3,X2,hAPP(c_Option_Ooption_OSome(X4),X6),X7,tc_Option_Ooption(X4)),X1) != hAPP(c_Option_Ooption_OSome(X4),X5) ),
c_0_2829,
[final] ).
cnf(c_0_3740,plain,
( X4 = X6
| hAPP(c_Fun_Ofun__upd(X1,X2,hAPP(c_Option_Ooption_OSome(X3),X4),X5,tc_Option_Ooption(X3)),X2) != hAPP(c_Option_Ooption_OSome(X3),X6) ),
c_0_2830,
[final] ).
cnf(c_0_3741,plain,
( hBOOL(hAPP(hAPP(c_in(X2),X5),X4))
| c_Finite__Set_Ofold(X1,X6,hAPP(hAPP(c_Set_Oinsert(X2),X5),X4),X2,X3) = hAPP(hAPP(X1,X5),c_Finite__Set_Ofold(X1,X6,X4,X2,X3))
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| ~ c_Finite__Set_Ofinite(X4,X2) ),
c_0_2831,
[final] ).
cnf(c_0_3742,plain,
( X1 = X2
| c_Fun_Ofun__upd(X3,X4,hAPP(c_Option_Ooption_OSome(X5),X1),X6,tc_Option_Ooption(X5)) != c_Fun_Ofun__upd(X7,X4,hAPP(c_Option_Ooption_OSome(X5),X2),X6,tc_Option_Ooption(X5)) ),
c_0_2832,
[final] ).
cnf(c_0_3743,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)))),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_2833,
[final] ).
cnf(c_0_3744,plain,
( c_Finite__Set_Ofold(X1,hAPP(hAPP(X1,X5),X6),X4,X2,X3) = hAPP(hAPP(X1,X5),c_Finite__Set_Ofold(X1,X6,X4,X2,X3))
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| ~ c_Finite__Set_Ofinite(X4,X2) ),
c_0_2834,
[final] ).
cnf(c_0_3745,plain,
( c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X2),X3,hAPP(hAPP(c_Set_Oinsert(X2),X4),X1),X2,X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X4),c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X2),X3,X1,X2,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
c_0_2835,
[final] ).
cnf(c_0_3746,plain,
( c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X2),X3,hAPP(hAPP(c_Set_Oinsert(X2),X4),X1),X2,X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X4),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X2),X3,X1,X2,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2) ),
c_0_2836,
[final] ).
cnf(c_0_3747,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),c_Set_Ovimage(X5,X2,X4,X1)),c_Set_Ovimage(X5,X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
c_0_2837,
[final] ).
cnf(c_0_3748,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X3),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X2)) ),
c_0_2838,
[final] ).
cnf(c_0_3749,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))))
| ~ class_Lattices_Olattice(X1) ),
c_0_2839,
[final] ).
cnf(c_0_3750,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))))
| ~ class_Orderings_Olinorder(X1) ),
c_0_2840,
[final] ).
cnf(c_0_3751,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X2)) ),
c_0_2841,
[final] ).
cnf(c_0_3752,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)))))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_2842,
[final] ).
cnf(c_0_3753,plain,
( hAPP(X3,X2) = X5
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Ovimage(X3,hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))),X1,X4))) ),
c_0_2843,
[final] ).
cnf(c_0_3754,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Map_Orestrict__map(c_Fun_Ofun__upd(X4,X2,X5,X1,tc_Option_Ooption(X6)),X3,X1,X6) = c_Map_Orestrict__map(X4,X3,X1,X6) ),
c_0_2844,
[final] ).
cnf(c_0_3755,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X5)) ),
c_0_2845,
[final] ).
cnf(c_0_3756,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X5)) ),
c_0_2846,
[final] ).
cnf(c_0_3757,plain,
( hBOOL(hAPP(hAPP(c_in(X2),X5),X4))
| c_Finite__Set_Ofold(X1,X6,hAPP(hAPP(c_Set_Oinsert(X2),X5),X4),X2,X3) = c_Finite__Set_Ofold(X1,hAPP(hAPP(X1,X5),X6),X4,X2,X3)
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| ~ c_Finite__Set_Ofinite(X4,X2) ),
c_0_2847,
[final] ).
cnf(c_0_3758,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4))))
| ~ class_Lattices_Olattice(X1) ),
c_0_2848,
[final] ).
cnf(c_0_3759,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4))))
| ~ class_Orderings_Olinorder(X1) ),
c_0_2849,
[final] ).
cnf(c_0_3760,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X4,X2,X1)),X3)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),X5)
| ~ class_Ring__and__Field_Oring(X1) ),
c_0_2850,
[final] ).
cnf(c_0_3761,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X2,X5,X1)),X3)),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Oring(X1) ),
c_0_2851,
[final] ).
cnf(c_0_3762,plain,
( c_Fun_Ofun__upd(c_Map_Orestrict__map(X4,X3,X1,X5),X2,c_Option_Ooption_ONone(X5),X1,tc_Option_Ooption(X5)) = c_Map_Orestrict__map(X4,c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool)),X1,X5)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_2852,
[final] ).
cnf(c_0_3763,plain,
( c_Map_Omap__le(c_Map_Omap__add(X1,X5,X3,X4),X2,X3,X4)
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| ~ c_Map_Omap__le(X5,X2,X3,X4)
| ~ c_Map_Omap__le(X1,c_Map_Omap__add(X1,X5,X3,X4),X3,X4) ),
c_0_2853,
[final] ).
cnf(c_0_3764,plain,
( X1 = c_Option_Ooption_ONone(X2)
| c_Map_Odom(c_Fun_Ofun__upd(X3,X4,X1,X5,tc_Option_Ooption(X2)),X5,X2) = hAPP(hAPP(c_Set_Oinsert(X5),X4),c_Map_Odom(X3,X5,X2)) ),
c_0_2854,
[final] ).
cnf(c_0_3765,plain,
( hAPP(c_Fun_Ofun__upd(X1,X2,hAPP(c_Option_Ooption_OSome(X3),X4),X5,tc_Option_Ooption(X3)),X6) = hAPP(c_Option_Ooption_OSome(X3),X7)
| X6 = X2
| hAPP(X1,X6) != hAPP(c_Option_Ooption_OSome(X3),X7) ),
c_0_2855,
[final] ).
cnf(c_0_3766,plain,
( hBOOL(hAPP(hAPP(c_in(X1),c_Map_Osko__Map__Xmap__le__def__1__1(X2,X3,X1,X4)),c_Map_Odom(X2,X1,X4)))
| c_Map_Omap__le(X2,X3,X1,X4) ),
c_0_2856,
[final] ).
cnf(c_0_3767,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),X4)) ),
c_0_2857,
[final] ).
cnf(c_0_3768,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),X4)) ),
c_0_2858,
[final] ).
cnf(c_0_3769,plain,
( X1 = X2
| hAPP(c_Fun_Ofun__upd(X3,X2,X4,X5,X6),X1) = hAPP(X3,X1) ),
c_0_2859,
[final] ).
cnf(c_0_3770,plain,
( X1 = X2
| hAPP(c_Fun_Ofun__upd(X3,X2,X4,X5,X6),X1) = hAPP(X3,X1) ),
c_0_2860,
[final] ).
cnf(c_0_3771,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_Finite__Set_Osetsum(X1,X3,X2,X5)),c_Finite__Set_Osetsum(X1,X4,X2,X5)) = c_Finite__Set_Osetsum(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X4,X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_OrderedGroup_Ocomm__monoid__add(X5) ),
c_0_2861,
[final] ).
cnf(c_0_3772,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Finite__Set_Osetprod(X1,X3,X2,X5)),c_Finite__Set_Osetprod(X1,X4,X2,X5)) = c_Finite__Set_Osetprod(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X4,X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_OrderedGroup_Ocomm__monoid__mult(X5) ),
c_0_2862,
[final] ).
cnf(c_0_3773,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3)) ),
c_0_2863,
[final] ).
cnf(c_0_3774,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3)) ),
c_0_2864,
[final] ).
cnf(c_0_3775,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool))),X4)) ),
c_0_2865,
[final] ).
cnf(c_0_3776,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4))) ),
c_0_2866,
[final] ).
cnf(c_0_3777,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(X4,X3)),c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X5)) = c_Finite__Set_Osetsum(X4,X1,X2,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X5) ),
c_0_2867,
[final] ).
cnf(c_0_3778,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X1,tc_bool))),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X5)) ),
c_0_2868,
[final] ).
cnf(c_0_3779,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)),X2) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X4),X2)) ),
c_0_2869,
[final] ).
cnf(c_0_3780,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Fun_Ofun__upd(c_Map_Orestrict__map(X4,X3,X1,X5),X2,c_Option_Ooption_ONone(X5),X1,tc_Option_Ooption(X5)) = c_Map_Orestrict__map(X4,X3,X1,X5) ),
c_0_2870,
[final] ).
cnf(c_0_3781,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_2871,
[final] ).
cnf(c_0_3782,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_2872,
[final] ).
cnf(c_0_3783,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X4)),X5) = X6
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X5) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),X6)
| ~ class_Ring__and__Field_Oring(X1) ),
c_0_2873,
[final] ).
cnf(c_0_3784,plain,
( X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),c_HOL_Ominus__class_Ominus(X3,X4,X2)),X5)),X6)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X4),X5)),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X5)),X6)
| ~ class_Ring__and__Field_Oring(X2) ),
c_0_2874,
[final] ).
cnf(c_0_3785,plain,
( c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),c_Finite__Set_Osetsum(X4,X3,X2,X5),X5) = c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X1))
| ~ class_OrderedGroup_Oab__group__add(X5) ),
c_0_2875,
[final] ).
cnf(c_0_3786,plain,
( hAPP(X1,X2) = X3
| c_Fun_Ofun__upd(X1,X2,X3,X4,X5) != X1 ),
c_0_2876,
[final] ).
cnf(c_0_3787,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
c_0_2877,
[final] ).
cnf(c_0_3788,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)),X5)
| ~ class_Ring__and__Field_Osemiring(X1) ),
c_0_2878,
[final] ).
cnf(c_0_3789,plain,
( c_Map_Omap__le(X1,X2,X3,X4)
| hAPP(X1,c_Map_Osko__Map__Xmap__le__def__1__1(X1,X2,X3,X4)) != hAPP(X2,c_Map_Osko__Map__Xmap__le__def__1__1(X1,X2,X3,X4)) ),
c_0_2879,
[final] ).
cnf(c_0_3790,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
c_0_2880,
[final] ).
cnf(c_0_3791,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
c_0_2881,
[final] ).
cnf(c_0_3792,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_2882,
[final] ).
cnf(c_0_3793,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
c_0_2883,
[final] ).
cnf(c_0_3794,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
c_0_2884,
[final] ).
cnf(c_0_3795,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
c_0_2885,
[final] ).
cnf(c_0_3796,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
c_0_2886,
[final] ).
cnf(c_0_3797,plain,
( X3 = X4
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2),X4)) ),
c_0_2887,
[final] ).
cnf(c_0_3798,plain,
( hBOOL(hAPP(X2,hAPP(X1,X5)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X1,X2,X3,X4),X5)) ),
c_0_2888,
[final] ).
cnf(c_0_3799,plain,
( c_Map_Omap__add(X1,X2,X3,X4) = c_Map_Omap__add(X2,X1,X3,X4)
| ~ c_Map_Omap__le(X1,c_Map_Omap__add(X1,X2,X3,X4),X3,X4) ),
c_0_2889,
[final] ).
cnf(c_0_3800,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4))) ),
c_0_2890,
[final] ).
cnf(c_0_3801,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4))) ),
c_0_2891,
[final] ).
cnf(c_0_3802,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X5))
| ~ class_Orderings_Oorder(X1) ),
c_0_2892,
[final] ).
cnf(c_0_3803,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X5))
| ~ class_Orderings_Oorder(X1) ),
c_0_2893,
[final] ).
cnf(c_0_3804,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
c_0_2894,
[final] ).
cnf(c_0_3805,plain,
( c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X5) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),hAPP(X4,X3),X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Ring__and__Field_Oring(X5) ),
c_0_2895,
[final] ).
cnf(c_0_3806,plain,
( c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X5) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),hAPP(X4,X3),X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_OrderedGroup_Oab__group__add(X5) ),
c_0_2896,
[final] ).
cnf(c_0_3807,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ class_Orderings_Oorder(X1) ),
c_0_2897,
[final] ).
cnf(c_0_3808,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),c_HOL_Ozero__class_Ozero(X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3))))
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_2898,
[final] ).
cnf(c_0_3809,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),c_HOL_Ozero__class_Ozero(X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1))))
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_2899,
[final] ).
cnf(c_0_3810,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3))))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_2900,
[final] ).
cnf(c_0_3811,plain,
( c_Map_Omap__le(X1,c_Map_Omap__add(X1,X2,X3,X4),X3,X4)
| c_Map_Omap__add(X1,X2,X3,X4) != c_Map_Omap__add(X2,X1,X3,X4) ),
c_0_2901,
[final] ).
cnf(c_0_3812,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X4),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
c_0_2902,
[final] ).
cnf(c_0_3813,plain,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(X2),X3,X1,X2,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Oab__semigroup__mult(X2) ),
c_0_2903,
[final] ).
cnf(c_0_3814,plain,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = c_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(X2),X3,X1,X2,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
c_0_2904,
[final] ).
cnf(c_0_3815,plain,
( hBOOL(hAPP(hAPP(c_in(X2),X4),X3))
| hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = c_Finite__Set_Ofold(X1,X4,X3,X2,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
c_0_2905,
[final] ).
cnf(c_0_3816,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_2906,
[final] ).
cnf(c_0_3817,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_2907,
[final] ).
cnf(c_0_3818,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_2908,
[final] ).
cnf(c_0_3819,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_2909,
[final] ).
cnf(c_0_3820,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Opordered__semiring(X1) ),
c_0_2910,
[final] ).
cnf(c_0_3821,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Opordered__semiring(X1) ),
c_0_2911,
[final] ).
cnf(c_0_3822,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__semiring(X1) ),
c_0_2912,
[final] ).
cnf(c_0_3823,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__semiring(X1) ),
c_0_2913,
[final] ).
cnf(c_0_3824,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_2914,
[final] ).
cnf(c_0_3825,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_2915,
[final] ).
cnf(c_0_3826,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_2916,
[final] ).
cnf(c_0_3827,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_2917,
[final] ).
cnf(c_0_3828,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_2918,
[final] ).
cnf(c_0_3829,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_2919,
[final] ).
cnf(c_0_3830,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_2920,
[final] ).
cnf(c_0_3831,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_2921,
[final] ).
cnf(c_0_3832,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_2922,
[final] ).
cnf(c_0_3833,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_2923,
[final] ).
cnf(c_0_3834,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_2924,
[final] ).
cnf(c_0_3835,plain,
( c_Map_Omap__le(X2,X5,X3,X4)
| ~ c_Map_Omap__le(c_Map_Omap__add(X1,X2,X3,X4),X5,X3,X4) ),
c_0_2925,
[final] ).
cnf(c_0_3836,plain,
( c_Finite__Set_Ofold(c_Set_Oinsert(X2),X3,X1,X2,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_2926,
[final] ).
cnf(c_0_3837,plain,
( hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(X2),X3,X1,X2,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
c_0_2927,
[final] ).
cnf(c_0_3838,plain,
( hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = c_Finite__Set_Ofold(X1,X4,X3,X2,X2)
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
c_0_2928,
[final] ).
cnf(c_0_3839,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_2929,
[final] ).
cnf(c_0_3840,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_2930,
[final] ).
cnf(c_0_3841,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4)) ),
c_0_2931,
[final] ).
cnf(c_0_3842,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_2932,
[final] ).
cnf(c_0_3843,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_2933,
[final] ).
cnf(c_0_3844,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_2934,
[final] ).
cnf(c_0_3845,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_2935,
[final] ).
cnf(c_0_3846,plain,
( c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2)) = c_Finite__Set_Ocard(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1)) ),
c_0_2936,
[final] ).
cnf(c_0_3847,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X4),X2)),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
c_0_2937,
[final] ).
cnf(c_0_3848,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_2938,
[final] ).
cnf(c_0_3849,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_2939,
[final] ).
cnf(c_0_3850,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3)) ),
c_0_2940,
[final] ).
cnf(c_0_3851,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Map_Odom(X1,X3,X4)),c_Map_Odom(X2,X3,X4)))
| ~ c_Map_Omap__le(X1,X2,X3,X4) ),
c_0_2941,
[final] ).
cnf(c_0_3852,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),c_Complete__Lattice_OInf__class_OInf(X1,X2)) = c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X2),X3,X1,X2,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
c_0_2942,
[final] ).
cnf(c_0_3853,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),c_Complete__Lattice_OSup__class_OSup(X1,X2)) = c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X2),X3,X1,X2,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
c_0_2943,
[final] ).
cnf(c_0_3854,plain,
( c_Fun_Ofun__upd(X1,X2,hAPP(c_Option_Ooption_OSome(X3),X4),X5,tc_Option_Ooption(X3)) = X1
| hAPP(X1,X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
c_0_2944,
[final] ).
cnf(c_0_3855,plain,
( c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2)) = c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_2945,
[final] ).
cnf(c_0_3856,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X3),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))) ),
c_0_2946,
[final] ).
cnf(c_0_3857,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4))) ),
c_0_2947,
[final] ).
cnf(c_0_3858,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_Orderings_Oorder(X1) ),
c_0_2948,
[final] ).
cnf(c_0_3859,plain,
( c_Map_Omap__add(X1,X2,X3,X4) = c_Map_Omap__add(X2,X1,X3,X4)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),c_Map_Odom(X1,X3,X4)),c_Map_Odom(X2,X3,X4)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_2949,
[final] ).
cnf(c_0_3860,plain,
( c_Lattices_Olower__semilattice(c_COMBC(c_lessequals(X1),X1,X1,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(X1),X1,X1,tc_bool),c_Orderings_Oord__class_Omax(X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
c_0_2950,
[final] ).
cnf(c_0_3861,plain,
( c_Lattices_Olower__semilattice(c_COMBC(c_lessequals(X1),X1,X1,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(X1),X1,X1,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_2951,
[final] ).
cnf(c_0_3862,plain,
( c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X2),c_Orderings_Obot__class_Obot(X2),X1,X2,X2) = c_Complete__Lattice_OSup__class_OSup(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
c_0_2952,
[final] ).
cnf(c_0_3863,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_2953,
[final] ).
cnf(c_0_3864,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_2954,
[final] ).
cnf(c_0_3865,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_2955,
[final] ).
cnf(c_0_3866,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_2956,
[final] ).
cnf(c_0_3867,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X2 = hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))))) ),
c_0_2957,
[final] ).
cnf(c_0_3868,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X4)) ),
c_0_2958,
[final] ).
cnf(c_0_3869,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X3)),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1),X3))
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_2959,
[final] ).
cnf(c_0_3870,plain,
( hAPP(X3,X4) = c_HOL_Ozero__class_Ozero(X5)
| hBOOL(hAPP(hAPP(c_in(X2),X4),X1))
| c_Finite__Set_Osetprod(X3,c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X5) = c_Finite__Set_Osetprod(X3,X1,X2,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Ring__and__Field_Ofield(X5) ),
c_0_2960,
[final] ).
cnf(c_0_3871,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_Orderings_Oorder(X1) ),
c_0_2961,
[final] ).
cnf(c_0_3872,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4)) ),
c_0_2962,
[final] ).
cnf(c_0_3873,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X3),X4)) ),
c_0_2963,
[final] ).
cnf(c_0_3874,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
c_0_2964,
[final] ).
cnf(c_0_3875,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
c_0_2965,
[final] ).
cnf(c_0_3876,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X3),X4)) ),
c_0_2966,
[final] ).
cnf(c_0_3877,plain,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X5) = c_Finite__Set_Osetsum(X4,X1,X2,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Oab__group__add(X5) ),
c_0_2967,
[final] ).
cnf(c_0_3878,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OBODY(X1)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Option_Othe(hAPP(c_Com_Obody,X1),tc_Com_Ocom)),X2),X3)) ),
c_0_2968,
[final] ).
cnf(c_0_3879,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4))) ),
c_0_2969,
[final] ).
cnf(c_0_3880,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))) ),
c_0_2970,
[final] ).
cnf(c_0_3881,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4))) ),
c_0_2971,
[final] ).
cnf(c_0_3882,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4))) ),
c_0_2972,
[final] ).
cnf(c_0_3883,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3)) ),
c_0_2973,
[final] ).
cnf(c_0_3884,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool)),X1,tc_nat) = c_Finite__Set_Osetsum(X4,X3,X1,tc_nat) ),
c_0_2974,
[final] ).
cnf(c_0_3885,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X2,tc_bool)),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(X3,X2)),c_Finite__Set_Ocard(X1,X2))) ),
c_0_2975,
[final] ).
cnf(c_0_3886,plain,
( X1 = X2
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X3))
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
c_0_2976,
[final] ).
cnf(c_0_3887,plain,
( X1 = X2
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X3))
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
c_0_2977,
[final] ).
cnf(c_0_3888,plain,
( hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3))
| ~ hBOOL(hAPP(X1,hAPP(X2,X3))) ),
c_0_2978,
[final] ).
cnf(c_0_3889,plain,
( c_HOL_Ominus__class_Ominus(X3,c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
c_0_2979,
[final] ).
cnf(c_0_3890,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X4),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X3),X4))
| ~ class_HOL_Oord(X2) ),
c_0_2980,
[final] ).
cnf(c_0_3891,plain,
( c_Orderings_Olinorder(c_COMBC(X1,X3,X3,tc_bool),c_COMBC(X2,X3,X3,tc_bool),X3)
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
c_0_2981,
[final] ).
cnf(c_0_3892,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X3)) ),
c_0_2982,
[final] ).
cnf(c_0_3893,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_2983,
[final] ).
cnf(c_0_3894,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Omult__mono(X1) ),
c_0_2984,
[final] ).
cnf(c_0_3895,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Omult__mono(X1) ),
c_0_2985,
[final] ).
cnf(c_0_3896,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Omult__mono1(X1) ),
c_0_2986,
[final] ).
cnf(c_0_3897,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_2987,
[final] ).
cnf(c_0_3898,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_2988,
[final] ).
cnf(c_0_3899,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_2989,
[final] ).
cnf(c_0_3900,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_2990,
[final] ).
cnf(c_0_3901,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_2991,
[final] ).
cnf(c_0_3902,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
c_0_2992,
[final] ).
cnf(c_0_3903,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_2993,
[final] ).
cnf(c_0_3904,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_2994,
[final] ).
cnf(c_0_3905,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_2995,
[final] ).
cnf(c_0_3906,plain,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| c_Finite__Set_Osetsum(X4,hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2,X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(X4,X3)),c_Finite__Set_Osetsum(X4,X1,X2,X5))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X5) ),
c_0_2996,
[final] ).
cnf(c_0_3907,plain,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| c_Finite__Set_Osetprod(X4,hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2,X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(X4,X3)),c_Finite__Set_Osetprod(X4,X1,X2,X5))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X5) ),
c_0_2997,
[final] ).
cnf(c_0_3908,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_2998,
[final] ).
cnf(c_0_3909,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
c_0_2999,
[final] ).
cnf(c_0_3910,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
c_0_3000,
[final] ).
cnf(c_0_3911,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_3001,
[final] ).
cnf(c_0_3912,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_3002,
[final] ).
cnf(c_0_3913,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_3003,
[final] ).
cnf(c_0_3914,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_3004,
[final] ).
cnf(c_0_3915,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_3005,
[final] ).
cnf(c_0_3916,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_3006,
[final] ).
cnf(c_0_3917,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),X2)),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),X3)) = hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(X3,X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_3007,
[final] ).
cnf(c_0_3918,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),X2)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),X3)) = hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(X3,X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
c_0_3008,
[final] ).
cnf(c_0_3919,plain,
( c_Orderings_Olinorder(c_COMBC(c_lessequals(X1),X1,X1,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(X1),X1,X1,tc_bool),X1)
| ~ class_Orderings_Olinorder(X1) ),
c_0_3009,
[final] ).
cnf(c_0_3920,plain,
( X5 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| hBOOL(hAPP(hAPP(X1,X6),X7))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ c_Finite__Set_Ofinite(X5,X4)
| ~ hBOOL(hAPP(hAPP(X1,X6),hAPP(c_Finite__Set_Ofold1(X3,X4),X5)))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X7),X5)) ),
c_0_3010,
[final] ).
cnf(c_0_3921,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
c_0_3011,
[final] ).
cnf(c_0_3922,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
c_0_3012,
[final] ).
cnf(c_0_3923,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
c_0_3013,
[final] ).
cnf(c_0_3924,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
c_0_3014,
[final] ).
cnf(c_0_3925,plain,
( hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1) = X3
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(X1,X3,X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Orderings_Olinorder(X2) ),
c_0_3015,
[final] ).
cnf(c_0_3926,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
c_0_3016,
[final] ).
cnf(c_0_3927,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
c_0_3017,
[final] ).
cnf(c_0_3928,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ class_Orderings_Oorder(X1) ),
c_0_3018,
[final] ).
cnf(c_0_3929,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3019,
[final] ).
cnf(c_0_3930,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3020,
[final] ).
cnf(c_0_3931,plain,
( hAPP(c_Option_Ooption_OSome(X4),c_Map_Osko__Map__XdomD__1__1(X2,X3,X1,X4)) = hAPP(X3,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Map_Odom(X3,X1,X4))) ),
c_0_3021,
[final] ).
cnf(c_0_3932,plain,
( c_Map_Omap__le(X1,X5,X3,X4)
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| ~ c_Map_Omap__le(X2,X5,X3,X4) ),
c_0_3022,
[final] ).
cnf(c_0_3933,plain,
( hAPP(c_Map_Omap__add(X5,X3,X1,X4),X2) = hAPP(X3,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Map_Odom(X3,X1,X4))) ),
c_0_3023,
[final] ).
cnf(c_0_3934,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
c_0_3024,
[final] ).
cnf(c_0_3935,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
c_0_3025,
[final] ).
cnf(c_0_3936,plain,
( hBOOL(hAPP(X2,X4))
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4)) ),
c_0_3026,
[final] ).
cnf(c_0_3937,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X4),X3))
| ~ class_HOL_Oord(X2) ),
c_0_3027,
[final] ).
cnf(c_0_3938,plain,
( hAPP(hAPP(X1,hAPP(c_Finite__Set_Ofold1(X1,X2),X3)),hAPP(c_Finite__Set_Ofold1(X1,X2),X4)) = hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X4,X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
c_0_3028,
[final] ).
cnf(c_0_3939,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_3029,
[final] ).
cnf(c_0_3940,plain,
( hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4)) ),
c_0_3030,
[final] ).
cnf(c_0_3941,plain,
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4)) ),
c_0_3031,
[final] ).
cnf(c_0_3942,plain,
( hBOOL(hAPP(hAPP(X1,hAPP(c_Finite__Set_Ofold1(X3,X4),X5)),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ c_Finite__Set_Ofinite(X5,X4)
| ~ hBOOL(hAPP(hAPP(c_in(X4),X6),X5)) ),
c_0_3032,
[final] ).
cnf(c_0_3943,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_3033,
[final] ).
cnf(c_0_3944,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_3034,
[final] ).
cnf(c_0_3945,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_3035,
[final] ).
cnf(c_0_3946,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_3036,
[final] ).
cnf(c_0_3947,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_3037,
[final] ).
cnf(c_0_3948,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
c_0_3038,
[final] ).
cnf(c_0_3949,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3039,
[final] ).
cnf(c_0_3950,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_3040,
[final] ).
cnf(c_0_3951,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_3041,
[final] ).
cnf(c_0_3952,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_3042,
[final] ).
cnf(c_0_3953,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_3043,
[final] ).
cnf(c_0_3954,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_3044,
[final] ).
cnf(c_0_3955,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
c_0_3045,
[final] ).
cnf(c_0_3956,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
c_0_3046,
[final] ).
cnf(c_0_3957,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
c_0_3047,
[final] ).
cnf(c_0_3958,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
c_0_3048,
[final] ).
cnf(c_0_3959,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
c_0_3049,
[final] ).
cnf(c_0_3960,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3050,
[final] ).
cnf(c_0_3961,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3051,
[final] ).
cnf(c_0_3962,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3052,
[final] ).
cnf(c_0_3963,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3053,
[final] ).
cnf(c_0_3964,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3054,
[final] ).
cnf(c_0_3965,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3055,
[final] ).
cnf(c_0_3966,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_3056,
[final] ).
cnf(c_0_3967,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_3057,
[final] ).
cnf(c_0_3968,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_3058,
[final] ).
cnf(c_0_3969,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_3059,
[final] ).
cnf(c_0_3970,plain,
( hAPP(X1,X5) = hAPP(X2,X5)
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),c_Map_Odom(X1,X3,X4))) ),
c_0_3060,
[final] ).
cnf(c_0_3971,plain,
( X3 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X3)) ),
c_0_3061,
[final] ).
cnf(c_0_3972,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2)) ),
c_0_3062,
[final] ).
cnf(c_0_3973,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2)) ),
c_0_3063,
[final] ).
cnf(c_0_3974,plain,
( hBOOL(hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X5)),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X2,X5),X6)) ),
c_0_3064,
[final] ).
cnf(c_0_3975,plain,
( hBOOL(hAPP(hAPP(X2,hAPP(hAPP(X3,X5),X7)),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X2,X5),X6)) ),
c_0_3065,
[final] ).
cnf(c_0_3976,plain,
( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(X3,X5),X7)),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),X6)) ),
c_0_3066,
[final] ).
cnf(c_0_3977,plain,
( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(X3,X7),X5)),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),X6)) ),
c_0_3067,
[final] ).
cnf(c_0_3978,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X1)),X4))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X3),X4))
| ~ class_Orderings_Olinorder(X2) ),
c_0_3068,
[final] ).
cnf(c_0_3979,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X1)),X4))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X3),X4))
| ~ class_Orderings_Olinorder(X2) ),
c_0_3069,
[final] ).
cnf(c_0_3980,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
c_0_3070,
[final] ).
cnf(c_0_3981,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
c_0_3071,
[final] ).
cnf(c_0_3982,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
c_0_3072,
[final] ).
cnf(c_0_3983,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
c_0_3073,
[final] ).
cnf(c_0_3984,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Option_Othe(hAPP(c_Com_Obody,X1),tc_Com_Ocom)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OBODY(X1)),X2),X3)) ),
c_0_3074,
[final] ).
cnf(c_0_3985,plain,
( hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(X5,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(c_Map_Omap__add(X5,X1,X6,X3),X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
c_0_3075,
[final] ).
cnf(c_0_3986,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_3076,
[final] ).
cnf(c_0_3987,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_3077,
[final] ).
cnf(c_0_3988,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
c_0_3078,
[final] ).
cnf(c_0_3989,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
c_0_3079,
[final] ).
cnf(c_0_3990,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
c_0_3080,
[final] ).
cnf(c_0_3991,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_3081,
[final] ).
cnf(c_0_3992,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
c_0_3082,
[final] ).
cnf(c_0_3993,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_3083,
[final] ).
cnf(c_0_3994,plain,
( hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7)))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),X6))
| ~ hBOOL(hAPP(hAPP(X1,X5),X7)) ),
c_0_3084,
[final] ).
cnf(c_0_3995,plain,
( hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7)))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),X6))
| ~ hBOOL(hAPP(hAPP(X1,X5),X7)) ),
c_0_3085,
[final] ).
cnf(c_0_3996,plain,
( hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7)))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),X6))
| ~ hBOOL(hAPP(hAPP(X1,X5),X7)) ),
c_0_3086,
[final] ).
cnf(c_0_3997,plain,
( hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X5,X1,X6,X3),X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
c_0_3087,
[final] ).
cnf(c_0_3998,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_3088,
[final] ).
cnf(c_0_3999,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_3089,
[final] ).
cnf(c_0_4000,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3090,
[final] ).
cnf(c_0_4001,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3091,
[final] ).
cnf(c_0_4002,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3092,
[final] ).
cnf(c_0_4003,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3093,
[final] ).
cnf(c_0_4004,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_3094,
[final] ).
cnf(c_0_4005,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_3095,
[final] ).
cnf(c_0_4006,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_3096,
[final] ).
cnf(c_0_4007,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),X4),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X2) ),
c_0_3097,
[final] ).
cnf(c_0_4008,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_3098,
[final] ).
cnf(c_0_4009,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X2)),hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
c_0_3099,
[final] ).
cnf(c_0_4010,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_Finite__Set_Olinorder__class_OMin(X1),X3)),hAPP(c_Finite__Set_Olinorder__class_OMin(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
c_0_3100,
[final] ).
cnf(c_0_4011,plain,
( hBOOL(hAPP(hAPP(X1,X5),X7))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7))) ),
c_0_3101,
[final] ).
cnf(c_0_4012,plain,
( hBOOL(hAPP(hAPP(X1,X5),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7))) ),
c_0_3102,
[final] ).
cnf(c_0_4013,plain,
( hBOOL(hAPP(hAPP(X1,X5),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7))) ),
c_0_3103,
[final] ).
cnf(c_0_4014,plain,
( hBOOL(hAPP(hAPP(X1,X5),X7))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7))) ),
c_0_3104,
[final] ).
cnf(c_0_4015,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_3105,
[final] ).
cnf(c_0_4016,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_3106,
[final] ).
cnf(c_0_4017,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Map_Odom(X3,X1,X4)))
| hAPP(c_Map_Omap__add(X5,X3,X1,X4),X2) = hAPP(X5,X2) ),
c_0_3107,
[final] ).
cnf(c_0_4018,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Map_Odom(X3,X1,X4)))
| hAPP(c_Map_Omap__add(X3,X5,X1,X4),X2) = hAPP(X5,X2) ),
c_0_3108,
[final] ).
cnf(c_0_4019,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_3109,
[final] ).
cnf(c_0_4020,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X3),X4))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X3),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),X1))
| ~ class_Orderings_Olinorder(X2) ),
c_0_3110,
[final] ).
cnf(c_0_4021,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X2),X3),X4))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X3),hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),X1))
| ~ class_Lattices_Olower__semilattice(X2) ),
c_0_3111,
[final] ).
cnf(c_0_4022,plain,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X4,X1,X5,X3),X2) != c_Option_Ooption_ONone(X3) ),
c_0_3112,
[final] ).
cnf(c_0_4023,plain,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X1,X4,X5,X3),X2) != c_Option_Ooption_ONone(X3) ),
c_0_3113,
[final] ).
cnf(c_0_4024,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))))) ),
c_0_3114,
[final] ).
cnf(c_0_4025,plain,
( X1 = X2
| X1 = X3
| hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X3),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) ),
c_0_3115,
[final] ).
cnf(c_0_4026,plain,
( X1 = X2
| X3 = X2
| hAPP(hAPP(c_Set_Oinsert(X4),X3),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) ),
c_0_3116,
[final] ).
cnf(c_0_4027,plain,
( X1 = X2
| X3 = X2
| hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X2),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) ),
c_0_3117,
[final] ).
cnf(c_0_4028,plain,
( X1 = X2
| X1 = X3
| hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X2),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) ),
c_0_3118,
[final] ).
cnf(c_0_4029,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))
| ~ class_HOL_Oord(X2) ),
c_0_3119,
[final] ).
cnf(c_0_4030,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_3120,
[final] ).
cnf(c_0_4031,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OlessThan(X2,X1)),c_SetInterval_Oord__class_OlessThan(X3,X1)))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3121,
[final] ).
cnf(c_0_4032,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),X1)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),X3)) = hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
c_0_3122,
[final] ).
cnf(c_0_4033,plain,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))) = X3
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_3123,
[final] ).
cnf(c_0_4034,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_3124,
[final] ).
cnf(c_0_4035,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_3125,
[final] ).
cnf(c_0_4036,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_3126,
[final] ).
cnf(c_0_4037,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_3127,
[final] ).
cnf(c_0_4038,plain,
( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(X3,X5),X6)),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4) ),
c_0_3128,
[final] ).
cnf(c_0_4039,plain,
( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(X3,X5),X6)),X5))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4) ),
c_0_3129,
[final] ).
cnf(c_0_4040,plain,
( X1 = X2
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| ~ c_Map_Omap__le(X2,X1,X3,X4) ),
c_0_3130,
[final] ).
cnf(c_0_4041,plain,
( X1 = X2
| c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X1,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X6,X7,X2,X5) ),
c_0_3131,
[final] ).
cnf(c_0_4042,plain,
( X1 = X2
| c_Hoare__Mirabelle_Otriple_Otriple(X3,X1,X4,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X6,X2,X7,X5) ),
c_0_3132,
[final] ).
cnf(c_0_4043,plain,
( X1 = X2
| c_Hoare__Mirabelle_Otriple_Otriple(X1,X3,X4,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X2,X6,X7,X5) ),
c_0_3133,
[final] ).
cnf(c_0_4044,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(X3,X5)),hAPP(X4,X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X3),X4))
| ~ class_HOL_Oord(X2) ),
c_0_3134,
[final] ).
cnf(c_0_4045,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
c_0_3135,
[final] ).
cnf(c_0_4046,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
c_0_3136,
[final] ).
cnf(c_0_4047,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
c_0_3137,
[final] ).
cnf(c_0_4048,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
c_0_3138,
[final] ).
cnf(c_0_4049,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
c_0_3139,
[final] ).
cnf(c_0_4050,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
c_0_3140,
[final] ).
cnf(c_0_4051,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_3141,
[final] ).
cnf(c_0_4052,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
c_0_3142,
[final] ).
cnf(c_0_4053,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_3143,
[final] ).
cnf(c_0_4054,plain,
( hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(X1,X3,X2)),X1))
| hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1) = X3
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Orderings_Olinorder(X2) ),
c_0_3144,
[final] ).
cnf(c_0_4055,plain,
( hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(X1,X3,X2)),X1))
| hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1) = X3
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Orderings_Olinorder(X2) ),
c_0_3145,
[final] ).
cnf(c_0_4056,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X1,tc_bool))) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
c_0_3146,
[final] ).
cnf(c_0_4057,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_3147,
[final] ).
cnf(c_0_4058,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool)),X2) ),
c_0_3148,
[final] ).
cnf(c_0_4059,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
c_0_3149,
[final] ).
cnf(c_0_4060,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
c_0_3150,
[final] ).
cnf(c_0_4061,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3)) ),
c_0_3151,
[final] ).
cnf(c_0_4062,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
c_0_3152,
[final] ).
cnf(c_0_4063,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
c_0_3153,
[final] ).
cnf(c_0_4064,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X5),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3154,
[final] ).
cnf(c_0_4065,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2)) ),
c_0_3155,
[final] ).
cnf(c_0_4066,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
c_0_3156,
[final] ).
cnf(c_0_4067,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2)) ),
c_0_3157,
[final] ).
cnf(c_0_4068,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2)) ),
c_0_3158,
[final] ).
cnf(c_0_4069,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2)) ),
c_0_3159,
[final] ).
cnf(c_0_4070,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(X3,X2)),c_Finite__Set_Ocard(X1,X2)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X2,tc_bool)),X3),X1)) ),
c_0_3160,
[final] ).
cnf(c_0_4071,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3161,
[final] ).
cnf(c_0_4072,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3162,
[final] ).
cnf(c_0_4073,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3163,
[final] ).
cnf(c_0_4074,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(X1,hAPP(c_Finite__Set_Ofold1(X1,X2),X3)),hAPP(c_Finite__Set_Ofold1(X1,X2),X4)) = hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4))
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X4,X2) ),
c_0_3164,
[final] ).
cnf(c_0_4075,plain,
( hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1) = X3
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X3),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(X1,X3,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Orderings_Olinorder(X2) ),
c_0_3165,
[final] ).
cnf(c_0_4076,plain,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2) = c_Finite__Set_Ocard(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_3166,
[final] ).
cnf(c_0_4077,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_3167,
[final] ).
cnf(c_0_4078,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
c_0_3168,
[final] ).
cnf(c_0_4079,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_3169,
[final] ).
cnf(c_0_4080,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_3170,
[final] ).
cnf(c_0_4081,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_3171,
[final] ).
cnf(c_0_4082,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_3172,
[final] ).
cnf(c_0_4083,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_3173,
[final] ).
cnf(c_0_4084,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
c_0_3174,
[final] ).
cnf(c_0_4085,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
c_0_3175,
[final] ).
cnf(c_0_4086,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X2),X1)),X3))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Lattices_Olower__semilattice(X2) ),
c_0_3176,
[final] ).
cnf(c_0_4087,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3177,
[final] ).
cnf(c_0_4088,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3178,
[final] ).
cnf(c_0_4089,plain,
( hAPP(hAPP(X3,hAPP(hAPP(X3,X5),X6)),X7) = hAPP(hAPP(X3,X5),hAPP(hAPP(X3,X6),X7))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4) ),
c_0_3179,
[final] ).
cnf(c_0_4090,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_3180,
[final] ).
cnf(c_0_4091,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_3181,
[final] ).
cnf(c_0_4092,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_3182,
[final] ).
cnf(c_0_4093,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_3183,
[final] ).
cnf(c_0_4094,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X1),X3),X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X3,X2)) ),
c_0_3184,
[final] ).
cnf(c_0_4095,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
c_0_3185,
[final] ).
cnf(c_0_4096,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3186,
[final] ).
cnf(c_0_4097,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3187,
[final] ).
cnf(c_0_4098,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3188,
[final] ).
cnf(c_0_4099,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3189,
[final] ).
cnf(c_0_4100,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_3190,
[final] ).
cnf(c_0_4101,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_3191,
[final] ).
cnf(c_0_4102,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3192,
[final] ).
cnf(c_0_4103,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3193,
[final] ).
cnf(c_0_4104,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3194,
[final] ).
cnf(c_0_4105,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3195,
[final] ).
cnf(c_0_4106,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_3196,
[final] ).
cnf(c_0_4107,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_3197,
[final] ).
cnf(c_0_4108,plain,
( hAPP(c_Map_Orestrict__map(X4,X3,X1,X5),X2) = hAPP(X4,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_3198,
[final] ).
cnf(c_0_4109,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_3199,
[final] ).
cnf(c_0_4110,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_3200,
[final] ).
cnf(c_0_4111,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),X4),X2) ),
c_0_3201,
[final] ).
cnf(c_0_4112,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_3202,
[final] ).
cnf(c_0_4113,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_3203,
[final] ).
cnf(c_0_4114,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3204,
[final] ).
cnf(c_0_4115,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3205,
[final] ).
cnf(c_0_4116,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3206,
[final] ).
cnf(c_0_4117,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3207,
[final] ).
cnf(c_0_4118,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_3208,
[final] ).
cnf(c_0_4119,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_3209,
[final] ).
cnf(c_0_4120,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_3210,
[final] ).
cnf(c_0_4121,plain,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X1,X4)),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X4),X3),X5)) ),
c_0_3211,
[final] ).
cnf(c_0_4122,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X1),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_3212,
[final] ).
cnf(c_0_4123,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_3213,
[final] ).
cnf(c_0_4124,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) ),
c_0_3214,
[final] ).
cnf(c_0_4125,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X3),X4),X2),tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3) ),
c_0_3215,
[final] ).
cnf(c_0_4126,plain,
( hAPP(hAPP(X3,X5),hAPP(hAPP(X3,X6),X7)) = hAPP(hAPP(X3,X6),hAPP(hAPP(X3,X5),X7))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4) ),
c_0_3216,
[final] ).
cnf(c_0_4127,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4)
| ~ class_Orderings_Olinorder(X1) ),
c_0_3217,
[final] ).
cnf(c_0_4128,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4)
| ~ class_Lattices_Odistrib__lattice(X1) ),
c_0_3218,
[final] ).
cnf(c_0_4129,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4)
| ~ class_OrderedGroup_Olordered__ab__group__add__join(X1) ),
c_0_3219,
[final] ).
cnf(c_0_4130,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_3220,
[final] ).
cnf(c_0_4131,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4)
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1) ),
c_0_3221,
[final] ).
cnf(c_0_4132,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_3222,
[final] ).
cnf(c_0_4133,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4)
| ~ class_Lattices_Odistrib__lattice(X1) ),
c_0_3223,
[final] ).
cnf(c_0_4134,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_3224,
[final] ).
cnf(c_0_4135,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4)
| ~ class_Orderings_Olinorder(X1) ),
c_0_3225,
[final] ).
cnf(c_0_4136,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
c_0_3226,
[final] ).
cnf(c_0_4137,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3227,
[final] ).
cnf(c_0_4138,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3228,
[final] ).
cnf(c_0_4139,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
c_0_3229,
[final] ).
cnf(c_0_4140,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OlessThan(X2,X1)),c_SetInterval_Oord__class_OlessThan(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3230,
[final] ).
cnf(c_0_4141,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hAPP(c_Map_Orestrict__map(X4,X3,X1,X5),X2) = c_Option_Ooption_ONone(X5) ),
c_0_3231,
[final] ).
cnf(c_0_4142,plain,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(c_Option_Ooption_OSome(X4),X6)
| hAPP(X2,X5) != c_Option_Ooption_ONone(X4)
| hAPP(X1,X5) != hAPP(c_Option_Ooption_OSome(X4),X6) ),
c_0_3232,
[final] ).
cnf(c_0_4143,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X3)) ),
c_0_3233,
[final] ).
cnf(c_0_4144,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3234,
[final] ).
cnf(c_0_4145,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3235,
[final] ).
cnf(c_0_4146,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3236,
[final] ).
cnf(c_0_4147,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3237,
[final] ).
cnf(c_0_4148,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3238,
[final] ).
cnf(c_0_4149,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3239,
[final] ).
cnf(c_0_4150,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_3240,
[final] ).
cnf(c_0_4151,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_3241,
[final] ).
cnf(c_0_4152,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_3242,
[final] ).
cnf(c_0_4153,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_3243,
[final] ).
cnf(c_0_4154,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
c_0_3244,
[final] ).
cnf(c_0_4155,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X2) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
c_0_3245,
[final] ).
cnf(c_0_4156,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
c_0_3246,
[final] ).
cnf(c_0_4157,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X2) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
c_0_3247,
[final] ).
cnf(c_0_4158,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X3) ),
c_0_3248,
[final] ).
cnf(c_0_4159,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))) ),
c_0_3249,
[final] ).
cnf(c_0_4160,plain,
( c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
c_0_3250,
[final] ).
cnf(c_0_4161,plain,
( c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
c_0_3251,
[final] ).
cnf(c_0_4162,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_3252,
[final] ).
cnf(c_0_4163,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
c_0_3253,
[final] ).
cnf(c_0_4164,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1)),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X3)) = hAPP(c_Finite__Set_Olinorder__class_OMax(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_3254,
[final] ).
cnf(c_0_4165,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X2),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1)),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X3)) = hAPP(c_Finite__Set_Olinorder__class_OMin(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_3255,
[final] ).
cnf(c_0_4166,plain,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(c_Option_Ooption_OSome(X4),X6)
| hAPP(X2,X5) != hAPP(c_Option_Ooption_OSome(X4),X6) ),
c_0_3256,
[final] ).
cnf(c_0_4167,plain,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(c_Option_Ooption_OSome(X4),X6)
| hAPP(X2,X5) != hAPP(c_Option_Ooption_OSome(X4),X6) ),
c_0_3257,
[final] ).
cnf(c_0_4168,plain,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = c_Option_Ooption_ONone(X4)
| hAPP(X2,X5) != c_Option_Ooption_ONone(X4)
| hAPP(X1,X5) != c_Option_Ooption_ONone(X4) ),
c_0_3258,
[final] ).
cnf(c_0_4169,plain,
( c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) ),
c_0_3259,
[final] ).
cnf(c_0_4170,plain,
( hAPP(hAPP(X3,X6),X5) = X5
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),X6)) ),
c_0_3260,
[final] ).
cnf(c_0_4171,plain,
( hAPP(hAPP(X3,X5),X6) = X5
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),X6)) ),
c_0_3261,
[final] ).
cnf(c_0_4172,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_3262,
[final] ).
cnf(c_0_4173,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_3263,
[final] ).
cnf(c_0_4174,plain,
( hAPP(hAPP(X3,X5),hAPP(hAPP(X3,X5),X6)) = hAPP(hAPP(X3,X5),X6)
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4) ),
c_0_3264,
[final] ).
cnf(c_0_4175,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ c_Lattices_Olower__semilattice(X1,X4,X5,X6)
| hAPP(hAPP(X5,X2),X3) != X2 ),
c_0_3265,
[final] ).
cnf(c_0_4176,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_HOL_Ominus__class_Ominus(X2,X4,X1)),c_HOL_Ominus__class_Ominus(X3,X4,X1)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3),X4,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_3266,
[final] ).
cnf(c_0_4177,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_HOL_Ominus__class_Ominus(X2,X4,X1)),c_HOL_Ominus__class_Ominus(X3,X4,X1)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3),X4,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_3267,
[final] ).
cnf(c_0_4178,plain,
( hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(X2,X4)) ),
c_0_3268,
[final] ).
cnf(c_0_4179,plain,
( hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X4)) ),
c_0_3269,
[final] ).
cnf(c_0_4180,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
c_0_3270,
[final] ).
cnf(c_0_4181,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Map_Odom(X3,X1,X4)))
| hAPP(X3,X2) != c_Option_Ooption_ONone(X4) ),
c_0_3271,
[final] ).
cnf(c_0_4182,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X2))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3272,
[final] ).
cnf(c_0_4183,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3273,
[final] ).
cnf(c_0_4184,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X2))
| ~ class_Lattices_Olattice(X1) ),
c_0_3274,
[final] ).
cnf(c_0_4185,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X3))
| ~ class_Lattices_Olattice(X1) ),
c_0_3275,
[final] ).
cnf(c_0_4186,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X3))
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_3276,
[final] ).
cnf(c_0_4187,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X2))
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_3277,
[final] ).
cnf(c_0_4188,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3278,
[final] ).
cnf(c_0_4189,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
c_0_3279,
[final] ).
cnf(c_0_4190,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
| ~ class_OrderedGroup_Olordered__ab__group__add__join(X1) ),
c_0_3280,
[final] ).
cnf(c_0_4191,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_3281,
[final] ).
cnf(c_0_4192,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3282,
[final] ).
cnf(c_0_4193,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1) ),
c_0_3283,
[final] ).
cnf(c_0_4194,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_3284,
[final] ).
cnf(c_0_4195,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
c_0_3285,
[final] ).
cnf(c_0_4196,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3286,
[final] ).
cnf(c_0_4197,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3287,
[final] ).
cnf(c_0_4198,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3288,
[final] ).
cnf(c_0_4199,plain,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) != X3 ),
c_0_3289,
[final] ).
cnf(c_0_4200,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_HOL_Ozero__class_Ozero(X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_HOL_Ozero__class_Ozero(X2)),X1))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
c_0_3290,
[final] ).
cnf(c_0_4201,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_HOL_Ozero__class_Ozero(X2)),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_HOL_Ozero__class_Ozero(X2)),X3))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
c_0_3291,
[final] ).
cnf(c_0_4202,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X1,X2),c_ATP__Linkup_Osko__Finite__Set__Xfinite__nonempty__imp__fold1Set__1__1(X1,X3,X2)))
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_3292,
[final] ).
cnf(c_0_4203,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4))
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_3293,
[final] ).
cnf(c_0_4204,plain,
( c_HOL_Ominus__class_Ominus(c_Map_Odom(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X2),X4),X5),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Map_Odom(X1,X2,X3),X5,tc_fun(X2,tc_bool))
| hAPP(X1,X4) != c_Option_Ooption_ONone(X3) ),
c_0_3294,
[final] ).
cnf(c_0_4205,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4) ),
c_0_3295,
[final] ).
cnf(c_0_4206,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool)) = X3 ),
c_0_3296,
[final] ).
cnf(c_0_4207,plain,
( c_Finite__Set_Ofinite(X2,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ c_Finite__Set_Ofinite(X3,X1) ),
c_0_3297,
[final] ).
cnf(c_0_4208,plain,
( c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X1)) ),
c_0_3298,
[final] ).
cnf(c_0_4209,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X1),X2),X4),X3,tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_HOL_Ominus__class_Ominus(X4,X3,tc_fun(X1,tc_bool))) ),
c_0_3299,
[final] ).
cnf(c_0_4210,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_3300,
[final] ).
cnf(c_0_4211,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3301,
[final] ).
cnf(c_0_4212,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3302,
[final] ).
cnf(c_0_4213,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3303,
[final] ).
cnf(c_0_4214,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3304,
[final] ).
cnf(c_0_4215,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3305,
[final] ).
cnf(c_0_4216,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3306,
[final] ).
cnf(c_0_4217,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3307,
[final] ).
cnf(c_0_4218,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3308,
[final] ).
cnf(c_0_4219,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_3309,
[final] ).
cnf(c_0_4220,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_3310,
[final] ).
cnf(c_0_4221,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_3311,
[final] ).
cnf(c_0_4222,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_3312,
[final] ).
cnf(c_0_4223,plain,
( c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X1) ),
c_0_3313,
[final] ).
cnf(c_0_4224,plain,
( c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X1) ),
c_0_3314,
[final] ).
cnf(c_0_4225,plain,
( c_Finite__Set_Osetprod(X1,X2,X3,X4) = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2))
| hAPP(X1,X5) != c_HOL_Ozero__class_Ozero(X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| ~ class_Ring__and__Field_Ono__zero__divisors(X4) ),
c_0_3315,
[final] ).
cnf(c_0_4226,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_3316,
[final] ).
cnf(c_0_4227,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_3317,
[final] ).
cnf(c_0_4228,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_3318,
[final] ).
cnf(c_0_4229,plain,
( c_Finite__Set_Osetprod(X1,X2,X3,X4) = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2))
| hAPP(X1,X5) != c_HOL_Ozero__class_Ozero(X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
c_0_3319,
[final] ).
cnf(c_0_4230,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X2),X2),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
c_0_3320,
[final] ).
cnf(c_0_4231,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Oab__semigroup__mult(X2) ),
c_0_3321,
[final] ).
cnf(c_0_4232,plain,
( hAPP(hAPP(X3,X5),X6) = hAPP(hAPP(X3,X6),X5)
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4) ),
c_0_3322,
[final] ).
cnf(c_0_4233,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1)),X3))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Orderings_Olinorder(X2) ),
c_0_3323,
[final] ).
cnf(c_0_4234,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(X3,X2,X1) != c_HOL_Ominus__class_Ominus(X5,X4,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_3324,
[final] ).
cnf(c_0_4235,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(X5,X4,X1) != c_HOL_Ominus__class_Ominus(X3,X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_3325,
[final] ).
cnf(c_0_4236,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_3326,
[final] ).
cnf(c_0_4237,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(X4,X5,X1) != c_HOL_Ominus__class_Ominus(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
c_0_3327,
[final] ).
cnf(c_0_4238,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Orderings_Opreorder(X1) ),
c_0_3328,
[final] ).
cnf(c_0_4239,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| ~ class_Orderings_Oorder(X1) ),
c_0_3329,
[final] ).
cnf(c_0_4240,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ class_Orderings_Oorder(X1) ),
c_0_3330,
[final] ).
cnf(c_0_4241,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ class_Orderings_Oorder(X1) ),
c_0_3331,
[final] ).
cnf(c_0_4242,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| ~ class_Orderings_Oorder(X1) ),
c_0_3332,
[final] ).
cnf(c_0_4243,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Orderings_Opreorder(X1) ),
c_0_3333,
[final] ).
cnf(c_0_4244,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Orderings_Opreorder(X1) ),
c_0_3334,
[final] ).
cnf(c_0_4245,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Orderings_Opreorder(X1) ),
c_0_3335,
[final] ).
cnf(c_0_4246,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),X4),X3))
| hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = hAPP(hAPP(X1,X4),hAPP(c_Finite__Set_Ofold1(X1,X2),X3))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
c_0_3336,
[final] ).
cnf(c_0_4247,plain,
( hAPP(hAPP(X3,X5),X5) = X5
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4) ),
c_0_3337,
[final] ).
cnf(c_0_4248,plain,
( hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,X1)),X2),X3),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(X2,v_x)),hAPP(X3,v_x))
| ~ class_Lattices_Olattice(X1) ),
c_0_3338,
[final] ).
cnf(c_0_4249,plain,
( hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,X1)),X2),X3),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(X2,v_x)),hAPP(X3,v_x))
| ~ class_Lattices_Olattice(X1) ),
c_0_3339,
[final] ).
cnf(c_0_4250,plain,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X1),X2),X4),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_3340,
[final] ).
cnf(c_0_4251,plain,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_SetInterval_Oord__class_OlessThan(X2,X1),tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))
| ~ class_Orderings_Oorder(X1) ),
c_0_3341,
[final] ).
cnf(c_0_4252,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_3342,
[final] ).
cnf(c_0_4253,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Olattice(X1) ),
c_0_3343,
[final] ).
cnf(c_0_4254,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_3344,
[final] ).
cnf(c_0_4255,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3345,
[final] ).
cnf(c_0_4256,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_3346,
[final] ).
cnf(c_0_4257,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
c_0_3347,
[final] ).
cnf(c_0_4258,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3348,
[final] ).
cnf(c_0_4259,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3349,
[final] ).
cnf(c_0_4260,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3350,
[final] ).
cnf(c_0_4261,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3351,
[final] ).
cnf(c_0_4262,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
c_0_3352,
[final] ).
cnf(c_0_4263,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3353,
[final] ).
cnf(c_0_4264,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3354,
[final] ).
cnf(c_0_4265,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3355,
[final] ).
cnf(c_0_4266,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
| ~ class_Lattices_Olattice(X1) ),
c_0_3356,
[final] ).
cnf(c_0_4267,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_3357,
[final] ).
cnf(c_0_4268,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X3)) ),
c_0_3358,
[final] ).
cnf(c_0_4269,plain,
( c_OrderedGroup_Oab__semigroup__idem__mult(X3,X4)
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4) ),
c_0_3359,
[final] ).
cnf(c_0_4270,plain,
( X2 = X4
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4)) ),
c_0_3360,
[final] ).
cnf(c_0_4271,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
c_0_3361,
[final] ).
cnf(c_0_4272,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_Complete__Lattice_OInf__class_OInf(X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
c_0_3362,
[final] ).
cnf(c_0_4273,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X4)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
c_0_3363,
[final] ).
cnf(c_0_4274,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X2),X3),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Orderings_Olinorder(X2) ),
c_0_3364,
[final] ).
cnf(c_0_4275,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| hAPP(hAPP(c_Set_Oinsert(X3),X4),X1) != hAPP(hAPP(c_Set_Oinsert(X3),X4),X2) ),
c_0_3365,
[final] ).
cnf(c_0_4276,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(X3,X2)) ),
c_0_3366,
[final] ).
cnf(c_0_4277,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),X4),X2) ),
c_0_3367,
[final] ).
cnf(c_0_4278,plain,
( c_Finite__Set_Osetsum(c_COMBK(c_HOL_Ozero__class_Ozero(X1),X1,X2),X3,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_3368,
[final] ).
cnf(c_0_4279,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Map_Odom(X3,X1,X4)))
| hAPP(X3,X2) != hAPP(c_Option_Ooption_OSome(X4),X5) ),
c_0_3369,
[final] ).
cnf(c_0_4280,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
c_0_3370,
[final] ).
cnf(c_0_4281,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord__class_OlessThan(X3,X1)))
| ~ class_HOL_Oord(X1) ),
c_0_3371,
[final] ).
cnf(c_0_4282,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) ),
c_0_3372,
[final] ).
cnf(c_0_4283,plain,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = X1
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_3373,
[final] ).
cnf(c_0_4284,plain,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
c_0_3374,
[final] ).
cnf(c_0_4285,plain,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
c_0_3375,
[final] ).
cnf(c_0_4286,plain,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ hBOOL(hAPP(hAPP(X2,X5),X4)) ),
c_0_3376,
[final] ).
cnf(c_0_4287,plain,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X5))
| ~ hBOOL(hAPP(hAPP(X2,X5),X4)) ),
c_0_3377,
[final] ).
cnf(c_0_4288,plain,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ hBOOL(hAPP(hAPP(X1,X5),X4)) ),
c_0_3378,
[final] ).
cnf(c_0_4289,plain,
( ~ hBOOL(hAPP(hAPP(X1,X2),X2))
| ~ c_Orderings_Olinorder(X3,X1,X4)
| ~ hBOOL(hAPP(hAPP(X3,X2),X2)) ),
c_0_3379,
[final] ).
cnf(c_0_4290,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Oorder(X1) ),
c_0_3380,
[final] ).
cnf(c_0_4291,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Oorder(X1) ),
c_0_3381,
[final] ).
cnf(c_0_4292,plain,
( X3 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Oorder(X1) ),
c_0_3382,
[final] ).
cnf(c_0_4293,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3383,
[final] ).
cnf(c_0_4294,plain,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3384,
[final] ).
cnf(c_0_4295,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3385,
[final] ).
cnf(c_0_4296,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Opreorder(X1) ),
c_0_3386,
[final] ).
cnf(c_0_4297,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
c_0_3387,
[final] ).
cnf(c_0_4298,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Oorder(X1) ),
c_0_3388,
[final] ).
cnf(c_0_4299,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3389,
[final] ).
cnf(c_0_4300,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Opreorder(X1) ),
c_0_3390,
[final] ).
cnf(c_0_4301,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Opreorder(X1) ),
c_0_3391,
[final] ).
cnf(c_0_4302,plain,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hBOOL(hAPP(hAPP(c_in(X4),X2),c_Map_Odom(X1,X4,X3))) ),
c_0_3392,
[final] ).
cnf(c_0_4303,plain,
( X4 = X3
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X4)) ),
c_0_3393,
[final] ).
cnf(c_0_4304,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OlessThan(X2,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1) ),
c_0_3394,
[final] ).
cnf(c_0_4305,plain,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X3),X4)),X5) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
c_0_3395,
[final] ).
cnf(c_0_4306,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = hAPP(hAPP(X1,X4),hAPP(c_Finite__Set_Ofold1(X1,X2),X3))
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
c_0_3396,
[final] ).
cnf(c_0_4307,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord__class_OlessThan(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_HOL_Oord(X1) ),
c_0_3397,
[final] ).
cnf(c_0_4308,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Complete__Lattice_OSup__class_OSup(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
c_0_3398,
[final] ).
cnf(c_0_4309,plain,
( hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))) = X3
| ~ c_Orderings_Olinorder(X4,X5,X6) ),
c_0_3399,
[final] ).
cnf(c_0_4310,plain,
( X1 = X2
| hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) != hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) ),
c_0_3400,
[final] ).
cnf(c_0_4311,plain,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X1),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_3401,
[final] ).
cnf(c_0_4312,plain,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_3402,
[final] ).
cnf(c_0_4313,plain,
( hAPP(hAPP(X1,X4),hAPP(hAPP(X1,X5),X6)) = hAPP(hAPP(X1,X5),hAPP(hAPP(X1,X4),X6))
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3) ),
c_0_3403,
[final] ).
cnf(c_0_4314,plain,
( c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2) = c_Finite__Set_Ocard(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1)) ),
c_0_3404,
[final] ).
cnf(c_0_4315,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2)))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3405,
[final] ).
cnf(c_0_4316,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3406,
[final] ).
cnf(c_0_4317,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)))
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_3407,
[final] ).
cnf(c_0_4318,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)))
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_3408,
[final] ).
cnf(c_0_4319,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)))
| ~ class_Lattices_Olattice(X1) ),
c_0_3409,
[final] ).
cnf(c_0_4320,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)))
| ~ class_Lattices_Olattice(X1) ),
c_0_3410,
[final] ).
cnf(c_0_4321,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1)),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_3411,
[final] ).
cnf(c_0_4322,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1)),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_3412,
[final] ).
cnf(c_0_4323,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1)) ),
c_0_3413,
[final] ).
cnf(c_0_4324,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Olattice(X1) ),
c_0_3414,
[final] ).
cnf(c_0_4325,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_3415,
[final] ).
cnf(c_0_4326,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
c_0_3416,
[final] ).
cnf(c_0_4327,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_3417,
[final] ).
cnf(c_0_4328,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3418,
[final] ).
cnf(c_0_4329,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3419,
[final] ).
cnf(c_0_4330,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3420,
[final] ).
cnf(c_0_4331,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3421,
[final] ).
cnf(c_0_4332,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4))
| ~ class_Lattices_Olattice(X1) ),
c_0_3422,
[final] ).
cnf(c_0_4333,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_3423,
[final] ).
cnf(c_0_4334,plain,
( c_Finite__Set_Osetsum(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
c_0_3424,
[final] ).
cnf(c_0_4335,plain,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| ~ class_Orderings_Oorder(X1) ),
c_0_3425,
[final] ).
cnf(c_0_4336,plain,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1) ),
c_0_3426,
[final] ).
cnf(c_0_4337,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),c_Suc(X2))) ),
c_0_3427,
[final] ).
cnf(c_0_4338,plain,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| X4 = X5
| ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
c_0_3428,
[final] ).
cnf(c_0_4339,plain,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| X4 = X5
| ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
c_0_3429,
[final] ).
cnf(c_0_4340,plain,
( c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2) ),
c_0_3430,
[final] ).
cnf(c_0_4341,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X1) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
c_0_3431,
[final] ).
cnf(c_0_4342,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
c_0_3432,
[final] ).
cnf(c_0_4343,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),hAPP(c_Finite__Set_Olattice__class_OInf__fin(X2),X1)) = X3
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Lattices_Olattice(X2) ),
c_0_3433,
[final] ).
cnf(c_0_4344,plain,
( X3 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
c_0_3434,
[final] ).
cnf(c_0_4345,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| ~ class_Orderings_Oorder(X3) ),
c_0_3435,
[final] ).
cnf(c_0_4346,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
c_0_3436,
[final] ).
cnf(c_0_4347,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
c_0_3437,
[final] ).
cnf(c_0_4348,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
c_0_3438,
[final] ).
cnf(c_0_4349,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ class_Orderings_Oorder(X3) ),
c_0_3439,
[final] ).
cnf(c_0_4350,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3440,
[final] ).
cnf(c_0_4351,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3441,
[final] ).
cnf(c_0_4352,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X4),X1),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_3442,
[final] ).
cnf(c_0_4353,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
c_0_3443,
[final] ).
cnf(c_0_4354,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
c_0_3444,
[final] ).
cnf(c_0_4355,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),X2)) ),
c_0_3445,
[final] ).
cnf(c_0_4356,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),c_Suc(X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
c_0_3446,
[final] ).
cnf(c_0_4357,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),c_Suc(X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
c_0_3447,
[final] ).
cnf(c_0_4358,plain,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2) = c_Suc(c_Finite__Set_Ocard(X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_3448,
[final] ).
cnf(c_0_4359,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X3) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
c_0_3449,
[final] ).
cnf(c_0_4360,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1))
| hBOOL(hAPP(hAPP(X3,X2),X1)) ),
c_0_3450,
[final] ).
cnf(c_0_4361,plain,
( c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Osetsum(X3,X1,X2,X4) = c_HOL_Ozero__class_Ozero(X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
c_0_3451,
[final] ).
cnf(c_0_4362,plain,
( c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Osetsum(X3,X1,X2,X4) = c_HOL_Ozero__class_Ozero(X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
c_0_3452,
[final] ).
cnf(c_0_4363,plain,
( c_Suc(X1) = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
c_0_3453,
[final] ).
cnf(c_0_4364,plain,
( c_HOL_Ominus__class_Ominus(hAPP(X1,v_x),hAPP(X2,v_x),X3) = hAPP(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(t_a,X3)),v_x)
| ~ class_HOL_Ominus(X3) ),
c_0_3454,
[final] ).
cnf(c_0_4365,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X2),X3),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1)) = hAPP(c_Finite__Set_Olinorder__class_OMin(X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_3455,
[final] ).
cnf(c_0_4366,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),X3),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1)) = hAPP(c_Finite__Set_Olinorder__class_OMax(X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
c_0_3456,
[final] ).
cnf(c_0_4367,plain,
( X3 = hAPP(c_Option_Ooption_OSome(X1),X2)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Option_Oset(X3,X1))) ),
c_0_3457,
[final] ).
cnf(c_0_4368,plain,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Map_Odom(X3,X1,X4)) = c_Map_Odom(X3,X1,X4)
| hAPP(X3,X2) != hAPP(c_Option_Ooption_OSome(X4),X5) ),
c_0_3458,
[final] ).
cnf(c_0_4369,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2))) ),
c_0_3459,
[final] ).
cnf(c_0_4370,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| X2 = X1
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2))) ),
c_0_3460,
[final] ).
cnf(c_0_4371,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2))) ),
c_0_3461,
[final] ).
cnf(c_0_4372,plain,
( hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5)) = hAPP(hAPP(X1,X4),hAPP(hAPP(X1,X3),X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
c_0_3462,
[final] ).
cnf(c_0_4373,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
c_0_3463,
[final] ).
cnf(c_0_4374,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
c_0_3464,
[final] ).
cnf(c_0_4375,plain,
( hBOOL(hAPP(hAPP(c_in(X3),X4),X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hAPP(hAPP(c_Set_Oinsert(X3),X4),X5) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_3465,
[final] ).
cnf(c_0_4376,plain,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| hBOOL(hAPP(hAPP(X2,X5),X4))
| X4 = X5
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
c_0_3466,
[final] ).
cnf(c_0_4377,plain,
( X4 = X5
| hBOOL(hAPP(hAPP(X2,X4),X5))
| hBOOL(hAPP(hAPP(X2,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
c_0_3467,
[final] ).
cnf(c_0_4378,plain,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| X4 = X5
| hBOOL(hAPP(hAPP(X2,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
c_0_3468,
[final] ).
cnf(c_0_4379,plain,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| hBOOL(hAPP(hAPP(X2,X5),X4))
| X5 = X4
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
c_0_3469,
[final] ).
cnf(c_0_4380,plain,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
c_0_3470,
[final] ).
cnf(c_0_4381,plain,
( hBOOL(hAPP(hAPP(X1,X4),X5))
| hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
c_0_3471,
[final] ).
cnf(c_0_4382,plain,
( hBOOL(hAPP(hAPP(X1,X4),X5))
| hBOOL(hAPP(hAPP(X2,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
c_0_3472,
[final] ).
cnf(c_0_4383,plain,
( hBOOL(hAPP(hAPP(X1,X4),X5))
| hBOOL(hAPP(hAPP(X2,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
c_0_3473,
[final] ).
cnf(c_0_4384,plain,
( hBOOL(hAPP(hAPP(X1,X2),X2))
| hBOOL(hAPP(hAPP(X3,X2),X2))
| ~ c_Orderings_Olinorder(X1,X3,X4) ),
c_0_3474,
[final] ).
cnf(c_0_4385,plain,
( hAPP(c_Finite__Set_Olinorder__class_OMin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) = X2
| ~ class_Orderings_Olinorder(X1) ),
c_0_3475,
[final] ).
cnf(c_0_4386,plain,
( hAPP(c_Finite__Set_Olinorder__class_OMax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) = X2
| ~ class_Orderings_Olinorder(X1) ),
c_0_3476,
[final] ).
cnf(c_0_4387,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
c_0_3477,
[final] ).
cnf(c_0_4388,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3478,
[final] ).
cnf(c_0_4389,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3479,
[final] ).
cnf(c_0_4390,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3480,
[final] ).
cnf(c_0_4391,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X2) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3481,
[final] ).
cnf(c_0_4392,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_3482,
[final] ).
cnf(c_0_4393,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_3483,
[final] ).
cnf(c_0_4394,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_3484,
[final] ).
cnf(c_0_4395,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_3485,
[final] ).
cnf(c_0_4396,plain,
( c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
c_0_3486,
[final] ).
cnf(c_0_4397,plain,
( c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
c_0_3487,
[final] ).
cnf(c_0_4398,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X4,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,X1,X3) ),
c_0_3488,
[final] ).
cnf(c_0_4399,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X2),X1))
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
c_0_3489,
[final] ).
cnf(c_0_4400,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| X2 = X3
| ~ class_Orderings_Olinorder(X1) ),
c_0_3490,
[final] ).
cnf(c_0_4401,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X2),X1))
| ~ class_Orderings_Olinorder(X3) ),
c_0_3491,
[final] ).
cnf(c_0_4402,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3492,
[final] ).
cnf(c_0_4403,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
c_0_3493,
[final] ).
cnf(c_0_4404,plain,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_3494,
[final] ).
cnf(c_0_4405,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3495,
[final] ).
cnf(c_0_4406,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3496,
[final] ).
cnf(c_0_4407,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3497,
[final] ).
cnf(c_0_4408,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3498,
[final] ).
cnf(c_0_4409,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3499,
[final] ).
cnf(c_0_4410,plain,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X2,X4),X4)) ),
c_0_3500,
[final] ).
cnf(c_0_4411,plain,
( ~ hBOOL(hAPP(hAPP(X1,X2),X2))
| ~ c_Orderings_Olinorder(X3,X1,X4) ),
c_0_3501,
[final] ).
cnf(c_0_4412,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)
| ~ class_Orderings_Olinorder(X1) ),
c_0_3502,
[final] ).
cnf(c_0_4413,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
c_0_3503,
[final] ).
cnf(c_0_4414,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Olattice(X1) ),
c_0_3504,
[final] ).
cnf(c_0_4415,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_3505,
[final] ).
cnf(c_0_4416,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)
| ~ class_Orderings_Olinorder(X1) ),
c_0_3506,
[final] ).
cnf(c_0_4417,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)
| ~ class_Lattices_Olattice(X1) ),
c_0_3507,
[final] ).
cnf(c_0_4418,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_3508,
[final] ).
cnf(c_0_4419,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
c_0_3509,
[final] ).
cnf(c_0_4420,plain,
( c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Complete__Lattice_OSup__class_OSup(X3,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
c_0_3510,
[final] ).
cnf(c_0_4421,plain,
( c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Complete__Lattice_OInf__class_OInf(X3,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
c_0_3511,
[final] ).
cnf(c_0_4422,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X1)) ),
c_0_3512,
[final] ).
cnf(c_0_4423,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),c_Suc(X1))) ),
c_0_3513,
[final] ).
cnf(c_0_4424,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
c_0_3514,
[final] ).
cnf(c_0_4425,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) != X3
| ~ class_Orderings_Olinorder(X1) ),
c_0_3515,
[final] ).
cnf(c_0_4426,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) != X2
| ~ class_Orderings_Olinorder(X1) ),
c_0_3516,
[final] ).
cnf(c_0_4427,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) != X3
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_3517,
[final] ).
cnf(c_0_4428,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) != X2
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_3518,
[final] ).
cnf(c_0_4429,plain,
( c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1) ),
c_0_3519,
[final] ).
cnf(c_0_4430,plain,
( X1 = c_COMBK(c_Option_Ooption_ONone(X2),tc_Option_Ooption(X2),X3)
| c_Map_Odom(X1,X3,X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_3520,
[final] ).
cnf(c_0_4431,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| ~ class_Orderings_Oorder(X1) ),
c_0_3521,
[final] ).
cnf(c_0_4432,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1) ),
c_0_3522,
[final] ).
cnf(c_0_4433,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1)) ),
c_0_3523,
[final] ).
cnf(c_0_4434,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1)) ),
c_0_3524,
[final] ).
cnf(c_0_4435,plain,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_3525,
[final] ).
cnf(c_0_4436,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_3526,
[final] ).
cnf(c_0_4437,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_3527,
[final] ).
cnf(c_0_4438,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_3528,
[final] ).
cnf(c_0_4439,plain,
( hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X3),X4)) = hAPP(hAPP(X1,X3),X4)
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2) ),
c_0_3529,
[final] ).
cnf(c_0_4440,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2))
| ~ class_Orderings_Oorder(X1) ),
c_0_3530,
[final] ).
cnf(c_0_4441,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2))
| ~ class_Orderings_Olinorder(X1) ),
c_0_3531,
[final] ).
cnf(c_0_4442,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2))
| ~ class_Orderings_Opreorder(X1) ),
c_0_3532,
[final] ).
cnf(c_0_4443,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3) ),
c_0_3533,
[final] ).
cnf(c_0_4444,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
c_0_3534,
[final] ).
cnf(c_0_4445,plain,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
c_0_3535,
[final] ).
cnf(c_0_4446,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
c_0_3536,
[final] ).
cnf(c_0_4447,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,X2) = hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))
| ~ class_Orderings_Oorder(X2) ),
c_0_3537,
[final] ).
cnf(c_0_4448,plain,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X3,X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
c_0_3538,
[final] ).
cnf(c_0_4449,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) ),
c_0_3539,
[final] ).
cnf(c_0_4450,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) ),
c_0_3540,
[final] ).
cnf(c_0_4451,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)) = X2
| ~ class_Orderings_Olinorder(X1) ),
c_0_3541,
[final] ).
cnf(c_0_4452,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)) = X2
| ~ class_Orderings_Olinorder(X1) ),
c_0_3542,
[final] ).
cnf(c_0_4453,plain,
( hBOOL(hAPP(hAPP(c_in(X3),X2),X1))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_3543,
[final] ).
cnf(c_0_4454,plain,
( X2 = X1
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X1),X2)) ),
c_0_3544,
[final] ).
cnf(c_0_4455,plain,
( c_Hoare__Mirabelle_Ohoare__valids(X1,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3) ),
c_0_3545,
[final] ).
cnf(c_0_4456,plain,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_3546,
[final] ).
cnf(c_0_4457,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_Orderings_Obot__class_Obot(X1)),X2))
| ~ class_Orderings_Obot(X1) ),
c_0_3547,
[final] ).
cnf(c_0_4458,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| ~ class_Orderings_Oorder(X1) ),
c_0_3548,
[final] ).
cnf(c_0_4459,plain,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| ~ class_Orderings_Opreorder(X1) ),
c_0_3549,
[final] ).
cnf(c_0_4460,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3550,
[final] ).
cnf(c_0_4461,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_3551,
[final] ).
cnf(c_0_4462,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3552,
[final] ).
cnf(c_0_4463,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3553,
[final] ).
cnf(c_0_4464,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3554,
[final] ).
cnf(c_0_4465,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_3555,
[final] ).
cnf(c_0_4466,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
c_0_3556,
[final] ).
cnf(c_0_4467,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X2)
| ~ class_Orderings_Olinorder(X1) ),
c_0_3557,
[final] ).
cnf(c_0_4468,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2)
| ~ class_Orderings_Olinorder(X1) ),
c_0_3558,
[final] ).
cnf(c_0_4469,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
c_0_3559,
[final] ).
cnf(c_0_4470,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_3560,
[final] ).
cnf(c_0_4471,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
c_0_3561,
[final] ).
cnf(c_0_4472,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
c_0_3562,
[final] ).
cnf(c_0_4473,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
c_0_3563,
[final] ).
cnf(c_0_4474,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
c_0_3564,
[final] ).
cnf(c_0_4475,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != X3
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_3565,
[final] ).
cnf(c_0_4476,plain,
( hAPP(hAPP(X1,X3),X4) = hAPP(hAPP(X1,X4),X3)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
c_0_3566,
[final] ).
cnf(c_0_4477,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
c_0_3567,
[final] ).
cnf(c_0_4478,plain,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
c_0_3568,
[final] ).
cnf(c_0_4479,plain,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
c_0_3569,
[final] ).
cnf(c_0_4480,plain,
( X1 = c_Orderings_Obot__class_Obot(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),X1) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
c_0_3570,
[final] ).
cnf(c_0_4481,plain,
( X1 = c_Orderings_Obot__class_Obot(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X1),X3) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
c_0_3571,
[final] ).
cnf(c_0_4482,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(c_Finite__Set_Olattice__class_OInf__fin(X2),X1) = c_Complete__Lattice_OInf__class_OInf(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
c_0_3572,
[final] ).
cnf(c_0_4483,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
c_0_3573,
[final] ).
cnf(c_0_4484,plain,
( c_Finite__Set_Ofun__left__comm(X1,X2,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
c_0_3574,
[final] ).
cnf(c_0_4485,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_3575,
[final] ).
cnf(c_0_4486,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3576,
[final] ).
cnf(c_0_4487,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
c_0_3577,
[final] ).
cnf(c_0_4488,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
c_0_3578,
[final] ).
cnf(c_0_4489,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3579,
[final] ).
cnf(c_0_4490,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X2) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
c_0_3580,
[final] ).
cnf(c_0_4491,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
c_0_3581,
[final] ).
cnf(c_0_4492,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Ozero__class_Ozero(X2)) = X1
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_3582,
[final] ).
cnf(c_0_4493,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
c_0_3583,
[final] ).
cnf(c_0_4494,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3584,
[final] ).
cnf(c_0_4495,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_3585,
[final] ).
cnf(c_0_4496,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_3586,
[final] ).
cnf(c_0_4497,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3587,
[final] ).
cnf(c_0_4498,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
c_0_3588,
[final] ).
cnf(c_0_4499,plain,
( X1 = c_Option_Ooption_ONone(X2)
| c_Option_Oset(X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
c_0_3589,
[final] ).
cnf(c_0_4500,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3590,
[final] ).
cnf(c_0_4501,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
c_0_3591,
[final] ).
cnf(c_0_4502,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
c_0_3592,
[final] ).
cnf(c_0_4503,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
c_0_3593,
[final] ).
cnf(c_0_4504,plain,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_3594,
[final] ).
cnf(c_0_4505,plain,
( c_Finite__Set_Ofun__left__comm(c_HOL_Otimes__class_Otimes(X1),X1,X1)
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
c_0_3595,
[final] ).
cnf(c_0_4506,plain,
( c_Finite__Set_Ofun__left__comm(c_HOL_Oplus__class_Oplus(X1),X1,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_3596,
[final] ).
cnf(c_0_4507,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
c_0_3597,
[final] ).
cnf(c_0_4508,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
c_0_3598,
[final] ).
cnf(c_0_4509,plain,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_3599,
[final] ).
cnf(c_0_4510,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Orderings_Obot__class_Obot(X1)) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
c_0_3600,
[final] ).
cnf(c_0_4511,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_3601,
[final] ).
cnf(c_0_4512,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
c_0_3602,
[final] ).
cnf(c_0_4513,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
c_0_3603,
[final] ).
cnf(c_0_4514,plain,
( X1 = X2
| hAPP(c_Option_Ooption_OSome(X3),X1) != hAPP(c_Option_Ooption_OSome(X3),X2) ),
c_0_3604,
[final] ).
cnf(c_0_4515,plain,
( hAPP(hAPP(X1,X3),X3) = X3
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2) ),
c_0_3605,
[final] ).
cnf(c_0_4516,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X2) = X2
| ~ class_Orderings_Olinorder(X1) ),
c_0_3606,
[final] ).
cnf(c_0_4517,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X2) = X2
| ~ class_Orderings_Olinorder(X1) ),
c_0_3607,
[final] ).
cnf(c_0_4518,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X2) = X2
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_3608,
[final] ).
cnf(c_0_4519,plain,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2) = X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
c_0_3609,
[final] ).
cnf(c_0_4520,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X2) = X2
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_3610,
[final] ).
cnf(c_0_4521,plain,
( X1 = X2
| c_SetInterval_Oord__class_OlessThan(X1,X3) != c_SetInterval_Oord__class_OlessThan(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_3611,
[final] ).
cnf(c_0_4522,plain,
( X1 = X2
| c_Com_Ocom_OSemi(X3,X1) != c_Com_Ocom_OSemi(X4,X2) ),
c_0_3612,
[final] ).
cnf(c_0_4523,plain,
( X1 = X2
| c_Com_Ocom_OSemi(X1,X3) != c_Com_Ocom_OSemi(X2,X4) ),
c_0_3613,
[final] ).
cnf(c_0_4524,plain,
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2))
| ~ class_Finite__Set_Ofinite_Ofinite(X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
c_0_3614,
[final] ).
cnf(c_0_4525,plain,
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
c_0_3615,
[final] ).
cnf(c_0_4526,plain,
( class_Lattices_Oupper__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
c_0_3616,
[final] ).
cnf(c_0_4527,plain,
( class_Lattices_Olower__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
c_0_3617,
[final] ).
cnf(c_0_4528,plain,
( class_Lattices_Odistrib__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
c_0_3618,
[final] ).
cnf(c_0_4529,plain,
( class_Lattices_Obounded__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
c_0_3619,
[final] ).
cnf(c_0_4530,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
c_0_3620,
[final] ).
cnf(c_0_4531,plain,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
c_0_3621,
[final] ).
cnf(c_0_4532,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
c_0_3622,
[final] ).
cnf(c_0_4533,plain,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
c_0_3623,
[final] ).
cnf(c_0_4534,plain,
( class_HOL_Ominus(tc_fun(X2,X1))
| ~ class_HOL_Ominus(X1) ),
c_0_3624,
[final] ).
cnf(c_0_4535,plain,
( class_HOL_Oord(tc_fun(X2,X1))
| ~ class_HOL_Oord(X1) ),
c_0_3625,
[final] ).
cnf(c_0_4536,plain,
( c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X1),X1) = c_Finite__Set_Olattice__class_OInf__fin(X1)
| ~ class_Lattices_Olattice(X1) ),
c_0_3626,
[final] ).
cnf(c_0_4537,plain,
( c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(X1),X1) = c_Finite__Set_Olinorder__class_OMax(X1)
| ~ class_Orderings_Olinorder(X1) ),
c_0_3627,
[final] ).
cnf(c_0_4538,plain,
( c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X1),X1) = c_Finite__Set_Olinorder__class_OMin(X1)
| ~ class_Orderings_Olinorder(X1) ),
c_0_3628,
[final] ).
cnf(c_0_4539,plain,
( c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omin(X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
c_0_3629,
[final] ).
cnf(c_0_4540,plain,
( c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omax(X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
c_0_3630,
[final] ).
cnf(c_0_4541,plain,
( c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Oupper__semilattice__class_Osup(X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
c_0_3631,
[final] ).
cnf(c_0_4542,plain,
( c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Olower__semilattice__class_Oinf(X1),X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
c_0_3632,
[final] ).
cnf(c_0_4543,plain,
( c_Orderings_Oord__class_Omax(X1) = c_Lattices_Oupper__semilattice__class_Osup(X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ class_Orderings_Olinorder(X1) ),
c_0_3633,
[final] ).
cnf(c_0_4544,plain,
( c_Orderings_Oord__class_Omin(X1) = c_Lattices_Olower__semilattice__class_Oinf(X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ class_Orderings_Olinorder(X1) ),
c_0_3634,
[final] ).
cnf(c_0_4545,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
c_0_3635,
[final] ).
cnf(c_0_4546,plain,
( class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(X1))
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
c_0_3636,
[final] ).
cnf(c_0_4547,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
c_0_3637,
[final] ).
cnf(c_0_4548,plain,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
c_0_3638,
[final] ).
cnf(c_0_4549,plain,
( X1 = X2
| c_Com_Ocom_OBODY(X1) != c_Com_Ocom_OBODY(X2) ),
c_0_3639,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_3640_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_3640]) ).
cnf(c_0_3640_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_3640]) ).
cnf(c_0_3641_0,axiom,
( hAPP(hAPP(X6,X11),hAPP(X2,X10)) = c_Finite__Set_Ofold(X6,X11,X10,X9,X9)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ c_Finite__Set_Ofinite(X10,X9) ),
inference(literals_permutation,[status(thm)],[c_0_3641]) ).
cnf(c_0_3641_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(hAPP(X6,X11),hAPP(X2,X10)) = c_Finite__Set_Ofold(X6,X11,X10,X9,X9)
| ~ c_Finite__Set_Ofinite(X10,X9) ),
inference(literals_permutation,[status(thm)],[c_0_3641]) ).
cnf(c_0_3641_2,axiom,
( ~ c_Finite__Set_Ofinite(X10,X9)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(hAPP(X6,X11),hAPP(X2,X10)) = c_Finite__Set_Ofold(X6,X11,X10,X9,X9) ),
inference(literals_permutation,[status(thm)],[c_0_3641]) ).
cnf(c_0_3642_0,axiom,
( hAPP(hAPP(X5,X11),hAPP(X1,X10)) = c_Finite__Set_Ofold(X5,X11,X10,X9,X9)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ c_Finite__Set_Ofinite(X10,X9) ),
inference(literals_permutation,[status(thm)],[c_0_3642]) ).
cnf(c_0_3642_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(hAPP(X5,X11),hAPP(X1,X10)) = c_Finite__Set_Ofold(X5,X11,X10,X9,X9)
| ~ c_Finite__Set_Ofinite(X10,X9) ),
inference(literals_permutation,[status(thm)],[c_0_3642]) ).
cnf(c_0_3642_2,axiom,
( ~ c_Finite__Set_Ofinite(X10,X9)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(hAPP(X5,X11),hAPP(X1,X10)) = c_Finite__Set_Ofold(X5,X11,X10,X9,X9) ),
inference(literals_permutation,[status(thm)],[c_0_3642]) ).
cnf(c_0_3643_0,axiom,
( hAPP(X2,X10) = c_Finite__Set_Ofold(X6,X7,X10,X9,X9)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ c_Finite__Set_Ofinite(X10,X9) ),
inference(literals_permutation,[status(thm)],[c_0_3643]) ).
cnf(c_0_3643_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(X2,X10) = c_Finite__Set_Ofold(X6,X7,X10,X9,X9)
| ~ c_Finite__Set_Ofinite(X10,X9) ),
inference(literals_permutation,[status(thm)],[c_0_3643]) ).
cnf(c_0_3643_2,axiom,
( ~ c_Finite__Set_Ofinite(X10,X9)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(X2,X10) = c_Finite__Set_Ofold(X6,X7,X10,X9,X9) ),
inference(literals_permutation,[status(thm)],[c_0_3643]) ).
cnf(c_0_3644_0,axiom,
( hAPP(X1,X10) = c_Finite__Set_Ofold(X5,X8,X10,X9,X9)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ c_Finite__Set_Ofinite(X10,X9) ),
inference(literals_permutation,[status(thm)],[c_0_3644]) ).
cnf(c_0_3644_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(X1,X10) = c_Finite__Set_Ofold(X5,X8,X10,X9,X9)
| ~ c_Finite__Set_Ofinite(X10,X9) ),
inference(literals_permutation,[status(thm)],[c_0_3644]) ).
cnf(c_0_3644_2,axiom,
( ~ c_Finite__Set_Ofinite(X10,X9)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(X1,X10) = c_Finite__Set_Ofold(X5,X8,X10,X9,X9) ),
inference(literals_permutation,[status(thm)],[c_0_3644]) ).
cnf(c_0_3645_0,axiom,
( hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X9),X10),hAPP(hAPP(c_Set_Oinsert(X9),X11),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))))) = 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_3645]) ).
cnf(c_0_3645_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X9),X10),hAPP(hAPP(c_Set_Oinsert(X9),X11),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))))) = hAPP(hAPP(X5,X10),X11) ),
inference(literals_permutation,[status(thm)],[c_0_3645]) ).
cnf(c_0_3646_0,axiom,
( hAPP(X2,hAPP(hAPP(c_Set_Oinsert(X9),X10),hAPP(hAPP(c_Set_Oinsert(X9),X11),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))))) = 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_3646]) ).
cnf(c_0_3646_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(X2,hAPP(hAPP(c_Set_Oinsert(X9),X10),hAPP(hAPP(c_Set_Oinsert(X9),X11),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))))) = hAPP(hAPP(X6,X10),X11) ),
inference(literals_permutation,[status(thm)],[c_0_3646]) ).
cnf(c_0_3647_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_3647]) ).
cnf(c_0_3647_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_3647]) ).
cnf(c_0_3647_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_3647]) ).
cnf(c_0_3648_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_3648]) ).
cnf(c_0_3648_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_3648]) ).
cnf(c_0_3648_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_3648]) ).
cnf(c_0_3649_0,axiom,
( hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X9),X10),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)))) = X10
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_3649]) ).
cnf(c_0_3649_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X9),X10),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)))) = X10 ),
inference(literals_permutation,[status(thm)],[c_0_3649]) ).
cnf(c_0_3650_0,axiom,
( hAPP(X2,hAPP(hAPP(c_Set_Oinsert(X9),X10),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)))) = X10
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9) ),
inference(literals_permutation,[status(thm)],[c_0_3650]) ).
cnf(c_0_3650_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(X2,hAPP(hAPP(c_Set_Oinsert(X9),X10),c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)))) = X10 ),
inference(literals_permutation,[status(thm)],[c_0_3650]) ).
cnf(c_0_3651_0,axiom,
( hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X9),X10),X11)) = 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_3651]) ).
cnf(c_0_3651_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X9),X10),X11)) = hAPP(hAPP(X5,X10),hAPP(X1,X11)) ),
inference(literals_permutation,[status(thm)],[c_0_3651]) ).
cnf(c_0_3652_0,axiom,
( hAPP(X2,hAPP(hAPP(c_Set_Oinsert(X9),X10),X11)) = 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_3652]) ).
cnf(c_0_3652_1,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| hAPP(X2,hAPP(hAPP(c_Set_Oinsert(X9),X10),X11)) = hAPP(hAPP(X6,X10),hAPP(X2,X11)) ),
inference(literals_permutation,[status(thm)],[c_0_3652]) ).
cnf(c_0_3653_0,axiom,
( X10 = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))
| c_Finite__Set_Olattice_OSup__fin(X6,X10,X9) = hAPP(X2,X10)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ c_Finite__Set_Ofinite(X10,X9) ),
inference(literals_permutation,[status(thm)],[c_0_3653]) ).
cnf(c_0_3653_1,axiom,
( c_Finite__Set_Olattice_OSup__fin(X6,X10,X9) = hAPP(X2,X10)
| X10 = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ c_Finite__Set_Ofinite(X10,X9) ),
inference(literals_permutation,[status(thm)],[c_0_3653]) ).
cnf(c_0_3653_2,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| c_Finite__Set_Olattice_OSup__fin(X6,X10,X9) = hAPP(X2,X10)
| X10 = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))
| ~ c_Finite__Set_Ofinite(X10,X9) ),
inference(literals_permutation,[status(thm)],[c_0_3653]) ).
cnf(c_0_3653_3,axiom,
( ~ c_Finite__Set_Ofinite(X10,X9)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| c_Finite__Set_Olattice_OSup__fin(X6,X10,X9) = hAPP(X2,X10)
| X10 = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_3653]) ).
cnf(c_0_3654_0,axiom,
( X10 = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))
| c_Finite__Set_Olattice_OInf__fin(X5,X10,X9) = hAPP(X1,X10)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ c_Finite__Set_Ofinite(X10,X9) ),
inference(literals_permutation,[status(thm)],[c_0_3654]) ).
cnf(c_0_3654_1,axiom,
( c_Finite__Set_Olattice_OInf__fin(X5,X10,X9) = hAPP(X1,X10)
| X10 = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| ~ c_Finite__Set_Ofinite(X10,X9) ),
inference(literals_permutation,[status(thm)],[c_0_3654]) ).
cnf(c_0_3654_2,axiom,
( ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| c_Finite__Set_Olattice_OInf__fin(X5,X10,X9) = hAPP(X1,X10)
| X10 = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))
| ~ c_Finite__Set_Ofinite(X10,X9) ),
inference(literals_permutation,[status(thm)],[c_0_3654]) ).
cnf(c_0_3654_3,axiom,
( ~ c_Finite__Set_Ofinite(X10,X9)
| ~ c_Complete__Lattice_Ocomplete__lattice(X1,X2,X3,X4,X5,X6,X7,X8,X9)
| c_Finite__Set_Olattice_OInf__fin(X5,X10,X9) = hAPP(X1,X10)
| X10 = c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_3654]) ).
cnf(c_0_3655_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_3655]) ).
cnf(c_0_3655_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_3655]) ).
cnf(c_0_3656_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_3656]) ).
cnf(c_0_3656_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_3656]) ).
cnf(c_0_3657_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X4,X3,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X1,X2,X3,X4)),tc_fun(tc_Com_Ostate,tc_bool),t_a),X4,c_COMBK(hAPP(X3,v_sko__Hoare__Mirabelle__Xescape__1(X1,X2,X3,X4)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_3657]) ).
cnf(c_0_3657_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X1,X2,X3,X4)),tc_fun(tc_Com_Ostate,tc_bool),t_a),X4,c_COMBK(hAPP(X3,v_sko__Hoare__Mirabelle__Xescape__1(X1,X2,X3,X4)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X4,X3,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_3657]) ).
cnf(c_0_3658_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,c_HOL_Ozero__class_Ozero(X4),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X4,X2)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,c_HOL_Ozero__class_Ozero(X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X4,X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,c_HOL_Ozero__class_Ozero(X4),X1,X4,X2)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,c_HOL_Ozero__class_Ozero(X4),X3,X4,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_3658]) ).
cnf(c_0_3658_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,c_HOL_Ozero__class_Ozero(X4),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X4,X2)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,c_HOL_Ozero__class_Ozero(X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X4,X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,c_HOL_Ozero__class_Ozero(X4),X1,X4,X2)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,c_HOL_Ozero__class_Ozero(X4),X3,X4,X2))
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_3658]) ).
cnf(c_0_3658_2,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,c_HOL_Ozero__class_Ozero(X4),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X4,X2)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,c_HOL_Ozero__class_Ozero(X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X4,X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,c_HOL_Ozero__class_Ozero(X4),X1,X4,X2)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,c_HOL_Ozero__class_Ozero(X4),X3,X4,X2))
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_3658]) ).
cnf(c_0_3658_3,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,c_HOL_Ozero__class_Ozero(X4),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X4,X2)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,c_HOL_Ozero__class_Ozero(X4),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X4,X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,c_HOL_Ozero__class_Ozero(X4),X1,X4,X2)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,c_HOL_Ozero__class_Ozero(X4),X3,X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3658]) ).
cnf(c_0_3659_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X1,X6,X5,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X6,X5,X3,X2,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3659]) ).
cnf(c_0_3659_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X1,X6,X5,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X6,X5,X3,X2,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3659]) ).
cnf(c_0_3659_2,axiom,
( ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X1,X6,X5,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X6,X5,X3,X2,X4)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_3659]) ).
cnf(c_0_3660_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X1,X6,X5,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X1,X6,X5,X3,X2,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3660]) ).
cnf(c_0_3660_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X1,X6,X5,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X1,X6,X5,X3,X2,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3660]) ).
cnf(c_0_3660_2,axiom,
( ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X1,X6,X5,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X1,X6,X5,X3,X2,X4)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_3660]) ).
cnf(c_0_3661_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X4,X1,X3)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X5,X1,X3)) = c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X5),X1,X3)
| ~ c_Finite__Set_Ofinite(X4,X3)
| ~ c_Finite__Set_Ofinite(X5,X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X5) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3661]) ).
cnf(c_0_3661_1,axiom,
( ~ c_Finite__Set_Ofinite(X4,X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X4,X1,X3)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X5,X1,X3)) = c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X5),X1,X3)
| ~ c_Finite__Set_Ofinite(X5,X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X5) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3661]) ).
cnf(c_0_3661_2,axiom,
( ~ c_Finite__Set_Ofinite(X5,X3)
| ~ c_Finite__Set_Ofinite(X4,X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X4,X1,X3)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X5,X1,X3)) = c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X5),X1,X3)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X5) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3661]) ).
cnf(c_0_3661_3,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X5) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X5,X3)
| ~ c_Finite__Set_Ofinite(X4,X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X4,X1,X3)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X5,X1,X3)) = c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X5),X1,X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3661]) ).
cnf(c_0_3661_4,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X5) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X5,X3)
| ~ c_Finite__Set_Ofinite(X4,X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X4,X1,X3)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),X5,X1,X3)) = c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X1),X2,c_HOL_Ozero__class_Ozero(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X5),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3661]) ).
cnf(c_0_3662_0,axiom,
( hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X1,X6,X7,X3,X2,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X7,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X1,X6,X7,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3662]) ).
cnf(c_0_3662_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X7,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X1,X6,X7,X3,X2,X4)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X1,X6,X7,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3662]) ).
cnf(c_0_3662_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X7,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X1,X6,X7,X3,X2,X4)))
| ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X1,X6,X7,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3662]) ).
cnf(c_0_3662_3,axiom,
( ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X1,X6,X7,X3)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X7,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X1,X6,X7,X3,X2,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3662]) ).
cnf(c_0_3663_0,axiom,
( hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X6,X7,X3,X2,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X7,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X1,X6,X7,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3663]) ).
cnf(c_0_3663_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X7,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X6,X7,X3,X2,X4)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X1,X6,X7,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3663]) ).
cnf(c_0_3663_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X7,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X6,X7,X3,X2,X4)))
| ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X1,X6,X7,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3663]) ).
cnf(c_0_3663_3,axiom,
( ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X1,X6,X7,X3)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X7,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X6,X7,X3,X2,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3663]) ).
cnf(c_0_3664_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,X6,hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X4,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(X5,X3)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,X6,X1,X4,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_3664]) ).
cnf(c_0_3664_1,axiom,
( c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,X6,hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X4,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(X5,X3)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,X6,X1,X4,X2))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_3664]) ).
cnf(c_0_3664_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,X6,hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X4,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(X5,X3)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,X6,X1,X4,X2))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_3664]) ).
cnf(c_0_3664_3,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,X6,hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X4,X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),hAPP(X5,X3)),c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X5,X6,X1,X4,X2))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3664]) ).
cnf(c_0_3665_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(X4),X5,X6,hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X4,X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),hAPP(X5,X3)),c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(X4),X5,X6,X1,X4,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Oab__semigroup__mult(X4) ),
inference(literals_permutation,[status(thm)],[c_0_3665]) ).
cnf(c_0_3665_1,axiom,
( c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(X4),X5,X6,hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X4,X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),hAPP(X5,X3)),c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(X4),X5,X6,X1,X4,X2))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Oab__semigroup__mult(X4) ),
inference(literals_permutation,[status(thm)],[c_0_3665]) ).
cnf(c_0_3665_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(X4),X5,X6,hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X4,X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),hAPP(X5,X3)),c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(X4),X5,X6,X1,X4,X2))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_OrderedGroup_Oab__semigroup__mult(X4) ),
inference(literals_permutation,[status(thm)],[c_0_3665]) ).
cnf(c_0_3665_3,axiom,
( ~ class_OrderedGroup_Oab__semigroup__mult(X4)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(X4),X5,X6,hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X4,X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),hAPP(X5,X3)),c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(X4),X5,X6,X1,X4,X2))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3665]) ).
cnf(c_0_3666_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X4),X5),X3))
| c_Finite__Set_Ofold__image(X1,X6,X7,hAPP(hAPP(c_Set_Oinsert(X4),X5),X3),X2,X4) = hAPP(hAPP(X1,hAPP(X6,X5)),c_Finite__Set_Ofold__image(X1,X6,X7,X3,X2,X4))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3666]) ).
cnf(c_0_3666_1,axiom,
( c_Finite__Set_Ofold__image(X1,X6,X7,hAPP(hAPP(c_Set_Oinsert(X4),X5),X3),X2,X4) = hAPP(hAPP(X1,hAPP(X6,X5)),c_Finite__Set_Ofold__image(X1,X6,X7,X3,X2,X4))
| hBOOL(hAPP(hAPP(c_in(X4),X5),X3))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3666]) ).
cnf(c_0_3666_2,axiom,
( ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| c_Finite__Set_Ofold__image(X1,X6,X7,hAPP(hAPP(c_Set_Oinsert(X4),X5),X3),X2,X4) = hAPP(hAPP(X1,hAPP(X6,X5)),c_Finite__Set_Ofold__image(X1,X6,X7,X3,X2,X4))
| hBOOL(hAPP(hAPP(c_in(X4),X5),X3))
| ~ c_Finite__Set_Ofinite(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3666]) ).
cnf(c_0_3666_3,axiom,
( ~ c_Finite__Set_Ofinite(X3,X4)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| c_Finite__Set_Ofold__image(X1,X6,X7,hAPP(hAPP(c_Set_Oinsert(X4),X5),X3),X2,X4) = hAPP(hAPP(X1,hAPP(X6,X5)),c_Finite__Set_Ofold__image(X1,X6,X7,X3,X2,X4))
| hBOOL(hAPP(hAPP(c_in(X4),X5),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3666]) ).
cnf(c_0_3667_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X1,X1),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X3))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3667]) ).
cnf(c_0_3667_1,axiom,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X1,X1),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X3))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3667]) ).
cnf(c_0_3667_2,axiom,
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1),X4))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X1,X1),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X3))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3667]) ).
cnf(c_0_3667_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1),X4))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X1,X1),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3667]) ).
cnf(c_0_3667_4,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1),X4))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X1,X1),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3667]) ).
cnf(c_0_3668_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X1,X1),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X2,X3,X1,X1),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X3))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3668]) ).
cnf(c_0_3668_1,axiom,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X1,X1),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X2,X3,X1,X1),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X3))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3668]) ).
cnf(c_0_3668_2,axiom,
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X2,X3,X1,X1),X4))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X1,X1),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X3))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3668]) ).
cnf(c_0_3668_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X2,X3,X1,X1),X4))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X1,X1),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3668]) ).
cnf(c_0_3668_4,axiom,
( ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X5),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X2,X3,X1,X1),X4))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X1,X1),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3668]) ).
cnf(c_0_3669_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X4))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X6,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool))),X2,X2),X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X3,X4,X2,X2),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X6),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3669]) ).
cnf(c_0_3669_1,axiom,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X6,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool))),X2,X2),X5))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X4))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X3,X4,X2,X2),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X6),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3669]) ).
cnf(c_0_3669_2,axiom,
( ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X6,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool))),X2,X2),X5))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X3,X4,X2,X2),X5))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X6),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3669]) ).
cnf(c_0_3669_3,axiom,
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X3,X4,X2,X2),X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X6,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool))),X2,X2),X5))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X6),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3669]) ).
cnf(c_0_3669_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X2),X6),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X3,X4,X2,X2),X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X6,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool))),X2,X2),X5))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3669]) ).
cnf(c_0_3670_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),X6)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X4)),X5)),X6))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3670]) ).
cnf(c_0_3670_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X4)),X5)),X6))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3670]) ).
cnf(c_0_3670_2,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X4)),X5)),X6))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),X6))) ),
inference(literals_permutation,[status(thm)],[c_0_3670]) ).
cnf(c_0_3671_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),X6)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X4)),X5)),X6))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3671]) ).
cnf(c_0_3671_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X4)),X5)),X6))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3671]) ).
cnf(c_0_3671_2,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X4)),X5)),X6))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),X6))) ),
inference(literals_permutation,[status(thm)],[c_0_3671]) ).
cnf(c_0_3672_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,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool)),X6,X1,X7) ),
inference(literals_permutation,[status(thm)],[c_0_3672]) ).
cnf(c_0_3672_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,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool)),X6,X1,X7) ),
inference(literals_permutation,[status(thm)],[c_0_3672]) ).
cnf(c_0_3672_2,axiom,
( ~ c_Nitpick_Ofold__graph_H(X4,X5,c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),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_3672]) ).
cnf(c_0_3673_0,axiom,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X6),hAPP(hAPP(X1,X5),X7)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))),tc_fun(X4,tc_bool)),X4,X6),X7))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X5),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3673]) ).
cnf(c_0_3673_1,axiom,
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))),tc_fun(X4,tc_bool)),X4,X6),X7))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X6),hAPP(hAPP(X1,X5),X7)))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X5),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3673]) ).
cnf(c_0_3673_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X4),X5),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))),tc_fun(X4,tc_bool)),X4,X6),X7))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X6),hAPP(hAPP(X1,X5),X7))) ),
inference(literals_permutation,[status(thm)],[c_0_3673]) ).
cnf(c_0_3674_0,axiom,
( X7 = X6
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X4,X5,X2,X3),X6))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X4,X5,X2,X3),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_3674]) ).
cnf(c_0_3674_1,axiom,
( ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| X7 = X6
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X4,X5,X2,X3),X6))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X4,X5,X2,X3),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_3674]) ).
cnf(c_0_3674_2,axiom,
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X4,X5,X2,X3),X6))
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| X7 = X6
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X4,X5,X2,X3),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_3674]) ).
cnf(c_0_3674_3,axiom,
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X4,X5,X2,X3),X7))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X4,X5,X2,X3),X6))
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| X7 = X6 ),
inference(literals_permutation,[status(thm)],[c_0_3674]) ).
cnf(c_0_3675_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2)),c_Finite__Set_Ocard(X1,X2)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3675]) ).
cnf(c_0_3675_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2)),c_Finite__Set_Ocard(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3675]) ).
cnf(c_0_3675_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2)),c_Finite__Set_Ocard(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3675]) ).
cnf(c_0_3675_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X2),X4),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2)),c_Finite__Set_Ocard(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3675]) ).
cnf(c_0_3676_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X2,X5,X1)),X3)),X4)),X6))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3676]) ).
cnf(c_0_3676_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X2,X5,X1)),X3)),X4)),X6))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3676]) ).
cnf(c_0_3676_2,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X2,X5,X1)),X3)),X4)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_3676]) ).
cnf(c_0_3677_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X2,X5,X1)),X3)),X4)),X6))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3677]) ).
cnf(c_0_3677_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X2,X5,X1)),X3)),X4)),X6))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3677]) ).
cnf(c_0_3677_2,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X2,X5,X1)),X3)),X4)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_3677]) ).
cnf(c_0_3678_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1,X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X4)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X2,X3,X1,X1),X4))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3678]) ).
cnf(c_0_3678_1,axiom,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1,X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X4)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X2,X3,X1,X1),X4))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3678]) ).
cnf(c_0_3678_2,axiom,
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X2,X3,X1,X1),X4))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1,X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X4)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3678]) ).
cnf(c_0_3678_3,axiom,
( ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X2,X3,X1,X1),X4))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1,X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X4)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3678]) ).
cnf(c_0_3679_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1,X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X4)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3679]) ).
cnf(c_0_3679_1,axiom,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1,X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X4)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3679]) ).
cnf(c_0_3679_2,axiom,
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1),X4))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1,X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X4)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3679]) ).
cnf(c_0_3679_3,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X2,X3,X1,X1),X4))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1,X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X4)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3679]) ).
cnf(c_0_3680_0,axiom,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,hAPP(hAPP(c_Set_Oinsert(X3),X4),X5),X3,X6),hAPP(hAPP(X1,X4),X7)))
| hBOOL(hAPP(hAPP(c_in(X3),X4),X5))
| ~ c_Finite__Set_Ofun__left__comm(X1,X3,X6)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X5,X3,X6),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_3680]) ).
cnf(c_0_3680_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X3),X4),X5))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,hAPP(hAPP(c_Set_Oinsert(X3),X4),X5),X3,X6),hAPP(hAPP(X1,X4),X7)))
| ~ c_Finite__Set_Ofun__left__comm(X1,X3,X6)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X5,X3,X6),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_3680]) ).
cnf(c_0_3680_2,axiom,
( ~ c_Finite__Set_Ofun__left__comm(X1,X3,X6)
| hBOOL(hAPP(hAPP(c_in(X3),X4),X5))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,hAPP(hAPP(c_Set_Oinsert(X3),X4),X5),X3,X6),hAPP(hAPP(X1,X4),X7)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X5,X3,X6),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_3680]) ).
cnf(c_0_3680_3,axiom,
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X5,X3,X6),X7))
| ~ c_Finite__Set_Ofun__left__comm(X1,X3,X6)
| hBOOL(hAPP(hAPP(c_in(X3),X4),X5))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,hAPP(hAPP(c_Set_Oinsert(X3),X4),X5),X3,X6),hAPP(hAPP(X1,X4),X7))) ),
inference(literals_permutation,[status(thm)],[c_0_3680]) ).
cnf(c_0_3681_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X4))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X6,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),X2,X2),hAPP(hAPP(X1,X6),X5)))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X3,X4,X2,X2),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_3681]) ).
cnf(c_0_3681_1,axiom,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X6,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),X2,X2),hAPP(hAPP(X1,X6),X5)))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X4))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X3,X4,X2,X2),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_3681]) ).
cnf(c_0_3681_2,axiom,
( ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X6,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),X2,X2),hAPP(hAPP(X1,X6),X5)))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X4))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X3,X4,X2,X2),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_3681]) ).
cnf(c_0_3681_3,axiom,
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X3,X4,X2,X2),X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X6,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),X2,X2),hAPP(hAPP(X1,X6),X5)))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3681]) ).
cnf(c_0_3682_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1,X6),hAPP(hAPP(X4,X2),X7)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X5,X3,X1,X6),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_3682]) ).
cnf(c_0_3682_1,axiom,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1,X6),hAPP(hAPP(X4,X2),X7)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X5,X3,X1,X6),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_3682]) ).
cnf(c_0_3682_2,axiom,
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X5,X3,X1,X6),X7))
| hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X5,hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1,X6),hAPP(hAPP(X4,X2),X7)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3682]) ).
cnf(c_0_3683_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),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))) ),
inference(literals_permutation,[status(thm)],[c_0_3683]) ).
cnf(c_0_3683_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),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)))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3683]) ).
cnf(c_0_3684_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq12__1(X6,X2,X5,X4)),v_sko__Hoare__Mirabelle__Xconseq12__3(X6,X2,X5,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3684]) ).
cnf(c_0_3684_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq12__1(X6,X2,X5,X4)),v_sko__Hoare__Mirabelle__Xconseq12__3(X6,X2,X5,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3684]) ).
cnf(c_0_3684_2,axiom,
( ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq12__1(X6,X2,X5,X4)),v_sko__Hoare__Mirabelle__Xconseq12__3(X6,X2,X5,X4)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_3684]) ).
cnf(c_0_3685_0,axiom,
( hBOOL(hAPP(hAPP(X1,c_Finite__Set_Ofold(X3,X7,X5,X4,X4)),hAPP(hAPP(X3,X6),X7)))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ c_Finite__Set_Ofinite(X5,X4)
| ~ hBOOL(hAPP(hAPP(c_in(X4),X6),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_3685]) ).
cnf(c_0_3685_1,axiom,
( ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,c_Finite__Set_Ofold(X3,X7,X5,X4,X4)),hAPP(hAPP(X3,X6),X7)))
| ~ c_Finite__Set_Ofinite(X5,X4)
| ~ hBOOL(hAPP(hAPP(c_in(X4),X6),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_3685]) ).
cnf(c_0_3685_2,axiom,
( ~ c_Finite__Set_Ofinite(X5,X4)
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,c_Finite__Set_Ofold(X3,X7,X5,X4,X4)),hAPP(hAPP(X3,X6),X7)))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X6),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_3685]) ).
cnf(c_0_3685_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X4),X6),X5))
| ~ c_Finite__Set_Ofinite(X5,X4)
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,c_Finite__Set_Ofold(X3,X7,X5,X4,X4)),hAPP(hAPP(X3,X6),X7))) ),
inference(literals_permutation,[status(thm)],[c_0_3685]) ).
cnf(c_0_3686_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)),X6)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X3,X4,X1)),X5)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3686]) ).
cnf(c_0_3686_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X3,X4,X1)),X5)),X6)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3686]) ).
cnf(c_0_3686_2,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X3,X4,X1)),X5)),X6)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)),X6))) ),
inference(literals_permutation,[status(thm)],[c_0_3686]) ).
cnf(c_0_3687_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)),X6)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X3,X4,X1)),X5)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3687]) ).
cnf(c_0_3687_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X3,X4,X1)),X5)),X6)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3687]) ).
cnf(c_0_3687_2,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X3,X4,X1)),X5)),X6)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)),X6))) ),
inference(literals_permutation,[status(thm)],[c_0_3687]) ).
cnf(c_0_3688_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X5,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Com_Ocom_OBODY(X3),X4,X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool))),X1)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Com_Ocom_OBODY(X3),X4,X1)),X5),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Option_Othe(hAPP(c_Com_Obody,X3),tc_Com_Ocom),X4,X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool))),X1) ),
inference(literals_permutation,[status(thm)],[c_0_3688]) ).
cnf(c_0_3688_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Com_Ocom_OBODY(X3),X4,X1)),X5),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Option_Othe(hAPP(c_Com_Obody,X3),tc_Com_Ocom),X4,X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool))),X1)
| c_Hoare__Mirabelle_Ohoare__derivs(X5,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),c_Hoare__Mirabelle_Otriple_Otriple(X2,c_Com_Ocom_OBODY(X3),X4,X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_bool))),X1) ),
inference(literals_permutation,[status(thm)],[c_0_3688]) ).
cnf(c_0_3689_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X2),c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X2),X4,X1,X2,X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3689]) ).
cnf(c_0_3689_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X2),X4,X1,X2,X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3689]) ).
cnf(c_0_3689_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X2),X4,X1,X2,X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4)))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3689]) ).
cnf(c_0_3689_3,axiom,
( ~ class_Lattices_Olower__semilattice(X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X2),X4,X1,X2,X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3689]) ).
cnf(c_0_3690_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Com_Ocom_OSemi(X4,X6),X7,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X5,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X6,X7,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3690]) ).
cnf(c_0_3690_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X5,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Com_Ocom_OSemi(X4,X6),X7,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X6,X7,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3690]) ).
cnf(c_0_3690_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X6,X7,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X5,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Com_Ocom_OSemi(X4,X6),X7,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3690]) ).
cnf(c_0_3691_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X5,X2,X1)),X3)),X6)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3691]) ).
cnf(c_0_3691_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X5,X2,X1)),X3)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3691]) ).
cnf(c_0_3691_2,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X5,X2,X1)),X3)),X6))) ),
inference(literals_permutation,[status(thm)],[c_0_3691]) ).
cnf(c_0_3692_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X5,X2,X1)),X3)),X6)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3692]) ).
cnf(c_0_3692_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X5,X2,X1)),X3)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3692]) ).
cnf(c_0_3692_2,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X5,X2,X1)),X3)),X6))) ),
inference(literals_permutation,[status(thm)],[c_0_3692]) ).
cnf(c_0_3693_0,axiom,
( c_Finite__Set_Ofold(X1,X4,X5,X2,X3) = X6
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X4,X5,X2,X3),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_3693]) ).
cnf(c_0_3693_1,axiom,
( ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| c_Finite__Set_Ofold(X1,X4,X5,X2,X3) = X6
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X4,X5,X2,X3),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_3693]) ).
cnf(c_0_3693_2,axiom,
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X4,X5,X2,X3),X6))
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| c_Finite__Set_Ofold(X1,X4,X5,X2,X3) = X6 ),
inference(literals_permutation,[status(thm)],[c_0_3693]) ).
cnf(c_0_3694_0,axiom,
( hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq12__1(X5,X2,X6,X4)),v_sko__Hoare__Mirabelle__Xconseq12__2(X5,X2,X6,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X6,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_3694]) ).
cnf(c_0_3694_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X6,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq12__1(X5,X2,X6,X4)),v_sko__Hoare__Mirabelle__Xconseq12__2(X5,X2,X6,X4)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_3694]) ).
cnf(c_0_3694_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X6,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq12__1(X5,X2,X6,X4)),v_sko__Hoare__Mirabelle__Xconseq12__2(X5,X2,X6,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3694]) ).
cnf(c_0_3695_0,axiom,
( hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xconseq12__3(X6,X2,X7,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X7,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xconseq12__2(X6,X2,X7,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3695]) ).
cnf(c_0_3695_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X7,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xconseq12__3(X6,X2,X7,X4)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xconseq12__2(X6,X2,X7,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3695]) ).
cnf(c_0_3695_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X7,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xconseq12__3(X6,X2,X7,X4)))
| ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xconseq12__2(X6,X2,X7,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3695]) ).
cnf(c_0_3695_3,axiom,
( ~ hBOOL(hAPP(hAPP(X2,X5),v_sko__Hoare__Mirabelle__Xconseq12__2(X6,X2,X7,X4)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X3,X7,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xconseq12__3(X6,X2,X7,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3695]) ).
cnf(c_0_3696_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X4),X2),X3))
| hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X4),X5))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_3696]) ).
cnf(c_0_3696_1,axiom,
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X4),X5))
| hBOOL(hAPP(hAPP(c_in(X4),X2),X3))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_3696]) ).
cnf(c_0_3696_2,axiom,
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X4),X5))
| hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,hAPP(hAPP(c_Set_Oinsert(X4),X2),X3),X4),X5))
| hBOOL(hAPP(hAPP(c_in(X4),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3696]) ).
cnf(c_0_3697_0,axiom,
( X5 = X2
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_3697]) ).
cnf(c_0_3697_1,axiom,
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X4),X5))
| X5 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3697]) ).
cnf(c_0_3698_0,axiom,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Option_Ooption_Ooption__case(X4,X2,hAPP(c_Option_Ooption_OSome(t_b),X3),t_a,t_b))) ),
inference(literals_permutation,[status(thm)],[c_0_3698]) ).
cnf(c_0_3698_1,axiom,
( ~ hBOOL(hAPP(X1,c_Option_Ooption_Ooption__case(X4,X2,hAPP(c_Option_Ooption_OSome(t_b),X3),t_a,t_b)))
| hBOOL(hAPP(X1,hAPP(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3698]) ).
cnf(c_0_3699_0,axiom,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(X1,c_Option_Ooption_Ooption__case(X4,X2,hAPP(c_Option_Ooption_OSome(t_b),X3),t_a,t_b))) ),
inference(literals_permutation,[status(thm)],[c_0_3699]) ).
cnf(c_0_3699_1,axiom,
( ~ hBOOL(hAPP(X1,c_Option_Ooption_Ooption__case(X4,X2,hAPP(c_Option_Ooption_OSome(t_b),X3),t_a,t_b)))
| hBOOL(hAPP(X1,hAPP(X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3699]) ).
cnf(c_0_3700_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Option_Ooption_Ooption__case(X2,X3,c_Option_Ooption_ONone(t_b),t_a,t_b))) ),
inference(literals_permutation,[status(thm)],[c_0_3700]) ).
cnf(c_0_3700_1,axiom,
( ~ hBOOL(hAPP(X1,c_Option_Ooption_Ooption__case(X2,X3,c_Option_Ooption_ONone(t_b),t_a,t_b)))
| hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3700]) ).
cnf(c_0_3701_0,axiom,
( c_Finite__Set_Ofinite(X3,X4)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_3701]) ).
cnf(c_0_3701_1,axiom,
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),X6))
| c_Finite__Set_Ofinite(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3701]) ).
cnf(c_0_3702_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),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)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3702]) ).
cnf(c_0_3702_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),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))) ),
inference(literals_permutation,[status(thm)],[c_0_3702]) ).
cnf(c_0_3703_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_3703]) ).
cnf(c_0_3703_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_3703]) ).
cnf(c_0_3704_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Com_Ocom_OBODY(X4),X5,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Option_Othe(hAPP(c_Com_Obody,X4),tc_Com_Ocom),X5,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3704]) ).
cnf(c_0_3704_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Option_Othe(hAPP(c_Com_Obody,X4),tc_Com_Ocom),X5,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X3,c_Com_Ocom_OBODY(X4),X5,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3704]) ).
cnf(c_0_3705_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X1,X3,tc_Com_Ostate)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X1,X3,tc_Com_Ostate)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))),tc_Com_Ostate) ),
inference(literals_permutation,[status(thm)],[c_0_3705]) ).
cnf(c_0_3705_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))),tc_Com_Ostate)
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X1,X3,tc_Com_Ostate)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X1,X3,tc_Com_Ostate)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))),tc_Com_Ostate) ),
inference(literals_permutation,[status(thm)],[c_0_3705]) ).
cnf(c_0_3705_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X1,X3,tc_Com_Ostate)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))),tc_Com_Ostate)
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X1,X3,tc_Com_Ostate)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))),tc_Com_Ostate) ),
inference(literals_permutation,[status(thm)],[c_0_3705]) ).
cnf(c_0_3706_0,axiom,
( c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X3,c_HOL_Ozero__class_Ozero(X4),X1,X4,X2) = c_Finite__Set_Osetsum(X3,X1,X2,X4)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_3706]) ).
cnf(c_0_3706_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X3,c_HOL_Ozero__class_Ozero(X4),X1,X4,X2) = c_Finite__Set_Osetsum(X3,X1,X2,X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_3706]) ).
cnf(c_0_3706_2,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X4),X3,c_HOL_Ozero__class_Ozero(X4),X1,X4,X2) = c_Finite__Set_Osetsum(X3,X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3706]) ).
cnf(c_0_3707_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xconseq1__1(X5,X2)),v_sko__Hoare__Mirabelle__Xconseq1__2(X5,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3707]) ).
cnf(c_0_3707_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xconseq1__1(X5,X2)),v_sko__Hoare__Mirabelle__Xconseq1__2(X5,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3707]) ).
cnf(c_0_3707_2,axiom,
( ~ hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xconseq1__1(X5,X2)),v_sko__Hoare__Mirabelle__Xconseq1__2(X5,X2)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_3707]) ).
cnf(c_0_3708_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq2__1(X5,X4)),v_sko__Hoare__Mirabelle__Xconseq2__2(X5,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3708]) ).
cnf(c_0_3708_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq2__1(X5,X4)),v_sko__Hoare__Mirabelle__Xconseq2__2(X5,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3708]) ).
cnf(c_0_3708_2,axiom,
( ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq2__1(X5,X4)),v_sko__Hoare__Mirabelle__Xconseq2__2(X5,X4)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_3708]) ).
cnf(c_0_3709_0,axiom,
( hBOOL(hAPP(hAPP(X4,v_sko__Hoare__Mirabelle__Xconseq2__1(X5,X4)),v_sko__Hoare__Mirabelle__Xconseq2__2(X5,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_3709]) ).
cnf(c_0_3709_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X4,v_sko__Hoare__Mirabelle__Xconseq2__1(X5,X4)),v_sko__Hoare__Mirabelle__Xconseq2__2(X5,X4)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_3709]) ).
cnf(c_0_3709_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X5,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X4,v_sko__Hoare__Mirabelle__Xconseq2__1(X5,X4)),v_sko__Hoare__Mirabelle__Xconseq2__2(X5,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3709]) ).
cnf(c_0_3710_0,axiom,
( hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq1__1(X5,X2)),v_sko__Hoare__Mirabelle__Xconseq1__2(X5,X2)))
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_3710]) ).
cnf(c_0_3710_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq1__1(X5,X2)),v_sko__Hoare__Mirabelle__Xconseq1__2(X5,X2)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_3710]) ).
cnf(c_0_3710_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X3,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq1__1(X5,X2)),v_sko__Hoare__Mirabelle__Xconseq1__2(X5,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3710]) ).
cnf(c_0_3711_0,axiom,
( c_Fun_Ofun__upd(c_Map_Orestrict__map(X4,c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool)),X1,X6),X2,X5,X1,tc_Option_Ooption(X6)) = c_Map_Orestrict__map(c_Fun_Ofun__upd(X4,X2,X5,X1,tc_Option_Ooption(X6)),X3,X1,X6)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3711]) ).
cnf(c_0_3711_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Fun_Ofun__upd(c_Map_Orestrict__map(X4,c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool)),X1,X6),X2,X5,X1,tc_Option_Ooption(X6)) = c_Map_Orestrict__map(c_Fun_Ofun__upd(X4,X2,X5,X1,tc_Option_Ooption(X6)),X3,X1,X6) ),
inference(literals_permutation,[status(thm)],[c_0_3711]) ).
cnf(c_0_3712_0,axiom,
( c_Map_Omap__le(c_Fun_Ofun__upd(X1,X5,c_Option_Ooption_ONone(X4),X3,tc_Option_Ooption(X4)),c_Fun_Ofun__upd(X2,X5,hAPP(c_Option_Ooption_OSome(X4),X6),X3,tc_Option_Ooption(X4)),X3,X4)
| ~ c_Map_Omap__le(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3712]) ).
cnf(c_0_3712_1,axiom,
( ~ c_Map_Omap__le(X1,X2,X3,X4)
| c_Map_Omap__le(c_Fun_Ofun__upd(X1,X5,c_Option_Ooption_ONone(X4),X3,tc_Option_Ooption(X4)),c_Fun_Ofun__upd(X2,X5,hAPP(c_Option_Ooption_OSome(X4),X6),X3,tc_Option_Ooption(X4)),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3712]) ).
cnf(c_0_3713_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),X4)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X2),X4,X1,X2,X2)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Lattices_Oupper__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3713]) ).
cnf(c_0_3713_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),X4)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X2),X4,X1,X2,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Lattices_Oupper__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3713]) ).
cnf(c_0_3713_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),X4)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X2),X4,X1,X2,X2)))
| ~ class_Lattices_Oupper__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3713]) ).
cnf(c_0_3713_3,axiom,
( ~ class_Lattices_Oupper__semilattice(X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),X4)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X2),X4,X1,X2,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3713]) ).
cnf(c_0_3714_0,axiom,
( c_Map_Omap__le(c_Fun_Ofun__upd(X1,X5,X6,X3,tc_Option_Ooption(X4)),c_Fun_Ofun__upd(X2,X5,X6,X3,tc_Option_Ooption(X4)),X3,X4)
| ~ c_Map_Omap__le(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3714]) ).
cnf(c_0_3714_1,axiom,
( ~ c_Map_Omap__le(X1,X2,X3,X4)
| c_Map_Omap__le(c_Fun_Ofun__upd(X1,X5,X6,X3,tc_Option_Ooption(X4)),c_Fun_Ofun__upd(X2,X5,X6,X3,tc_Option_Ooption(X4)),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3714]) ).
cnf(c_0_3715_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3715]) ).
cnf(c_0_3715_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3715]) ).
cnf(c_0_3715_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3715]) ).
cnf(c_0_3715_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3715]) ).
cnf(c_0_3716_0,axiom,
( hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X2,X1,X3,X4)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X2,X1,X3,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X4,X3,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_3716]) ).
cnf(c_0_3716_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X4,X3,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X2,X1,X3,X4)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X2,X1,X3,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3716]) ).
cnf(c_0_3717_0,axiom,
( hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X2,X1,X3,X4)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X2,X1,X3,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X4,X3,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_3717]) ).
cnf(c_0_3717_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X4,X3,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X2,X1,X3,X4)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X2,X1,X3,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3717]) ).
cnf(c_0_3718_0,axiom,
( hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xescape__1(X2,X1,X3,X4)),v_sko__Hoare__Mirabelle__Xescape__2(X2,X1,X3,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X4,X3,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_3718]) ).
cnf(c_0_3718_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X4,X3,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xescape__1(X2,X1,X3,X4)),v_sko__Hoare__Mirabelle__Xescape__2(X2,X1,X3,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3718]) ).
cnf(c_0_3719_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3719]) ).
cnf(c_0_3719_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3719]) ).
cnf(c_0_3719_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3719]) ).
cnf(c_0_3719_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X4),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3719]) ).
cnf(c_0_3720_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3720]) ).
cnf(c_0_3720_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3720]) ).
cnf(c_0_3720_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3720]) ).
cnf(c_0_3720_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3720]) ).
cnf(c_0_3721_0,axiom,
( hAPP(hAPP(X1,X5),c_Finite__Set_Ofold(X1,X6,c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X2),X5),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X3)) = c_Finite__Set_Ofold(X1,X6,X4,X2,X3)
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| ~ c_Finite__Set_Ofinite(X4,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3721]) ).
cnf(c_0_3721_1,axiom,
( ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| hAPP(hAPP(X1,X5),c_Finite__Set_Ofold(X1,X6,c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X2),X5),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X3)) = c_Finite__Set_Ofold(X1,X6,X4,X2,X3)
| ~ c_Finite__Set_Ofinite(X4,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3721]) ).
cnf(c_0_3721_2,axiom,
( ~ c_Finite__Set_Ofinite(X4,X2)
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| hAPP(hAPP(X1,X5),c_Finite__Set_Ofold(X1,X6,c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X2),X5),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X3)) = c_Finite__Set_Ofold(X1,X6,X4,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3721]) ).
cnf(c_0_3721_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X2),X5),X4))
| ~ c_Finite__Set_Ofinite(X4,X2)
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| hAPP(hAPP(X1,X5),c_Finite__Set_Ofold(X1,X6,c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X2),X5),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X3)) = c_Finite__Set_Ofold(X1,X6,X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3721]) ).
cnf(c_0_3722_0,axiom,
( hAPP(hAPP(X1,X6),c_Finite__Set_Ofold(X1,X5,c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X3)) = c_Finite__Set_Ofold(X1,X5,hAPP(hAPP(c_Set_Oinsert(X2),X6),X4),X2,X3)
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| ~ c_Finite__Set_Ofinite(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3722]) ).
cnf(c_0_3722_1,axiom,
( ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| hAPP(hAPP(X1,X6),c_Finite__Set_Ofold(X1,X5,c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X3)) = c_Finite__Set_Ofold(X1,X5,hAPP(hAPP(c_Set_Oinsert(X2),X6),X4),X2,X3)
| ~ c_Finite__Set_Ofinite(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3722]) ).
cnf(c_0_3722_2,axiom,
( ~ c_Finite__Set_Ofinite(X4,X2)
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| hAPP(hAPP(X1,X6),c_Finite__Set_Ofold(X1,X5,c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X2),X6),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X3)) = c_Finite__Set_Ofold(X1,X5,hAPP(hAPP(c_Set_Oinsert(X2),X6),X4),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3722]) ).
cnf(c_0_3723_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2)),c_Finite__Set_Ocard(X1,X2)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3723]) ).
cnf(c_0_3723_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2)),c_Finite__Set_Ocard(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3723]) ).
cnf(c_0_3723_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2)),c_Finite__Set_Ocard(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3723]) ).
cnf(c_0_3724_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3724]) ).
cnf(c_0_3724_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3724]) ).
cnf(c_0_3724_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3724]) ).
cnf(c_0_3725_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Finite__Set_Osetsum(X5,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2,X4)),c_Finite__Set_Osetsum(X5,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2,X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Finite__Set_Osetsum(X5,X1,X2,X4)),c_Finite__Set_Osetsum(X5,X3,X2,X4))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_3725]) ).
cnf(c_0_3725_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Finite__Set_Osetsum(X5,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2,X4)),c_Finite__Set_Osetsum(X5,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2,X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Finite__Set_Osetsum(X5,X1,X2,X4)),c_Finite__Set_Osetsum(X5,X3,X2,X4))
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_3725]) ).
cnf(c_0_3725_2,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Finite__Set_Osetsum(X5,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2,X4)),c_Finite__Set_Osetsum(X5,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2,X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Finite__Set_Osetsum(X5,X1,X2,X4)),c_Finite__Set_Osetsum(X5,X3,X2,X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_3725]) ).
cnf(c_0_3725_3,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Finite__Set_Osetsum(X5,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2,X4)),c_Finite__Set_Osetsum(X5,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2,X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X4),c_Finite__Set_Osetsum(X5,X1,X2,X4)),c_Finite__Set_Osetsum(X5,X3,X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3725]) ).
cnf(c_0_3726_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),c_Finite__Set_Osetprod(X5,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2,X4)),c_Finite__Set_Osetprod(X5,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2,X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),c_Finite__Set_Osetprod(X5,X1,X2,X4)),c_Finite__Set_Osetprod(X5,X3,X2,X4))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X4) ),
inference(literals_permutation,[status(thm)],[c_0_3726]) ).
cnf(c_0_3726_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),c_Finite__Set_Osetprod(X5,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2,X4)),c_Finite__Set_Osetprod(X5,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2,X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),c_Finite__Set_Osetprod(X5,X1,X2,X4)),c_Finite__Set_Osetprod(X5,X3,X2,X4))
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X4) ),
inference(literals_permutation,[status(thm)],[c_0_3726]) ).
cnf(c_0_3726_2,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),c_Finite__Set_Osetprod(X5,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2,X4)),c_Finite__Set_Osetprod(X5,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2,X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),c_Finite__Set_Osetprod(X5,X1,X2,X4)),c_Finite__Set_Osetprod(X5,X3,X2,X4))
| ~ class_OrderedGroup_Ocomm__monoid__mult(X4) ),
inference(literals_permutation,[status(thm)],[c_0_3726]) ).
cnf(c_0_3726_3,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__mult(X4)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),c_Finite__Set_Osetprod(X5,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2,X4)),c_Finite__Set_Osetprod(X5,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2,X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X4),c_Finite__Set_Osetprod(X5,X1,X2,X4)),c_Finite__Set_Osetprod(X5,X3,X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3726]) ).
cnf(c_0_3727_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Map_Odom(X3,X1,X4)))
| c_Fun_Ofun__upd(c_Map_Omap__add(X5,X3,X1,X4),X2,hAPP(c_Option_Ooption_OSome(X4),X6),X1,tc_Option_Ooption(X4)) = c_Map_Omap__add(c_Fun_Ofun__upd(X5,X2,hAPP(c_Option_Ooption_OSome(X4),X6),X1,tc_Option_Ooption(X4)),X3,X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3727]) ).
cnf(c_0_3727_1,axiom,
( c_Fun_Ofun__upd(c_Map_Omap__add(X5,X3,X1,X4),X2,hAPP(c_Option_Ooption_OSome(X4),X6),X1,tc_Option_Ooption(X4)) = c_Map_Omap__add(c_Fun_Ofun__upd(X5,X2,hAPP(c_Option_Ooption_OSome(X4),X6),X1,tc_Option_Ooption(X4)),X3,X1,X4)
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_Map_Odom(X3,X1,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3727]) ).
cnf(c_0_3728_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3728]) ).
cnf(c_0_3728_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3728]) ).
cnf(c_0_3728_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3728]) ).
cnf(c_0_3728_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3728]) ).
cnf(c_0_3729_0,axiom,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_Finite__Set_Osetsum(X4,X1,X2,X5)),c_Finite__Set_Osetsum(X4,X3,X2,X5)),c_Finite__Set_Osetsum(X4,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2,X5),X5) = c_Finite__Set_Osetsum(X4,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_OrderedGroup_Oab__group__add(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3729]) ).
cnf(c_0_3729_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_Finite__Set_Osetsum(X4,X1,X2,X5)),c_Finite__Set_Osetsum(X4,X3,X2,X5)),c_Finite__Set_Osetsum(X4,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2,X5),X5) = c_Finite__Set_Osetsum(X4,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2,X5)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_OrderedGroup_Oab__group__add(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3729]) ).
cnf(c_0_3729_2,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_Finite__Set_Osetsum(X4,X1,X2,X5)),c_Finite__Set_Osetsum(X4,X3,X2,X5)),c_Finite__Set_Osetsum(X4,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2,X5),X5) = c_Finite__Set_Osetsum(X4,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2,X5)
| ~ class_OrderedGroup_Oab__group__add(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3729]) ).
cnf(c_0_3729_3,axiom,
( ~ class_OrderedGroup_Oab__group__add(X5)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_Finite__Set_Osetsum(X4,X1,X2,X5)),c_Finite__Set_Osetsum(X4,X3,X2,X5)),c_Finite__Set_Osetsum(X4,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2,X5),X5) = c_Finite__Set_Osetsum(X4,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2,X5) ),
inference(literals_permutation,[status(thm)],[c_0_3729]) ).
cnf(c_0_3730_0,axiom,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),hAPP(c_Finite__Set_Ofold1(X1,X2),X3)),X3))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),hAPP(hAPP(X1,c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1(X1,X2)),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2(X1,X2))),hAPP(hAPP(c_Set_Oinsert(X2),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1(X1,X2)),hAPP(hAPP(c_Set_Oinsert(X2),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2(X1,X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))))) ),
inference(literals_permutation,[status(thm)],[c_0_3730]) ).
cnf(c_0_3730_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),hAPP(c_Finite__Set_Ofold1(X1,X2),X3)),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),hAPP(hAPP(X1,c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1(X1,X2)),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2(X1,X2))),hAPP(hAPP(c_Set_Oinsert(X2),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1(X1,X2)),hAPP(hAPP(c_Set_Oinsert(X2),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2(X1,X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))))) ),
inference(literals_permutation,[status(thm)],[c_0_3730]) ).
cnf(c_0_3730_2,axiom,
( ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hBOOL(hAPP(hAPP(c_in(X2),hAPP(c_Finite__Set_Ofold1(X1,X2),X3)),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),hAPP(hAPP(X1,c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1(X1,X2)),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2(X1,X2))),hAPP(hAPP(c_Set_Oinsert(X2),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1(X1,X2)),hAPP(hAPP(c_Set_Oinsert(X2),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2(X1,X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))))) ),
inference(literals_permutation,[status(thm)],[c_0_3730]) ).
cnf(c_0_3730_3,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hBOOL(hAPP(hAPP(c_in(X2),hAPP(c_Finite__Set_Ofold1(X1,X2),X3)),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X2),hAPP(hAPP(X1,c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1(X1,X2)),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2(X1,X2))),hAPP(hAPP(c_Set_Oinsert(X2),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1(X1,X2)),hAPP(hAPP(c_Set_Oinsert(X2),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2(X1,X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))))) ),
inference(literals_permutation,[status(thm)],[c_0_3730]) ).
cnf(c_0_3730_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X2),hAPP(hAPP(X1,c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1(X1,X2)),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2(X1,X2))),hAPP(hAPP(c_Set_Oinsert(X2),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1(X1,X2)),hAPP(hAPP(c_Set_Oinsert(X2),c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2(X1,X2)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))))))
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hBOOL(hAPP(hAPP(c_in(X2),hAPP(c_Finite__Set_Ofold1(X1,X2),X3)),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_3730]) ).
cnf(c_0_3731_0,axiom,
( c_Fun_Ofun__upd(c_Map_Orestrict__map(X4,c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool)),X1,X5),X2,X6,X1,tc_Option_Ooption(X5)) = c_Fun_Ofun__upd(c_Map_Orestrict__map(X4,X3,X1,X5),X2,X6,X1,tc_Option_Ooption(X5))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3731]) ).
cnf(c_0_3731_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Fun_Ofun__upd(c_Map_Orestrict__map(X4,c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool)),X1,X5),X2,X6,X1,tc_Option_Ooption(X5)) = c_Fun_Ofun__upd(c_Map_Orestrict__map(X4,X3,X1,X5),X2,X6,X1,tc_Option_Ooption(X5)) ),
inference(literals_permutation,[status(thm)],[c_0_3731]) ).
cnf(c_0_3732_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3))),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3732]) ).
cnf(c_0_3732_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3))),c_HOL_Ozero__class_Ozero(X1)))
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3732]) ).
cnf(c_0_3732_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3))),c_HOL_Ozero__class_Ozero(X1)))
| X2 = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3732]) ).
cnf(c_0_3733_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3))),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3733]) ).
cnf(c_0_3733_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3))),c_HOL_Ozero__class_Ozero(X1)))
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3733]) ).
cnf(c_0_3733_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3))),c_HOL_Ozero__class_Ozero(X1)))
| X3 = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3733]) ).
cnf(c_0_3734_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3))),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3734]) ).
cnf(c_0_3734_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3))),c_HOL_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3734]) ).
cnf(c_0_3735_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3735]) ).
cnf(c_0_3735_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3735]) ).
cnf(c_0_3735_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3735]) ).
cnf(c_0_3736_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3736]) ).
cnf(c_0_3736_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3736]) ).
cnf(c_0_3736_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3736]) ).
cnf(c_0_3737_0,axiom,
( c_Finite__Set_Ofold(X3,X6,hAPP(hAPP(c_Set_Oinsert(X4),X7),X5),X4,X4) = hAPP(hAPP(X3,X7),c_Finite__Set_Ofold(X3,X6,X5,X4,X4))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ c_Finite__Set_Ofinite(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3737]) ).
cnf(c_0_3737_1,axiom,
( ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| c_Finite__Set_Ofold(X3,X6,hAPP(hAPP(c_Set_Oinsert(X4),X7),X5),X4,X4) = hAPP(hAPP(X3,X7),c_Finite__Set_Ofold(X3,X6,X5,X4,X4))
| ~ c_Finite__Set_Ofinite(X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3737]) ).
cnf(c_0_3737_2,axiom,
( ~ c_Finite__Set_Ofinite(X5,X4)
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| c_Finite__Set_Ofold(X3,X6,hAPP(hAPP(c_Set_Oinsert(X4),X7),X5),X4,X4) = hAPP(hAPP(X3,X7),c_Finite__Set_Ofold(X3,X6,X5,X4,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3737]) ).
cnf(c_0_3738_0,axiom,
( X1 = X2
| hAPP(X3,X4) = hAPP(c_Option_Ooption_OSome(X5),X2)
| hAPP(c_Fun_Ofun__upd(X3,X6,hAPP(c_Option_Ooption_OSome(X5),X1),X7,tc_Option_Ooption(X5)),X4) != hAPP(c_Option_Ooption_OSome(X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3738]) ).
cnf(c_0_3738_1,axiom,
( hAPP(X3,X4) = hAPP(c_Option_Ooption_OSome(X5),X2)
| X1 = X2
| hAPP(c_Fun_Ofun__upd(X3,X6,hAPP(c_Option_Ooption_OSome(X5),X1),X7,tc_Option_Ooption(X5)),X4) != hAPP(c_Option_Ooption_OSome(X5),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3738]) ).
cnf(c_0_3738_2,axiom,
( hAPP(c_Fun_Ofun__upd(X3,X6,hAPP(c_Option_Ooption_OSome(X5),X1),X7,tc_Option_Ooption(X5)),X4) != hAPP(c_Option_Ooption_OSome(X5),X2)
| hAPP(X3,X4) = hAPP(c_Option_Ooption_OSome(X5),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3738]) ).
cnf(c_0_3739_0,axiom,
( X1 = X2
| hAPP(X3,X1) = hAPP(c_Option_Ooption_OSome(X4),X5)
| hAPP(c_Fun_Ofun__upd(X3,X2,hAPP(c_Option_Ooption_OSome(X4),X6),X7,tc_Option_Ooption(X4)),X1) != hAPP(c_Option_Ooption_OSome(X4),X5) ),
inference(literals_permutation,[status(thm)],[c_0_3739]) ).
cnf(c_0_3739_1,axiom,
( hAPP(X3,X1) = hAPP(c_Option_Ooption_OSome(X4),X5)
| X1 = X2
| hAPP(c_Fun_Ofun__upd(X3,X2,hAPP(c_Option_Ooption_OSome(X4),X6),X7,tc_Option_Ooption(X4)),X1) != hAPP(c_Option_Ooption_OSome(X4),X5) ),
inference(literals_permutation,[status(thm)],[c_0_3739]) ).
cnf(c_0_3739_2,axiom,
( hAPP(c_Fun_Ofun__upd(X3,X2,hAPP(c_Option_Ooption_OSome(X4),X6),X7,tc_Option_Ooption(X4)),X1) != hAPP(c_Option_Ooption_OSome(X4),X5)
| hAPP(X3,X1) = hAPP(c_Option_Ooption_OSome(X4),X5)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3739]) ).
cnf(c_0_3740_0,axiom,
( X4 = X6
| hAPP(c_Fun_Ofun__upd(X1,X2,hAPP(c_Option_Ooption_OSome(X3),X4),X5,tc_Option_Ooption(X3)),X2) != hAPP(c_Option_Ooption_OSome(X3),X6) ),
inference(literals_permutation,[status(thm)],[c_0_3740]) ).
cnf(c_0_3740_1,axiom,
( hAPP(c_Fun_Ofun__upd(X1,X2,hAPP(c_Option_Ooption_OSome(X3),X4),X5,tc_Option_Ooption(X3)),X2) != hAPP(c_Option_Ooption_OSome(X3),X6)
| X4 = X6 ),
inference(literals_permutation,[status(thm)],[c_0_3740]) ).
cnf(c_0_3741_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),X5),X4))
| c_Finite__Set_Ofold(X1,X6,hAPP(hAPP(c_Set_Oinsert(X2),X5),X4),X2,X3) = hAPP(hAPP(X1,X5),c_Finite__Set_Ofold(X1,X6,X4,X2,X3))
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| ~ c_Finite__Set_Ofinite(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3741]) ).
cnf(c_0_3741_1,axiom,
( c_Finite__Set_Ofold(X1,X6,hAPP(hAPP(c_Set_Oinsert(X2),X5),X4),X2,X3) = hAPP(hAPP(X1,X5),c_Finite__Set_Ofold(X1,X6,X4,X2,X3))
| hBOOL(hAPP(hAPP(c_in(X2),X5),X4))
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| ~ c_Finite__Set_Ofinite(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3741]) ).
cnf(c_0_3741_2,axiom,
( ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| c_Finite__Set_Ofold(X1,X6,hAPP(hAPP(c_Set_Oinsert(X2),X5),X4),X2,X3) = hAPP(hAPP(X1,X5),c_Finite__Set_Ofold(X1,X6,X4,X2,X3))
| hBOOL(hAPP(hAPP(c_in(X2),X5),X4))
| ~ c_Finite__Set_Ofinite(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3741]) ).
cnf(c_0_3741_3,axiom,
( ~ c_Finite__Set_Ofinite(X4,X2)
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| c_Finite__Set_Ofold(X1,X6,hAPP(hAPP(c_Set_Oinsert(X2),X5),X4),X2,X3) = hAPP(hAPP(X1,X5),c_Finite__Set_Ofold(X1,X6,X4,X2,X3))
| hBOOL(hAPP(hAPP(c_in(X2),X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3741]) ).
cnf(c_0_3742_0,axiom,
( X1 = X2
| c_Fun_Ofun__upd(X3,X4,hAPP(c_Option_Ooption_OSome(X5),X1),X6,tc_Option_Ooption(X5)) != c_Fun_Ofun__upd(X7,X4,hAPP(c_Option_Ooption_OSome(X5),X2),X6,tc_Option_Ooption(X5)) ),
inference(literals_permutation,[status(thm)],[c_0_3742]) ).
cnf(c_0_3742_1,axiom,
( c_Fun_Ofun__upd(X3,X4,hAPP(c_Option_Ooption_OSome(X5),X1),X6,tc_Option_Ooption(X5)) != c_Fun_Ofun__upd(X7,X4,hAPP(c_Option_Ooption_OSome(X5),X2),X6,tc_Option_Ooption(X5))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3742]) ).
cnf(c_0_3743_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)))),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3743]) ).
cnf(c_0_3743_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)))),c_HOL_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3743]) ).
cnf(c_0_3744_0,axiom,
( c_Finite__Set_Ofold(X1,hAPP(hAPP(X1,X5),X6),X4,X2,X3) = hAPP(hAPP(X1,X5),c_Finite__Set_Ofold(X1,X6,X4,X2,X3))
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| ~ c_Finite__Set_Ofinite(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3744]) ).
cnf(c_0_3744_1,axiom,
( ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| c_Finite__Set_Ofold(X1,hAPP(hAPP(X1,X5),X6),X4,X2,X3) = hAPP(hAPP(X1,X5),c_Finite__Set_Ofold(X1,X6,X4,X2,X3))
| ~ c_Finite__Set_Ofinite(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3744]) ).
cnf(c_0_3744_2,axiom,
( ~ c_Finite__Set_Ofinite(X4,X2)
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| c_Finite__Set_Ofold(X1,hAPP(hAPP(X1,X5),X6),X4,X2,X3) = hAPP(hAPP(X1,X5),c_Finite__Set_Ofold(X1,X6,X4,X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3744]) ).
cnf(c_0_3745_0,axiom,
( c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X2),X3,hAPP(hAPP(c_Set_Oinsert(X2),X4),X1),X2,X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X4),c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X2),X3,X1,X2,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3745]) ).
cnf(c_0_3745_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X2),X3,hAPP(hAPP(c_Set_Oinsert(X2),X4),X1),X2,X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X4),c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X2),X3,X1,X2,X2))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3745]) ).
cnf(c_0_3745_2,axiom,
( ~ class_Lattices_Olower__semilattice(X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X2),X3,hAPP(hAPP(c_Set_Oinsert(X2),X4),X1),X2,X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X4),c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X2),X3,X1,X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3745]) ).
cnf(c_0_3746_0,axiom,
( c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X2),X3,hAPP(hAPP(c_Set_Oinsert(X2),X4),X1),X2,X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X4),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X2),X3,X1,X2,X2))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3746]) ).
cnf(c_0_3746_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X2),X3,hAPP(hAPP(c_Set_Oinsert(X2),X4),X1),X2,X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X4),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X2),X3,X1,X2,X2))
| ~ class_Lattices_Oupper__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3746]) ).
cnf(c_0_3746_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X2),X3,hAPP(hAPP(c_Set_Oinsert(X2),X4),X1),X2,X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X4),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X2),X3,X1,X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3746]) ).
cnf(c_0_3747_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),c_Set_Ovimage(X5,X2,X4,X1)),c_Set_Ovimage(X5,X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3747]) ).
cnf(c_0_3747_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),c_Set_Ovimage(X5,X2,X4,X1)),c_Set_Ovimage(X5,X3,X4,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3747]) ).
cnf(c_0_3748_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X3),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3748]) ).
cnf(c_0_3748_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3748]) ).
cnf(c_0_3748_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3748]) ).
cnf(c_0_3748_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3748]) ).
cnf(c_0_3749_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3749]) ).
cnf(c_0_3749_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_3749]) ).
cnf(c_0_3750_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3750]) ).
cnf(c_0_3750_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_3750]) ).
cnf(c_0_3751_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3751]) ).
cnf(c_0_3751_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3751]) ).
cnf(c_0_3751_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3751]) ).
cnf(c_0_3752_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)))))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3752]) ).
cnf(c_0_3752_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))))) ),
inference(literals_permutation,[status(thm)],[c_0_3752]) ).
cnf(c_0_3753_0,axiom,
( hAPP(X3,X2) = X5
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Ovimage(X3,hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))),X1,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3753]) ).
cnf(c_0_3753_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Set_Ovimage(X3,hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))),X1,X4)))
| hAPP(X3,X2) = X5 ),
inference(literals_permutation,[status(thm)],[c_0_3753]) ).
cnf(c_0_3754_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Map_Orestrict__map(c_Fun_Ofun__upd(X4,X2,X5,X1,tc_Option_Ooption(X6)),X3,X1,X6) = c_Map_Orestrict__map(X4,X3,X1,X6) ),
inference(literals_permutation,[status(thm)],[c_0_3754]) ).
cnf(c_0_3754_1,axiom,
( c_Map_Orestrict__map(c_Fun_Ofun__upd(X4,X2,X5,X1,tc_Option_Ooption(X6)),X3,X1,X6) = c_Map_Orestrict__map(X4,X3,X1,X6)
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3754]) ).
cnf(c_0_3755_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_3755]) ).
cnf(c_0_3755_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_3755]) ).
cnf(c_0_3755_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_3755]) ).
cnf(c_0_3756_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_3756]) ).
cnf(c_0_3756_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_3756]) ).
cnf(c_0_3756_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_3756]) ).
cnf(c_0_3757_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),X5),X4))
| c_Finite__Set_Ofold(X1,X6,hAPP(hAPP(c_Set_Oinsert(X2),X5),X4),X2,X3) = c_Finite__Set_Ofold(X1,hAPP(hAPP(X1,X5),X6),X4,X2,X3)
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| ~ c_Finite__Set_Ofinite(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3757]) ).
cnf(c_0_3757_1,axiom,
( c_Finite__Set_Ofold(X1,X6,hAPP(hAPP(c_Set_Oinsert(X2),X5),X4),X2,X3) = c_Finite__Set_Ofold(X1,hAPP(hAPP(X1,X5),X6),X4,X2,X3)
| hBOOL(hAPP(hAPP(c_in(X2),X5),X4))
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| ~ c_Finite__Set_Ofinite(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3757]) ).
cnf(c_0_3757_2,axiom,
( ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| c_Finite__Set_Ofold(X1,X6,hAPP(hAPP(c_Set_Oinsert(X2),X5),X4),X2,X3) = c_Finite__Set_Ofold(X1,hAPP(hAPP(X1,X5),X6),X4,X2,X3)
| hBOOL(hAPP(hAPP(c_in(X2),X5),X4))
| ~ c_Finite__Set_Ofinite(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3757]) ).
cnf(c_0_3757_3,axiom,
( ~ c_Finite__Set_Ofinite(X4,X2)
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| c_Finite__Set_Ofold(X1,X6,hAPP(hAPP(c_Set_Oinsert(X2),X5),X4),X2,X3) = c_Finite__Set_Ofold(X1,hAPP(hAPP(X1,X5),X6),X4,X2,X3)
| hBOOL(hAPP(hAPP(c_in(X2),X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3757]) ).
cnf(c_0_3758_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4))))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3758]) ).
cnf(c_0_3758_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_3758]) ).
cnf(c_0_3759_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4))))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3759]) ).
cnf(c_0_3759_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_3759]) ).
cnf(c_0_3760_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X4,X2,X1)),X3)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),X5)
| ~ class_Ring__and__Field_Oring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3760]) ).
cnf(c_0_3760_1,axiom,
( ~ class_Ring__and__Field_Oring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X4,X2,X1)),X3)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),X5) ),
inference(literals_permutation,[status(thm)],[c_0_3760]) ).
cnf(c_0_3761_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X2,X5,X1)),X3)),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Oring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3761]) ).
cnf(c_0_3761_1,axiom,
( ~ class_Ring__and__Field_Oring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X2,X5,X1)),X3)),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_3761]) ).
cnf(c_0_3762_0,axiom,
( c_Fun_Ofun__upd(c_Map_Orestrict__map(X4,X3,X1,X5),X2,c_Option_Ooption_ONone(X5),X1,tc_Option_Ooption(X5)) = c_Map_Orestrict__map(X4,c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool)),X1,X5)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3762]) ).
cnf(c_0_3762_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Fun_Ofun__upd(c_Map_Orestrict__map(X4,X3,X1,X5),X2,c_Option_Ooption_ONone(X5),X1,tc_Option_Ooption(X5)) = c_Map_Orestrict__map(X4,c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool)),X1,X5) ),
inference(literals_permutation,[status(thm)],[c_0_3762]) ).
cnf(c_0_3763_0,axiom,
( c_Map_Omap__le(c_Map_Omap__add(X1,X5,X3,X4),X2,X3,X4)
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| ~ c_Map_Omap__le(X5,X2,X3,X4)
| ~ c_Map_Omap__le(X1,c_Map_Omap__add(X1,X5,X3,X4),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3763]) ).
cnf(c_0_3763_1,axiom,
( ~ c_Map_Omap__le(X1,X2,X3,X4)
| c_Map_Omap__le(c_Map_Omap__add(X1,X5,X3,X4),X2,X3,X4)
| ~ c_Map_Omap__le(X5,X2,X3,X4)
| ~ c_Map_Omap__le(X1,c_Map_Omap__add(X1,X5,X3,X4),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3763]) ).
cnf(c_0_3763_2,axiom,
( ~ c_Map_Omap__le(X5,X2,X3,X4)
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| c_Map_Omap__le(c_Map_Omap__add(X1,X5,X3,X4),X2,X3,X4)
| ~ c_Map_Omap__le(X1,c_Map_Omap__add(X1,X5,X3,X4),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3763]) ).
cnf(c_0_3763_3,axiom,
( ~ c_Map_Omap__le(X1,c_Map_Omap__add(X1,X5,X3,X4),X3,X4)
| ~ c_Map_Omap__le(X5,X2,X3,X4)
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| c_Map_Omap__le(c_Map_Omap__add(X1,X5,X3,X4),X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3763]) ).
cnf(c_0_3764_0,axiom,
( X1 = c_Option_Ooption_ONone(X2)
| c_Map_Odom(c_Fun_Ofun__upd(X3,X4,X1,X5,tc_Option_Ooption(X2)),X5,X2) = hAPP(hAPP(c_Set_Oinsert(X5),X4),c_Map_Odom(X3,X5,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3764]) ).
cnf(c_0_3764_1,axiom,
( c_Map_Odom(c_Fun_Ofun__upd(X3,X4,X1,X5,tc_Option_Ooption(X2)),X5,X2) = hAPP(hAPP(c_Set_Oinsert(X5),X4),c_Map_Odom(X3,X5,X2))
| X1 = c_Option_Ooption_ONone(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3764]) ).
cnf(c_0_3765_0,axiom,
( hAPP(c_Fun_Ofun__upd(X1,X2,hAPP(c_Option_Ooption_OSome(X3),X4),X5,tc_Option_Ooption(X3)),X6) = hAPP(c_Option_Ooption_OSome(X3),X7)
| X6 = X2
| hAPP(X1,X6) != hAPP(c_Option_Ooption_OSome(X3),X7) ),
inference(literals_permutation,[status(thm)],[c_0_3765]) ).
cnf(c_0_3765_1,axiom,
( X6 = X2
| hAPP(c_Fun_Ofun__upd(X1,X2,hAPP(c_Option_Ooption_OSome(X3),X4),X5,tc_Option_Ooption(X3)),X6) = hAPP(c_Option_Ooption_OSome(X3),X7)
| hAPP(X1,X6) != hAPP(c_Option_Ooption_OSome(X3),X7) ),
inference(literals_permutation,[status(thm)],[c_0_3765]) ).
cnf(c_0_3765_2,axiom,
( hAPP(X1,X6) != hAPP(c_Option_Ooption_OSome(X3),X7)
| X6 = X2
| hAPP(c_Fun_Ofun__upd(X1,X2,hAPP(c_Option_Ooption_OSome(X3),X4),X5,tc_Option_Ooption(X3)),X6) = hAPP(c_Option_Ooption_OSome(X3),X7) ),
inference(literals_permutation,[status(thm)],[c_0_3765]) ).
cnf(c_0_3766_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_Map_Osko__Map__Xmap__le__def__1__1(X2,X3,X1,X4)),c_Map_Odom(X2,X1,X4)))
| c_Map_Omap__le(X2,X3,X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3766]) ).
cnf(c_0_3766_1,axiom,
( c_Map_Omap__le(X2,X3,X1,X4)
| hBOOL(hAPP(hAPP(c_in(X1),c_Map_Osko__Map__Xmap__le__def__1__1(X2,X3,X1,X4)),c_Map_Odom(X2,X1,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3766]) ).
cnf(c_0_3767_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3767]) ).
cnf(c_0_3767_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3767]) ).
cnf(c_0_3768_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3768]) ).
cnf(c_0_3768_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3768]) ).
cnf(c_0_3769_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_3769]) ).
cnf(c_0_3769_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_3769]) ).
cnf(c_0_3770_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_3770]) ).
cnf(c_0_3770_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_3770]) ).
cnf(c_0_3771_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_Finite__Set_Osetsum(X1,X3,X2,X5)),c_Finite__Set_Osetsum(X1,X4,X2,X5)) = c_Finite__Set_Osetsum(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X4,X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_OrderedGroup_Ocomm__monoid__add(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3771]) ).
cnf(c_0_3771_1,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_Finite__Set_Osetsum(X1,X3,X2,X5)),c_Finite__Set_Osetsum(X1,X4,X2,X5)) = c_Finite__Set_Osetsum(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5)
| ~ c_Finite__Set_Ofinite(X4,X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_OrderedGroup_Ocomm__monoid__add(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3771]) ).
cnf(c_0_3771_2,axiom,
( ~ c_Finite__Set_Ofinite(X4,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_Finite__Set_Osetsum(X1,X3,X2,X5)),c_Finite__Set_Osetsum(X1,X4,X2,X5)) = c_Finite__Set_Osetsum(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_OrderedGroup_Ocomm__monoid__add(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3771]) ).
cnf(c_0_3771_3,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X4,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_Finite__Set_Osetsum(X1,X3,X2,X5)),c_Finite__Set_Osetsum(X1,X4,X2,X5)) = c_Finite__Set_Osetsum(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5)
| ~ class_OrderedGroup_Ocomm__monoid__add(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3771]) ).
cnf(c_0_3771_4,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X4,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_Finite__Set_Osetsum(X1,X3,X2,X5)),c_Finite__Set_Osetsum(X1,X4,X2,X5)) = c_Finite__Set_Osetsum(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5) ),
inference(literals_permutation,[status(thm)],[c_0_3771]) ).
cnf(c_0_3772_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Finite__Set_Osetprod(X1,X3,X2,X5)),c_Finite__Set_Osetprod(X1,X4,X2,X5)) = c_Finite__Set_Osetprod(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X4,X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_OrderedGroup_Ocomm__monoid__mult(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3772]) ).
cnf(c_0_3772_1,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Finite__Set_Osetprod(X1,X3,X2,X5)),c_Finite__Set_Osetprod(X1,X4,X2,X5)) = c_Finite__Set_Osetprod(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5)
| ~ c_Finite__Set_Ofinite(X4,X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_OrderedGroup_Ocomm__monoid__mult(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3772]) ).
cnf(c_0_3772_2,axiom,
( ~ c_Finite__Set_Ofinite(X4,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Finite__Set_Osetprod(X1,X3,X2,X5)),c_Finite__Set_Osetprod(X1,X4,X2,X5)) = c_Finite__Set_Osetprod(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_OrderedGroup_Ocomm__monoid__mult(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3772]) ).
cnf(c_0_3772_3,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X4,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Finite__Set_Osetprod(X1,X3,X2,X5)),c_Finite__Set_Osetprod(X1,X4,X2,X5)) = c_Finite__Set_Osetprod(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3772]) ).
cnf(c_0_3772_4,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__mult(X5)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X4,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Finite__Set_Osetprod(X1,X3,X2,X5)),c_Finite__Set_Osetprod(X1,X4,X2,X5)) = c_Finite__Set_Osetprod(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5) ),
inference(literals_permutation,[status(thm)],[c_0_3772]) ).
cnf(c_0_3773_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3773]) ).
cnf(c_0_3773_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3773]) ).
cnf(c_0_3773_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3773]) ).
cnf(c_0_3774_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3774]) ).
cnf(c_0_3774_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3774]) ).
cnf(c_0_3774_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3774]) ).
cnf(c_0_3775_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool))),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3775]) ).
cnf(c_0_3775_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool))),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3775]) ).
cnf(c_0_3776_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool))),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3776]) ).
cnf(c_0_3776_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X3,tc_fun(X1,tc_bool))),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3776]) ).
cnf(c_0_3777_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(X4,X3)),c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X5)) = c_Finite__Set_Osetsum(X4,X1,X2,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3777]) ).
cnf(c_0_3777_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(X4,X3)),c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X5)) = c_Finite__Set_Osetsum(X4,X1,X2,X5)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3777]) ).
cnf(c_0_3777_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(X4,X3)),c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X5)) = c_Finite__Set_Osetsum(X4,X1,X2,X5)
| ~ class_OrderedGroup_Ocomm__monoid__add(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3777]) ).
cnf(c_0_3777_3,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(X4,X3)),c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X5)) = c_Finite__Set_Osetsum(X4,X1,X2,X5) ),
inference(literals_permutation,[status(thm)],[c_0_3777]) ).
cnf(c_0_3778_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X1,tc_bool))),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_3778]) ).
cnf(c_0_3778_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X1,tc_bool))),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_3778]) ).
cnf(c_0_3778_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_HOL_Ominus__class_Ominus(X2,X5,tc_fun(X1,tc_bool))),c_HOL_Ominus__class_Ominus(X3,X4,tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_3778]) ).
cnf(c_0_3779_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)),X2) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3779]) ).
cnf(c_0_3779_1,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)),X2) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X4),X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3779]) ).
cnf(c_0_3780_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Fun_Ofun__upd(c_Map_Orestrict__map(X4,X3,X1,X5),X2,c_Option_Ooption_ONone(X5),X1,tc_Option_Ooption(X5)) = c_Map_Orestrict__map(X4,X3,X1,X5) ),
inference(literals_permutation,[status(thm)],[c_0_3780]) ).
cnf(c_0_3780_1,axiom,
( c_Fun_Ofun__upd(c_Map_Orestrict__map(X4,X3,X1,X5),X2,c_Option_Ooption_ONone(X5),X1,tc_Option_Ooption(X5)) = c_Map_Orestrict__map(X4,X3,X1,X5)
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3780]) ).
cnf(c_0_3781_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_3781]) ).
cnf(c_0_3781_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_3781]) ).
cnf(c_0_3782_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_3782]) ).
cnf(c_0_3782_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_3782]) ).
cnf(c_0_3783_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X4)),X5) = X6
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X5) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),X6)
| ~ class_Ring__and__Field_Oring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3783]) ).
cnf(c_0_3783_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X5) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),X6)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X4)),X5) = X6
| ~ class_Ring__and__Field_Oring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3783]) ).
cnf(c_0_3783_2,axiom,
( ~ class_Ring__and__Field_Oring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X5) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),X6)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X4)),X5) = X6 ),
inference(literals_permutation,[status(thm)],[c_0_3783]) ).
cnf(c_0_3784_0,axiom,
( X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),c_HOL_Ominus__class_Ominus(X3,X4,X2)),X5)),X6)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X4),X5)),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X5)),X6)
| ~ class_Ring__and__Field_Oring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3784]) ).
cnf(c_0_3784_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X4),X5)),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X5)),X6)
| X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),c_HOL_Ominus__class_Ominus(X3,X4,X2)),X5)),X6)
| ~ class_Ring__and__Field_Oring(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3784]) ).
cnf(c_0_3784_2,axiom,
( ~ class_Ring__and__Field_Oring(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X4),X5)),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X5)),X6)
| X1 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),c_HOL_Ominus__class_Ominus(X3,X4,X2)),X5)),X6) ),
inference(literals_permutation,[status(thm)],[c_0_3784]) ).
cnf(c_0_3785_0,axiom,
( c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),c_Finite__Set_Osetsum(X4,X3,X2,X5),X5) = c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X1))
| ~ class_OrderedGroup_Oab__group__add(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3785]) ).
cnf(c_0_3785_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),c_Finite__Set_Osetsum(X4,X3,X2,X5),X5) = c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2,X5)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X1))
| ~ class_OrderedGroup_Oab__group__add(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3785]) ).
cnf(c_0_3785_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),c_Finite__Set_Osetsum(X4,X3,X2,X5),X5) = c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2,X5)
| ~ class_OrderedGroup_Oab__group__add(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3785]) ).
cnf(c_0_3785_3,axiom,
( ~ class_OrderedGroup_Oab__group__add(X5)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),c_Finite__Set_Osetsum(X4,X3,X2,X5),X5) = c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2,X5) ),
inference(literals_permutation,[status(thm)],[c_0_3785]) ).
cnf(c_0_3786_0,axiom,
( hAPP(X1,X2) = X3
| c_Fun_Ofun__upd(X1,X2,X3,X4,X5) != X1 ),
inference(literals_permutation,[status(thm)],[c_0_3786]) ).
cnf(c_0_3786_1,axiom,
( c_Fun_Ofun__upd(X1,X2,X3,X4,X5) != X1
| hAPP(X1,X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_3786]) ).
cnf(c_0_3787_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3787]) ).
cnf(c_0_3787_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X5))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3787]) ).
cnf(c_0_3787_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X5))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3787]) ).
cnf(c_0_3787_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X5))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3787]) ).
cnf(c_0_3787_4,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X5))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3787]) ).
cnf(c_0_3788_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)),X5)
| ~ class_Ring__and__Field_Osemiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3788]) ).
cnf(c_0_3788_1,axiom,
( ~ class_Ring__and__Field_Osemiring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)),X5) ),
inference(literals_permutation,[status(thm)],[c_0_3788]) ).
cnf(c_0_3789_0,axiom,
( c_Map_Omap__le(X1,X2,X3,X4)
| hAPP(X1,c_Map_Osko__Map__Xmap__le__def__1__1(X1,X2,X3,X4)) != hAPP(X2,c_Map_Osko__Map__Xmap__le__def__1__1(X1,X2,X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3789]) ).
cnf(c_0_3789_1,axiom,
( hAPP(X1,c_Map_Osko__Map__Xmap__le__def__1__1(X1,X2,X3,X4)) != hAPP(X2,c_Map_Osko__Map__Xmap__le__def__1__1(X1,X2,X3,X4))
| c_Map_Omap__le(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3789]) ).
cnf(c_0_3790_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3790]) ).
cnf(c_0_3790_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3790]) ).
cnf(c_0_3790_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3790]) ).
cnf(c_0_3791_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3791]) ).
cnf(c_0_3791_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3791]) ).
cnf(c_0_3791_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3791]) ).
cnf(c_0_3792_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_3792]) ).
cnf(c_0_3792_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_3792]) ).
cnf(c_0_3793_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3793]) ).
cnf(c_0_3793_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3793]) ).
cnf(c_0_3793_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3793]) ).
cnf(c_0_3793_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3793]) ).
cnf(c_0_3794_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3794]) ).
cnf(c_0_3794_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3794]) ).
cnf(c_0_3794_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3794]) ).
cnf(c_0_3794_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_3794]) ).
cnf(c_0_3795_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3795]) ).
cnf(c_0_3795_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3795]) ).
cnf(c_0_3795_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3795]) ).
cnf(c_0_3795_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3795]) ).
cnf(c_0_3796_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3796]) ).
cnf(c_0_3796_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3796]) ).
cnf(c_0_3796_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3796]) ).
cnf(c_0_3796_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_3796]) ).
cnf(c_0_3797_0,axiom,
( X3 = X4
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3797]) ).
cnf(c_0_3797_1,axiom,
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),X2),X4))
| X3 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_3797]) ).
cnf(c_0_3798_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_3798]) ).
cnf(c_0_3798_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_3798]) ).
cnf(c_0_3799_0,axiom,
( c_Map_Omap__add(X1,X2,X3,X4) = c_Map_Omap__add(X2,X1,X3,X4)
| ~ c_Map_Omap__le(X1,c_Map_Omap__add(X1,X2,X3,X4),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3799]) ).
cnf(c_0_3799_1,axiom,
( ~ c_Map_Omap__le(X1,c_Map_Omap__add(X1,X2,X3,X4),X3,X4)
| c_Map_Omap__add(X1,X2,X3,X4) = c_Map_Omap__add(X2,X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3799]) ).
cnf(c_0_3800_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3800]) ).
cnf(c_0_3800_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3800]) ).
cnf(c_0_3801_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3801]) ).
cnf(c_0_3801_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3801]) ).
cnf(c_0_3802_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3802]) ).
cnf(c_0_3802_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3802]) ).
cnf(c_0_3802_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3802]) ).
cnf(c_0_3802_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3802]) ).
cnf(c_0_3802_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1)))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3802]) ).
cnf(c_0_3802_5,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3802]) ).
cnf(c_0_3803_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3803]) ).
cnf(c_0_3803_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3803]) ).
cnf(c_0_3803_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3803]) ).
cnf(c_0_3803_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3803]) ).
cnf(c_0_3803_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1)))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3803]) ).
cnf(c_0_3803_5,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3803]) ).
cnf(c_0_3804_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3804]) ).
cnf(c_0_3804_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)),X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3804]) ).
cnf(c_0_3805_0,axiom,
( c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X5) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),hAPP(X4,X3),X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Ring__and__Field_Oring(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3805]) ).
cnf(c_0_3805_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X5) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),hAPP(X4,X3),X5)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Ring__and__Field_Oring(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3805]) ).
cnf(c_0_3805_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X5) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),hAPP(X4,X3),X5)
| ~ class_Ring__and__Field_Oring(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3805]) ).
cnf(c_0_3805_3,axiom,
( ~ class_Ring__and__Field_Oring(X5)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X5) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),hAPP(X4,X3),X5) ),
inference(literals_permutation,[status(thm)],[c_0_3805]) ).
cnf(c_0_3806_0,axiom,
( c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X5) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),hAPP(X4,X3),X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_OrderedGroup_Oab__group__add(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3806]) ).
cnf(c_0_3806_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X5) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),hAPP(X4,X3),X5)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_OrderedGroup_Oab__group__add(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3806]) ).
cnf(c_0_3806_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X5) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),hAPP(X4,X3),X5)
| ~ class_OrderedGroup_Oab__group__add(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3806]) ).
cnf(c_0_3806_3,axiom,
( ~ class_OrderedGroup_Oab__group__add(X5)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X5) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(X4,X1,X2,X5),hAPP(X4,X3),X5) ),
inference(literals_permutation,[status(thm)],[c_0_3806]) ).
cnf(c_0_3807_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3807]) ).
cnf(c_0_3807_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3807]) ).
cnf(c_0_3807_2,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_3807]) ).
cnf(c_0_3808_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),c_HOL_Ozero__class_Ozero(X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3))))
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3808]) ).
cnf(c_0_3808_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),c_HOL_Ozero__class_Ozero(X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3))))
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3808]) ).
cnf(c_0_3808_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),c_HOL_Ozero__class_Ozero(X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3))))
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3808]) ).
cnf(c_0_3809_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),c_HOL_Ozero__class_Ozero(X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1))))
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3809]) ).
cnf(c_0_3809_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),c_HOL_Ozero__class_Ozero(X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1))))
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3809]) ).
cnf(c_0_3809_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),c_HOL_Ozero__class_Ozero(X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1))))
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3809]) ).
cnf(c_0_3810_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3))))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3810]) ).
cnf(c_0_3810_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)))) ),
inference(literals_permutation,[status(thm)],[c_0_3810]) ).
cnf(c_0_3811_0,axiom,
( c_Map_Omap__le(X1,c_Map_Omap__add(X1,X2,X3,X4),X3,X4)
| c_Map_Omap__add(X1,X2,X3,X4) != c_Map_Omap__add(X2,X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3811]) ).
cnf(c_0_3811_1,axiom,
( c_Map_Omap__add(X1,X2,X3,X4) != c_Map_Omap__add(X2,X1,X3,X4)
| c_Map_Omap__le(X1,c_Map_Omap__add(X1,X2,X3,X4),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3811]) ).
cnf(c_0_3812_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X4),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3812]) ).
cnf(c_0_3812_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| hBOOL(hAPP(hAPP(c_in(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3812]) ).
cnf(c_0_3812_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| hBOOL(hAPP(hAPP(c_in(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3812]) ).
cnf(c_0_3812_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| hBOOL(hAPP(hAPP(c_in(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3812]) ).
cnf(c_0_3813_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(X2),X3,X1,X2,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Oab__semigroup__mult(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3813]) ).
cnf(c_0_3813_1,axiom,
( hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(X2),X3,X1,X2,X2)
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Oab__semigroup__mult(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3813]) ).
cnf(c_0_3813_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(X2),X3,X1,X2,X2)
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_OrderedGroup_Oab__semigroup__mult(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3813]) ).
cnf(c_0_3813_3,axiom,
( ~ class_OrderedGroup_Oab__semigroup__mult(X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(X2),X3,X1,X2,X2)
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3813]) ).
cnf(c_0_3814_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = c_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(X2),X3,X1,X2,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3814]) ).
cnf(c_0_3814_1,axiom,
( hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = c_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(X2),X3,X1,X2,X2)
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3814]) ).
cnf(c_0_3814_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = c_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(X2),X3,X1,X2,X2)
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3814]) ).
cnf(c_0_3814_3,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = c_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(X2),X3,X1,X2,X2)
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3814]) ).
cnf(c_0_3815_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),X4),X3))
| hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = c_Finite__Set_Ofold(X1,X4,X3,X2,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3815]) ).
cnf(c_0_3815_1,axiom,
( hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = c_Finite__Set_Ofold(X1,X4,X3,X2,X2)
| hBOOL(hAPP(hAPP(c_in(X2),X4),X3))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3815]) ).
cnf(c_0_3815_2,axiom,
( ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = c_Finite__Set_Ofold(X1,X4,X3,X2,X2)
| hBOOL(hAPP(hAPP(c_in(X2),X4),X3))
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3815]) ).
cnf(c_0_3815_3,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = c_Finite__Set_Ofold(X1,X4,X3,X2,X2)
| hBOOL(hAPP(hAPP(c_in(X2),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3815]) ).
cnf(c_0_3816_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3816]) ).
cnf(c_0_3816_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3816]) ).
cnf(c_0_3816_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3816]) ).
cnf(c_0_3816_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3816]) ).
cnf(c_0_3816_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3816]) ).
cnf(c_0_3816_5,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_3816]) ).
cnf(c_0_3817_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3817]) ).
cnf(c_0_3817_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3817]) ).
cnf(c_0_3817_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3817]) ).
cnf(c_0_3817_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3817]) ).
cnf(c_0_3817_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3817]) ).
cnf(c_0_3817_5,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_3817]) ).
cnf(c_0_3818_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3818]) ).
cnf(c_0_3818_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3818]) ).
cnf(c_0_3818_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3818]) ).
cnf(c_0_3818_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3818]) ).
cnf(c_0_3818_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3818]) ).
cnf(c_0_3818_5,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_3818]) ).
cnf(c_0_3819_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3819]) ).
cnf(c_0_3819_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3819]) ).
cnf(c_0_3819_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3819]) ).
cnf(c_0_3819_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3819]) ).
cnf(c_0_3819_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3819]) ).
cnf(c_0_3819_5,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_3819]) ).
cnf(c_0_3820_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Opordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3820]) ).
cnf(c_0_3820_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Opordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3820]) ).
cnf(c_0_3820_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Opordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3820]) ).
cnf(c_0_3820_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Opordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3820]) ).
cnf(c_0_3820_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ class_Ring__and__Field_Opordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3820]) ).
cnf(c_0_3820_5,axiom,
( ~ class_Ring__and__Field_Opordered__semiring(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_3820]) ).
cnf(c_0_3821_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Opordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3821]) ).
cnf(c_0_3821_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Opordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3821]) ).
cnf(c_0_3821_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Opordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3821]) ).
cnf(c_0_3821_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Opordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3821]) ).
cnf(c_0_3821_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)))
| ~ class_Ring__and__Field_Opordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3821]) ).
cnf(c_0_3821_5,axiom,
( ~ class_Ring__and__Field_Opordered__semiring(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_3821]) ).
cnf(c_0_3822_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3822]) ).
cnf(c_0_3822_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3822]) ).
cnf(c_0_3822_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3822]) ).
cnf(c_0_3822_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3822]) ).
cnf(c_0_3823_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3823]) ).
cnf(c_0_3823_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3823]) ).
cnf(c_0_3823_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ class_Ring__and__Field_Oordered__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3823]) ).
cnf(c_0_3823_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3823]) ).
cnf(c_0_3824_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3824]) ).
cnf(c_0_3824_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3824]) ).
cnf(c_0_3824_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3824]) ).
cnf(c_0_3824_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3824]) ).
cnf(c_0_3825_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3825]) ).
cnf(c_0_3825_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3825]) ).
cnf(c_0_3825_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3825]) ).
cnf(c_0_3825_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3825]) ).
cnf(c_0_3826_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3826]) ).
cnf(c_0_3826_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3826]) ).
cnf(c_0_3826_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3826]) ).
cnf(c_0_3826_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3826]) ).
cnf(c_0_3827_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3827]) ).
cnf(c_0_3827_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3827]) ).
cnf(c_0_3827_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3827]) ).
cnf(c_0_3827_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3827]) ).
cnf(c_0_3828_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3828]) ).
cnf(c_0_3828_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3828]) ).
cnf(c_0_3828_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3828]) ).
cnf(c_0_3828_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3828]) ).
cnf(c_0_3829_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3829]) ).
cnf(c_0_3829_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3829]) ).
cnf(c_0_3829_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3829]) ).
cnf(c_0_3829_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3829]) ).
cnf(c_0_3830_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3830]) ).
cnf(c_0_3830_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3830]) ).
cnf(c_0_3830_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3830]) ).
cnf(c_0_3830_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3830]) ).
cnf(c_0_3831_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3831]) ).
cnf(c_0_3831_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3831]) ).
cnf(c_0_3831_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3831]) ).
cnf(c_0_3831_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3831]) ).
cnf(c_0_3832_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_3832]) ).
cnf(c_0_3832_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_3832]) ).
cnf(c_0_3833_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_3833]) ).
cnf(c_0_3833_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_3833]) ).
cnf(c_0_3834_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_3834]) ).
cnf(c_0_3834_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_3834]) ).
cnf(c_0_3835_0,axiom,
( c_Map_Omap__le(X2,X5,X3,X4)
| ~ c_Map_Omap__le(c_Map_Omap__add(X1,X2,X3,X4),X5,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3835]) ).
cnf(c_0_3835_1,axiom,
( ~ c_Map_Omap__le(c_Map_Omap__add(X1,X2,X3,X4),X5,X3,X4)
| c_Map_Omap__le(X2,X5,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3835]) ).
cnf(c_0_3836_0,axiom,
( c_Finite__Set_Ofold(c_Set_Oinsert(X2),X3,X1,X2,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3836]) ).
cnf(c_0_3836_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofold(c_Set_Oinsert(X2),X3,X1,X2,tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3836]) ).
cnf(c_0_3837_0,axiom,
( hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(X2),X3,X1,X2,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3837]) ).
cnf(c_0_3837_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(X2),X3,X1,X2,X2)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3837]) ).
cnf(c_0_3837_2,axiom,
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(X2),X3,X1,X2,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3837]) ).
cnf(c_0_3838_0,axiom,
( hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = c_Finite__Set_Ofold(X1,X4,X3,X2,X2)
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3838]) ).
cnf(c_0_3838_1,axiom,
( ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2)
| hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = c_Finite__Set_Ofold(X1,X4,X3,X2,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3838]) ).
cnf(c_0_3838_2,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2)
| hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = c_Finite__Set_Ofold(X1,X4,X3,X2,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3838]) ).
cnf(c_0_3839_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3839]) ).
cnf(c_0_3839_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3839]) ).
cnf(c_0_3839_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3839]) ).
cnf(c_0_3839_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3839]) ).
cnf(c_0_3840_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3840]) ).
cnf(c_0_3840_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3840]) ).
cnf(c_0_3840_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3840]) ).
cnf(c_0_3840_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3840]) ).
cnf(c_0_3841_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3841]) ).
cnf(c_0_3841_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3841]) ).
cnf(c_0_3842_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3842]) ).
cnf(c_0_3842_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3842]) ).
cnf(c_0_3842_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3842]) ).
cnf(c_0_3842_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3842]) ).
cnf(c_0_3843_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3843]) ).
cnf(c_0_3843_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3843]) ).
cnf(c_0_3843_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3843]) ).
cnf(c_0_3843_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3843]) ).
cnf(c_0_3844_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3844]) ).
cnf(c_0_3844_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3844]) ).
cnf(c_0_3844_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3844]) ).
cnf(c_0_3844_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3844]) ).
cnf(c_0_3845_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3845]) ).
cnf(c_0_3845_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3845]) ).
cnf(c_0_3845_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3845]) ).
cnf(c_0_3845_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3845]) ).
cnf(c_0_3846_0,axiom,
( c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2)) = c_Finite__Set_Ocard(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3846]) ).
cnf(c_0_3846_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2)) = c_Finite__Set_Ocard(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3846]) ).
cnf(c_0_3846_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2)) = c_Finite__Set_Ocard(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3846]) ).
cnf(c_0_3847_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X4),X2)),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3847]) ).
cnf(c_0_3847_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X4),X2)),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3847]) ).
cnf(c_0_3848_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3848]) ).
cnf(c_0_3848_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3848]) ).
cnf(c_0_3848_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3848]) ).
cnf(c_0_3848_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3848]) ).
cnf(c_0_3849_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3849]) ).
cnf(c_0_3849_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3849]) ).
cnf(c_0_3849_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3849]) ).
cnf(c_0_3849_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3849]) ).
cnf(c_0_3850_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3850]) ).
cnf(c_0_3850_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3850]) ).
cnf(c_0_3850_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3850]) ).
cnf(c_0_3851_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Map_Odom(X1,X3,X4)),c_Map_Odom(X2,X3,X4)))
| ~ c_Map_Omap__le(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3851]) ).
cnf(c_0_3851_1,axiom,
( ~ c_Map_Omap__le(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Map_Odom(X1,X3,X4)),c_Map_Odom(X2,X3,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3851]) ).
cnf(c_0_3852_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),c_Complete__Lattice_OInf__class_OInf(X1,X2)) = c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X2),X3,X1,X2,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3852]) ).
cnf(c_0_3852_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),c_Complete__Lattice_OInf__class_OInf(X1,X2)) = c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X2),X3,X1,X2,X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3852]) ).
cnf(c_0_3852_2,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2),X3),c_Complete__Lattice_OInf__class_OInf(X1,X2)) = c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X2),X3,X1,X2,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3852]) ).
cnf(c_0_3853_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),c_Complete__Lattice_OSup__class_OSup(X1,X2)) = c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X2),X3,X1,X2,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3853]) ).
cnf(c_0_3853_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),c_Complete__Lattice_OSup__class_OSup(X1,X2)) = c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X2),X3,X1,X2,X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3853]) ).
cnf(c_0_3853_2,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),c_Complete__Lattice_OSup__class_OSup(X1,X2)) = c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X2),X3,X1,X2,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3853]) ).
cnf(c_0_3854_0,axiom,
( c_Fun_Ofun__upd(X1,X2,hAPP(c_Option_Ooption_OSome(X3),X4),X5,tc_Option_Ooption(X3)) = X1
| hAPP(X1,X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_3854]) ).
cnf(c_0_3854_1,axiom,
( hAPP(X1,X2) != hAPP(c_Option_Ooption_OSome(X3),X4)
| c_Fun_Ofun__upd(X1,X2,hAPP(c_Option_Ooption_OSome(X3),X4),X5,tc_Option_Ooption(X3)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3854]) ).
cnf(c_0_3855_0,axiom,
( c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2)) = c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3855]) ).
cnf(c_0_3855_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2)) = c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3855]) ).
cnf(c_0_3856_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X3),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3856]) ).
cnf(c_0_3856_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_in(X1),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3856]) ).
cnf(c_0_3856_2,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_in(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3856]) ).
cnf(c_0_3856_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_in(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3856]) ).
cnf(c_0_3857_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),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3857]) ).
cnf(c_0_3857_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),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3857]) ).
cnf(c_0_3857_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3857]) ).
cnf(c_0_3858_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3858]) ).
cnf(c_0_3858_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3858]) ).
cnf(c_0_3858_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1)))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3858]) ).
cnf(c_0_3858_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3858]) ).
cnf(c_0_3859_0,axiom,
( c_Map_Omap__add(X1,X2,X3,X4) = c_Map_Omap__add(X2,X1,X3,X4)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),c_Map_Odom(X1,X3,X4)),c_Map_Odom(X2,X3,X4)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_3859]) ).
cnf(c_0_3859_1,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),c_Map_Odom(X1,X3,X4)),c_Map_Odom(X2,X3,X4)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_Map_Omap__add(X1,X2,X3,X4) = c_Map_Omap__add(X2,X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3859]) ).
cnf(c_0_3860_0,axiom,
( c_Lattices_Olower__semilattice(c_COMBC(c_lessequals(X1),X1,X1,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(X1),X1,X1,tc_bool),c_Orderings_Oord__class_Omax(X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3860]) ).
cnf(c_0_3860_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_Lattices_Olower__semilattice(c_COMBC(c_lessequals(X1),X1,X1,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(X1),X1,X1,tc_bool),c_Orderings_Oord__class_Omax(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_3860]) ).
cnf(c_0_3861_0,axiom,
( c_Lattices_Olower__semilattice(c_COMBC(c_lessequals(X1),X1,X1,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(X1),X1,X1,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3861]) ).
cnf(c_0_3861_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| c_Lattices_Olower__semilattice(c_COMBC(c_lessequals(X1),X1,X1,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(X1),X1,X1,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_3861]) ).
cnf(c_0_3862_0,axiom,
( c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X2),c_Orderings_Obot__class_Obot(X2),X1,X2,X2) = c_Complete__Lattice_OSup__class_OSup(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3862]) ).
cnf(c_0_3862_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X2),c_Orderings_Obot__class_Obot(X2),X1,X2,X2) = c_Complete__Lattice_OSup__class_OSup(X1,X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3862]) ).
cnf(c_0_3862_2,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X2),c_Orderings_Obot__class_Obot(X2),X1,X2,X2) = c_Complete__Lattice_OSup__class_OSup(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3862]) ).
cnf(c_0_3863_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3863]) ).
cnf(c_0_3863_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3863]) ).
cnf(c_0_3863_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3863]) ).
cnf(c_0_3864_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3864]) ).
cnf(c_0_3864_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3864]) ).
cnf(c_0_3864_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3864]) ).
cnf(c_0_3865_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3865]) ).
cnf(c_0_3865_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3865]) ).
cnf(c_0_3865_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3865]) ).
cnf(c_0_3866_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3866]) ).
cnf(c_0_3866_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3866]) ).
cnf(c_0_3866_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3866]) ).
cnf(c_0_3867_0,axiom,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X2 = hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))))) ),
inference(literals_permutation,[status(thm)],[c_0_3867]) ).
cnf(c_0_3867_1,axiom,
( X2 = hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))))) ),
inference(literals_permutation,[status(thm)],[c_0_3867]) ).
cnf(c_0_3867_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))))
| X2 = hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_3867]) ).
cnf(c_0_3868_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3868]) ).
cnf(c_0_3868_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3868]) ).
cnf(c_0_3868_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3868]) ).
cnf(c_0_3869_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X3)),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1),X3))
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3869]) ).
cnf(c_0_3869_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X3)),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X1)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1),X3))
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3869]) ).
cnf(c_0_3869_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X3)),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X1)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3869]) ).
cnf(c_0_3869_3,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X3)),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X1)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3869]) ).
cnf(c_0_3869_4,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X3)),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X1)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_3869]) ).
cnf(c_0_3870_0,axiom,
( hAPP(X3,X4) = c_HOL_Ozero__class_Ozero(X5)
| hBOOL(hAPP(hAPP(c_in(X2),X4),X1))
| c_Finite__Set_Osetprod(X3,c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X5) = c_Finite__Set_Osetprod(X3,X1,X2,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3870]) ).
cnf(c_0_3870_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),X4),X1))
| hAPP(X3,X4) = c_HOL_Ozero__class_Ozero(X5)
| c_Finite__Set_Osetprod(X3,c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X5) = c_Finite__Set_Osetprod(X3,X1,X2,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3870]) ).
cnf(c_0_3870_2,axiom,
( c_Finite__Set_Osetprod(X3,c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X5) = c_Finite__Set_Osetprod(X3,X1,X2,X5)
| hBOOL(hAPP(hAPP(c_in(X2),X4),X1))
| hAPP(X3,X4) = c_HOL_Ozero__class_Ozero(X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3870]) ).
cnf(c_0_3870_3,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Osetprod(X3,c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X5) = c_Finite__Set_Osetprod(X3,X1,X2,X5)
| hBOOL(hAPP(hAPP(c_in(X2),X4),X1))
| hAPP(X3,X4) = c_HOL_Ozero__class_Ozero(X5)
| ~ class_Ring__and__Field_Ofield(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3870]) ).
cnf(c_0_3870_4,axiom,
( ~ class_Ring__and__Field_Ofield(X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Osetprod(X3,c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X5) = c_Finite__Set_Osetprod(X3,X1,X2,X5)
| hBOOL(hAPP(hAPP(c_in(X2),X4),X1))
| hAPP(X3,X4) = c_HOL_Ozero__class_Ozero(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3870]) ).
cnf(c_0_3871_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3871]) ).
cnf(c_0_3871_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3871]) ).
cnf(c_0_3871_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3871]) ).
cnf(c_0_3871_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3871]) ).
cnf(c_0_3872_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3872]) ).
cnf(c_0_3872_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3872]) ).
cnf(c_0_3873_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3873]) ).
cnf(c_0_3873_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3873]) ).
cnf(c_0_3873_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3873]) ).
cnf(c_0_3874_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3874]) ).
cnf(c_0_3874_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3874]) ).
cnf(c_0_3874_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3874]) ).
cnf(c_0_3875_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3875]) ).
cnf(c_0_3875_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3875]) ).
cnf(c_0_3875_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3875]) ).
cnf(c_0_3876_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3876]) ).
cnf(c_0_3876_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3876]) ).
cnf(c_0_3876_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3876]) ).
cnf(c_0_3877_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X5) = c_Finite__Set_Osetsum(X4,X1,X2,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Oab__group__add(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3877]) ).
cnf(c_0_3877_1,axiom,
( c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X5) = c_Finite__Set_Osetsum(X4,X1,X2,X5)
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Oab__group__add(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3877]) ).
cnf(c_0_3877_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X5) = c_Finite__Set_Osetsum(X4,X1,X2,X5)
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_OrderedGroup_Oab__group__add(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3877]) ).
cnf(c_0_3877_3,axiom,
( ~ class_OrderedGroup_Oab__group__add(X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2,X5) = c_Finite__Set_Osetsum(X4,X1,X2,X5)
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3877]) ).
cnf(c_0_3878_0,axiom,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OBODY(X1)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Option_Othe(hAPP(c_Com_Obody,X1),tc_Com_Ocom)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3878]) ).
cnf(c_0_3878_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Option_Othe(hAPP(c_Com_Obody,X1),tc_Com_Ocom)),X2),X3))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OBODY(X1)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3878]) ).
cnf(c_0_3879_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3879]) ).
cnf(c_0_3879_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3879]) ).
cnf(c_0_3879_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3879]) ).
cnf(c_0_3880_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3880]) ).
cnf(c_0_3880_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3880]) ).
cnf(c_0_3880_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3880]) ).
cnf(c_0_3881_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3881]) ).
cnf(c_0_3881_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3881]) ).
cnf(c_0_3882_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3882]) ).
cnf(c_0_3882_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3882]) ).
cnf(c_0_3883_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3883]) ).
cnf(c_0_3883_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3883]) ).
cnf(c_0_3883_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3883]) ).
cnf(c_0_3883_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X4),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3883]) ).
cnf(c_0_3884_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool)),X1,tc_nat) = c_Finite__Set_Osetsum(X4,X3,X1,tc_nat) ),
inference(literals_permutation,[status(thm)],[c_0_3884]) ).
cnf(c_0_3884_1,axiom,
( c_Finite__Set_Osetsum(X4,c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),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_3884]) ).
cnf(c_0_3885_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X2,tc_bool)),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(X3,X2)),c_Finite__Set_Ocard(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3885]) ).
cnf(c_0_3885_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X2,tc_bool)),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(X3,X2)),c_Finite__Set_Ocard(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3885]) ).
cnf(c_0_3885_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X2,tc_bool)),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(X3,X2)),c_Finite__Set_Ocard(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3885]) ).
cnf(c_0_3885_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(X3,X2)),c_Finite__Set_Ocard(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X2,tc_bool)),X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3885]) ).
cnf(c_0_3886_0,axiom,
( X1 = X2
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X3))
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3886]) ).
cnf(c_0_3886_1,axiom,
( X3 = X4
| X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X3))
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3886]) ).
cnf(c_0_3886_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X3))
| X3 = X4
| X1 = X2
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3886]) ).
cnf(c_0_3886_3,axiom,
( ~ class_Int_Onumber__ring(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X3))
| X3 = X4
| X1 = X2
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3886]) ).
cnf(c_0_3886_4,axiom,
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X3))
| X3 = X4
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3886]) ).
cnf(c_0_3887_0,axiom,
( X1 = X2
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X3))
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3887]) ).
cnf(c_0_3887_1,axiom,
( X3 = X4
| X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X3))
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3887]) ).
cnf(c_0_3887_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X3))
| X3 = X4
| X1 = X2
| ~ class_Int_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3887]) ).
cnf(c_0_3887_3,axiom,
( ~ class_Int_Onumber__ring(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X3))
| X3 = X4
| X1 = X2
| ~ class_Ring__and__Field_Oidom(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3887]) ).
cnf(c_0_3887_4,axiom,
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X2),X3))
| X3 = X4
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3887]) ).
cnf(c_0_3888_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_3888]) ).
cnf(c_0_3888_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_3888]) ).
cnf(c_0_3889_0,axiom,
( c_HOL_Ominus__class_Ominus(X3,c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3889]) ).
cnf(c_0_3889_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| c_HOL_Ominus__class_Ominus(X3,c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3889]) ).
cnf(c_0_3889_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| c_HOL_Ominus__class_Ominus(X3,c_HOL_Ominus__class_Ominus(X4,X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3889]) ).
cnf(c_0_3890_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X4),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X3),X4))
| ~ class_HOL_Oord(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3890]) ).
cnf(c_0_3890_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X3),X4))
| ~ class_HOL_Oord(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3890]) ).
cnf(c_0_3890_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X3),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X4),X3))
| ~ class_HOL_Oord(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3890]) ).
cnf(c_0_3890_3,axiom,
( ~ class_HOL_Oord(X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X3),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3890]) ).
cnf(c_0_3891_0,axiom,
( c_Orderings_Olinorder(c_COMBC(X1,X3,X3,tc_bool),c_COMBC(X2,X3,X3,tc_bool),X3)
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_3891]) ).
cnf(c_0_3891_1,axiom,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| c_Orderings_Olinorder(c_COMBC(X1,X3,X3,tc_bool),c_COMBC(X2,X3,X3,tc_bool),X3) ),
inference(literals_permutation,[status(thm)],[c_0_3891]) ).
cnf(c_0_3892_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3892]) ).
cnf(c_0_3892_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3892]) ).
cnf(c_0_3892_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3892]) ).
cnf(c_0_3893_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3893]) ).
cnf(c_0_3893_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3893]) ).
cnf(c_0_3893_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3893]) ).
cnf(c_0_3893_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3893]) ).
cnf(c_0_3894_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Omult__mono(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3894]) ).
cnf(c_0_3894_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Omult__mono(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3894]) ).
cnf(c_0_3894_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)))
| ~ class_Ring__and__Field_Omult__mono(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3894]) ).
cnf(c_0_3894_3,axiom,
( ~ class_Ring__and__Field_Omult__mono(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3894]) ).
cnf(c_0_3895_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Omult__mono(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3895]) ).
cnf(c_0_3895_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Omult__mono(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3895]) ).
cnf(c_0_3895_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Ring__and__Field_Omult__mono(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3895]) ).
cnf(c_0_3895_3,axiom,
( ~ class_Ring__and__Field_Omult__mono(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3895]) ).
cnf(c_0_3896_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Omult__mono1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3896]) ).
cnf(c_0_3896_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Omult__mono1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3896]) ).
cnf(c_0_3896_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Ring__and__Field_Omult__mono1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3896]) ).
cnf(c_0_3896_3,axiom,
( ~ class_Ring__and__Field_Omult__mono1(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3896]) ).
cnf(c_0_3897_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3897]) ).
cnf(c_0_3897_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3897]) ).
cnf(c_0_3897_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3897]) ).
cnf(c_0_3897_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3897]) ).
cnf(c_0_3898_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3898]) ).
cnf(c_0_3898_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3898]) ).
cnf(c_0_3898_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3898]) ).
cnf(c_0_3898_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3898]) ).
cnf(c_0_3899_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3899]) ).
cnf(c_0_3899_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3899]) ).
cnf(c_0_3899_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3899]) ).
cnf(c_0_3899_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3899]) ).
cnf(c_0_3900_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3900]) ).
cnf(c_0_3900_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3900]) ).
cnf(c_0_3900_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3900]) ).
cnf(c_0_3900_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3900]) ).
cnf(c_0_3901_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3901]) ).
cnf(c_0_3901_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3901]) ).
cnf(c_0_3901_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3901]) ).
cnf(c_0_3901_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3901]) ).
cnf(c_0_3902_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3902]) ).
cnf(c_0_3902_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3902]) ).
cnf(c_0_3902_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)))
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3902]) ).
cnf(c_0_3902_3,axiom,
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3902]) ).
cnf(c_0_3903_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3903]) ).
cnf(c_0_3903_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3903]) ).
cnf(c_0_3903_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3903]) ).
cnf(c_0_3903_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3903]) ).
cnf(c_0_3904_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3904]) ).
cnf(c_0_3904_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3904]) ).
cnf(c_0_3904_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3904]) ).
cnf(c_0_3904_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3904]) ).
cnf(c_0_3905_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3905]) ).
cnf(c_0_3905_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3905]) ).
cnf(c_0_3905_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3905]) ).
cnf(c_0_3905_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3905]) ).
cnf(c_0_3906_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| c_Finite__Set_Osetsum(X4,hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2,X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(X4,X3)),c_Finite__Set_Osetsum(X4,X1,X2,X5))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3906]) ).
cnf(c_0_3906_1,axiom,
( c_Finite__Set_Osetsum(X4,hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2,X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(X4,X3)),c_Finite__Set_Osetsum(X4,X1,X2,X5))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3906]) ).
cnf(c_0_3906_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Osetsum(X4,hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2,X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(X4,X3)),c_Finite__Set_Osetsum(X4,X1,X2,X5))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3906]) ).
cnf(c_0_3906_3,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Osetsum(X4,hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2,X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(X4,X3)),c_Finite__Set_Osetsum(X4,X1,X2,X5))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3906]) ).
cnf(c_0_3907_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| c_Finite__Set_Osetprod(X4,hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2,X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(X4,X3)),c_Finite__Set_Osetprod(X4,X1,X2,X5))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3907]) ).
cnf(c_0_3907_1,axiom,
( c_Finite__Set_Osetprod(X4,hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2,X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(X4,X3)),c_Finite__Set_Osetprod(X4,X1,X2,X5))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3907]) ).
cnf(c_0_3907_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Osetprod(X4,hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2,X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(X4,X3)),c_Finite__Set_Osetprod(X4,X1,X2,X5))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_OrderedGroup_Ocomm__monoid__mult(X5) ),
inference(literals_permutation,[status(thm)],[c_0_3907]) ).
cnf(c_0_3907_3,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__mult(X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Osetprod(X4,hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2,X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(X4,X3)),c_Finite__Set_Osetprod(X4,X1,X2,X5))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3907]) ).
cnf(c_0_3908_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3908]) ).
cnf(c_0_3908_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3908]) ).
cnf(c_0_3908_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3908]) ).
cnf(c_0_3908_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3908]) ).
cnf(c_0_3909_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3909]) ).
cnf(c_0_3909_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3909]) ).
cnf(c_0_3909_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3909]) ).
cnf(c_0_3909_3,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3909]) ).
cnf(c_0_3910_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3910]) ).
cnf(c_0_3910_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3910]) ).
cnf(c_0_3910_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3910]) ).
cnf(c_0_3910_3,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3910]) ).
cnf(c_0_3911_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3911]) ).
cnf(c_0_3911_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3911]) ).
cnf(c_0_3911_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3911]) ).
cnf(c_0_3911_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3911]) ).
cnf(c_0_3912_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3912]) ).
cnf(c_0_3912_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3912]) ).
cnf(c_0_3912_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3912]) ).
cnf(c_0_3912_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3912]) ).
cnf(c_0_3913_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3913]) ).
cnf(c_0_3913_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3913]) ).
cnf(c_0_3913_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3913]) ).
cnf(c_0_3913_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3913]) ).
cnf(c_0_3914_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3914]) ).
cnf(c_0_3914_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3914]) ).
cnf(c_0_3914_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3914]) ).
cnf(c_0_3914_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3914]) ).
cnf(c_0_3915_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3915]) ).
cnf(c_0_3915_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3915]) ).
cnf(c_0_3915_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3915]) ).
cnf(c_0_3915_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_3915]) ).
cnf(c_0_3916_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3916]) ).
cnf(c_0_3916_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3916]) ).
cnf(c_0_3916_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3916]) ).
cnf(c_0_3916_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3916]) ).
cnf(c_0_3917_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),X2)),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),X3)) = hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(X3,X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3917]) ).
cnf(c_0_3917_1,axiom,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),X2)),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),X3)) = hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(X3,X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3917]) ).
cnf(c_0_3917_2,axiom,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),X2)),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),X3)) = hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3))
| ~ c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(X3,X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3917]) ).
cnf(c_0_3917_3,axiom,
( ~ c_Finite__Set_Ofinite(X2,X1)
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),X2)),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),X3)) = hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3))
| ~ c_Finite__Set_Ofinite(X3,X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3917]) ).
cnf(c_0_3917_4,axiom,
( ~ c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(X2,X1)
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),X2)),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),X3)) = hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3917]) ).
cnf(c_0_3917_5,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(X2,X1)
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),X2)),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),X3)) = hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3917]) ).
cnf(c_0_3917_6,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(X2,X1)
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),X2)),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),X3)) = hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3917]) ).
cnf(c_0_3918_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),X2)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),X3)) = hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(X3,X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3918]) ).
cnf(c_0_3918_1,axiom,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),X2)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),X3)) = hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(X3,X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3918]) ).
cnf(c_0_3918_2,axiom,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),X2)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),X3)) = hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3))
| ~ c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(X3,X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3918]) ).
cnf(c_0_3918_3,axiom,
( ~ c_Finite__Set_Ofinite(X2,X1)
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),X2)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),X3)) = hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3))
| ~ c_Finite__Set_Ofinite(X3,X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3918]) ).
cnf(c_0_3918_4,axiom,
( ~ c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(X2,X1)
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),X2)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),X3)) = hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3918]) ).
cnf(c_0_3918_5,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(X2,X1)
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),X2)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),X3)) = hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3918]) ).
cnf(c_0_3918_6,axiom,
( ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(X2,X1)
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),X2)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),X3)) = hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3918]) ).
cnf(c_0_3919_0,axiom,
( c_Orderings_Olinorder(c_COMBC(c_lessequals(X1),X1,X1,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(X1),X1,X1,tc_bool),X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3919]) ).
cnf(c_0_3919_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_Orderings_Olinorder(c_COMBC(c_lessequals(X1),X1,X1,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(X1),X1,X1,tc_bool),X1) ),
inference(literals_permutation,[status(thm)],[c_0_3919]) ).
cnf(c_0_3920_0,axiom,
( X5 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| hBOOL(hAPP(hAPP(X1,X6),X7))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ c_Finite__Set_Ofinite(X5,X4)
| ~ hBOOL(hAPP(hAPP(X1,X6),hAPP(c_Finite__Set_Ofold1(X3,X4),X5)))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X7),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_3920]) ).
cnf(c_0_3920_1,axiom,
( hBOOL(hAPP(hAPP(X1,X6),X7))
| X5 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ c_Finite__Set_Ofinite(X5,X4)
| ~ hBOOL(hAPP(hAPP(X1,X6),hAPP(c_Finite__Set_Ofold1(X3,X4),X5)))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X7),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_3920]) ).
cnf(c_0_3920_2,axiom,
( ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,X6),X7))
| X5 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ c_Finite__Set_Ofinite(X5,X4)
| ~ hBOOL(hAPP(hAPP(X1,X6),hAPP(c_Finite__Set_Ofold1(X3,X4),X5)))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X7),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_3920]) ).
cnf(c_0_3920_3,axiom,
( ~ c_Finite__Set_Ofinite(X5,X4)
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,X6),X7))
| X5 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(hAPP(X1,X6),hAPP(c_Finite__Set_Ofold1(X3,X4),X5)))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X7),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_3920]) ).
cnf(c_0_3920_4,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X6),hAPP(c_Finite__Set_Ofold1(X3,X4),X5)))
| ~ c_Finite__Set_Ofinite(X5,X4)
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,X6),X7))
| X5 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X7),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_3920]) ).
cnf(c_0_3920_5,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X4),X7),X5))
| ~ hBOOL(hAPP(hAPP(X1,X6),hAPP(c_Finite__Set_Ofold1(X3,X4),X5)))
| ~ c_Finite__Set_Ofinite(X5,X4)
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,X6),X7))
| X5 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_3920]) ).
cnf(c_0_3921_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3921]) ).
cnf(c_0_3921_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3921]) ).
cnf(c_0_3921_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3921]) ).
cnf(c_0_3921_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_3921]) ).
cnf(c_0_3922_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3922]) ).
cnf(c_0_3922_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3922]) ).
cnf(c_0_3922_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5)))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3922]) ).
cnf(c_0_3922_3,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_3922]) ).
cnf(c_0_3923_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3923]) ).
cnf(c_0_3923_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3923]) ).
cnf(c_0_3923_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5)))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3923]) ).
cnf(c_0_3923_3,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_3923]) ).
cnf(c_0_3924_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3924]) ).
cnf(c_0_3924_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3924]) ).
cnf(c_0_3924_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5)))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3924]) ).
cnf(c_0_3924_3,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_3924]) ).
cnf(c_0_3925_0,axiom,
( hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1) = X3
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(X1,X3,X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3925]) ).
cnf(c_0_3925_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(X1,X3,X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3925]) ).
cnf(c_0_3925_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(X1,X3,X2)),X3))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1) = X3
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3925]) ).
cnf(c_0_3925_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(X1,X3,X2)),X3))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1) = X3
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3925]) ).
cnf(c_0_3925_4,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(X1,X3,X2)),X3))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_3925]) ).
cnf(c_0_3926_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3926]) ).
cnf(c_0_3926_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3926]) ).
cnf(c_0_3926_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3926]) ).
cnf(c_0_3927_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3927]) ).
cnf(c_0_3927_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3927]) ).
cnf(c_0_3927_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3927]) ).
cnf(c_0_3928_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3928]) ).
cnf(c_0_3928_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3928]) ).
cnf(c_0_3928_2,axiom,
( ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3928]) ).
cnf(c_0_3929_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3929]) ).
cnf(c_0_3929_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3929]) ).
cnf(c_0_3929_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3929]) ).
cnf(c_0_3929_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3929]) ).
cnf(c_0_3930_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3930]) ).
cnf(c_0_3930_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3930]) ).
cnf(c_0_3930_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3930]) ).
cnf(c_0_3930_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3930]) ).
cnf(c_0_3931_0,axiom,
( hAPP(c_Option_Ooption_OSome(X4),c_Map_Osko__Map__XdomD__1__1(X2,X3,X1,X4)) = hAPP(X3,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Map_Odom(X3,X1,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3931]) ).
cnf(c_0_3931_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Map_Odom(X3,X1,X4)))
| hAPP(c_Option_Ooption_OSome(X4),c_Map_Osko__Map__XdomD__1__1(X2,X3,X1,X4)) = hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3931]) ).
cnf(c_0_3932_0,axiom,
( c_Map_Omap__le(X1,X5,X3,X4)
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| ~ c_Map_Omap__le(X2,X5,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3932]) ).
cnf(c_0_3932_1,axiom,
( ~ c_Map_Omap__le(X1,X2,X3,X4)
| c_Map_Omap__le(X1,X5,X3,X4)
| ~ c_Map_Omap__le(X2,X5,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3932]) ).
cnf(c_0_3932_2,axiom,
( ~ c_Map_Omap__le(X2,X5,X3,X4)
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| c_Map_Omap__le(X1,X5,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_3932]) ).
cnf(c_0_3933_0,axiom,
( hAPP(c_Map_Omap__add(X5,X3,X1,X4),X2) = hAPP(X3,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Map_Odom(X3,X1,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3933]) ).
cnf(c_0_3933_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Map_Odom(X3,X1,X4)))
| hAPP(c_Map_Omap__add(X5,X3,X1,X4),X2) = hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3933]) ).
cnf(c_0_3934_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3934]) ).
cnf(c_0_3934_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3934]) ).
cnf(c_0_3934_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),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3934]) ).
cnf(c_0_3935_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3935]) ).
cnf(c_0_3935_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3935]) ).
cnf(c_0_3935_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),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3935]) ).
cnf(c_0_3936_0,axiom,
( hBOOL(hAPP(X2,X4))
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3936]) ).
cnf(c_0_3936_1,axiom,
( hBOOL(hAPP(X3,X4))
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3936]) ).
cnf(c_0_3936_2,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4))
| hBOOL(hAPP(X3,X4))
| hBOOL(hAPP(X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3936]) ).
cnf(c_0_3937_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X4),X3))
| ~ class_HOL_Oord(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3937]) ).
cnf(c_0_3937_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))
| ~ class_HOL_Oord(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3937]) ).
cnf(c_0_3937_2,axiom,
( ~ class_HOL_Oord(X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,X2)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3937]) ).
cnf(c_0_3938_0,axiom,
( hAPP(hAPP(X1,hAPP(c_Finite__Set_Ofold1(X1,X2),X3)),hAPP(c_Finite__Set_Ofold1(X1,X2),X4)) = hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X4,X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_3938]) ).
cnf(c_0_3938_1,axiom,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(X1,hAPP(c_Finite__Set_Ofold1(X1,X2),X3)),hAPP(c_Finite__Set_Ofold1(X1,X2),X4)) = hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X4,X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_3938]) ).
cnf(c_0_3938_2,axiom,
( X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(X1,hAPP(c_Finite__Set_Ofold1(X1,X2),X3)),hAPP(c_Finite__Set_Ofold1(X1,X2),X4)) = hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X4,X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_3938]) ).
cnf(c_0_3938_3,axiom,
( ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(X1,hAPP(c_Finite__Set_Ofold1(X1,X2),X3)),hAPP(c_Finite__Set_Ofold1(X1,X2),X4)) = hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4))
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X4,X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_3938]) ).
cnf(c_0_3938_4,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(X1,hAPP(c_Finite__Set_Ofold1(X1,X2),X3)),hAPP(c_Finite__Set_Ofold1(X1,X2),X4)) = hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4))
| ~ c_Finite__Set_Ofinite(X4,X2)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_3938]) ).
cnf(c_0_3938_5,axiom,
( ~ c_Finite__Set_Ofinite(X4,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(X1,hAPP(c_Finite__Set_Ofold1(X1,X2),X3)),hAPP(c_Finite__Set_Ofold1(X1,X2),X4)) = hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_3938]) ).
cnf(c_0_3938_6,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X4,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(X1,hAPP(c_Finite__Set_Ofold1(X1,X2),X3)),hAPP(c_Finite__Set_Ofold1(X1,X2),X4)) = hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3938]) ).
cnf(c_0_3939_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3939]) ).
cnf(c_0_3939_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3939]) ).
cnf(c_0_3939_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3939]) ).
cnf(c_0_3939_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_3939]) ).
cnf(c_0_3940_0,axiom,
( hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3940]) ).
cnf(c_0_3940_1,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4))
| hBOOL(hAPP(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3940]) ).
cnf(c_0_3941_0,axiom,
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3941]) ).
cnf(c_0_3941_1,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4))
| hBOOL(hAPP(X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3941]) ).
cnf(c_0_3942_0,axiom,
( hBOOL(hAPP(hAPP(X1,hAPP(c_Finite__Set_Ofold1(X3,X4),X5)),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ c_Finite__Set_Ofinite(X5,X4)
| ~ hBOOL(hAPP(hAPP(c_in(X4),X6),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_3942]) ).
cnf(c_0_3942_1,axiom,
( ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,hAPP(c_Finite__Set_Ofold1(X3,X4),X5)),X6))
| ~ c_Finite__Set_Ofinite(X5,X4)
| ~ hBOOL(hAPP(hAPP(c_in(X4),X6),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_3942]) ).
cnf(c_0_3942_2,axiom,
( ~ c_Finite__Set_Ofinite(X5,X4)
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,hAPP(c_Finite__Set_Ofold1(X3,X4),X5)),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X4),X6),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_3942]) ).
cnf(c_0_3942_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X4),X6),X5))
| ~ c_Finite__Set_Ofinite(X5,X4)
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,hAPP(c_Finite__Set_Ofold1(X3,X4),X5)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_3942]) ).
cnf(c_0_3943_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3943]) ).
cnf(c_0_3943_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3943]) ).
cnf(c_0_3943_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3943]) ).
cnf(c_0_3944_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3944]) ).
cnf(c_0_3944_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3944]) ).
cnf(c_0_3944_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3944]) ).
cnf(c_0_3945_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3945]) ).
cnf(c_0_3945_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3945]) ).
cnf(c_0_3945_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3945]) ).
cnf(c_0_3946_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3946]) ).
cnf(c_0_3946_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3946]) ).
cnf(c_0_3946_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3946]) ).
cnf(c_0_3947_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3947]) ).
cnf(c_0_3947_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3947]) ).
cnf(c_0_3947_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3947]) ).
cnf(c_0_3948_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3948]) ).
cnf(c_0_3948_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3948]) ).
cnf(c_0_3949_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3949]) ).
cnf(c_0_3949_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_3949]) ).
cnf(c_0_3950_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3950]) ).
cnf(c_0_3950_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3950]) ).
cnf(c_0_3950_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3950]) ).
cnf(c_0_3950_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)),c_HOL_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3950]) ).
cnf(c_0_3951_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3951]) ).
cnf(c_0_3951_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3951]) ).
cnf(c_0_3951_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3951]) ).
cnf(c_0_3951_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3951]) ).
cnf(c_0_3952_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3952]) ).
cnf(c_0_3952_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3952]) ).
cnf(c_0_3952_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3952]) ).
cnf(c_0_3952_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3952]) ).
cnf(c_0_3953_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3953]) ).
cnf(c_0_3953_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3953]) ).
cnf(c_0_3953_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3953]) ).
cnf(c_0_3953_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3953]) ).
cnf(c_0_3954_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3954]) ).
cnf(c_0_3954_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3954]) ).
cnf(c_0_3954_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3954]) ).
cnf(c_0_3954_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3954]) ).
cnf(c_0_3955_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3955]) ).
cnf(c_0_3955_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3955]) ).
cnf(c_0_3955_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3955]) ).
cnf(c_0_3955_3,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3955]) ).
cnf(c_0_3956_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3956]) ).
cnf(c_0_3956_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3956]) ).
cnf(c_0_3956_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3956]) ).
cnf(c_0_3956_3,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3956]) ).
cnf(c_0_3957_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3957]) ).
cnf(c_0_3957_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3957]) ).
cnf(c_0_3957_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3957]) ).
cnf(c_0_3957_3,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3957]) ).
cnf(c_0_3958_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3958]) ).
cnf(c_0_3958_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3958]) ).
cnf(c_0_3958_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3958]) ).
cnf(c_0_3958_3,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3958]) ).
cnf(c_0_3959_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3959]) ).
cnf(c_0_3959_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3959]) ).
cnf(c_0_3959_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3959]) ).
cnf(c_0_3959_3,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)),c_HOL_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3959]) ).
cnf(c_0_3960_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3960]) ).
cnf(c_0_3960_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3960]) ).
cnf(c_0_3960_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3960]) ).
cnf(c_0_3961_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3961]) ).
cnf(c_0_3961_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3961]) ).
cnf(c_0_3961_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3961]) ).
cnf(c_0_3962_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3962]) ).
cnf(c_0_3962_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3962]) ).
cnf(c_0_3962_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3962]) ).
cnf(c_0_3963_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3963]) ).
cnf(c_0_3963_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3963]) ).
cnf(c_0_3963_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3963]) ).
cnf(c_0_3964_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3964]) ).
cnf(c_0_3964_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3964]) ).
cnf(c_0_3964_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3964]) ).
cnf(c_0_3965_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3965]) ).
cnf(c_0_3965_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3965]) ).
cnf(c_0_3965_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3965]) ).
cnf(c_0_3966_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3966]) ).
cnf(c_0_3966_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3966]) ).
cnf(c_0_3966_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3966]) ).
cnf(c_0_3967_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3967]) ).
cnf(c_0_3967_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3967]) ).
cnf(c_0_3967_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3967]) ).
cnf(c_0_3968_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3968]) ).
cnf(c_0_3968_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3968]) ).
cnf(c_0_3968_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3968]) ).
cnf(c_0_3969_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3969]) ).
cnf(c_0_3969_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3969]) ).
cnf(c_0_3969_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_3969]) ).
cnf(c_0_3970_0,axiom,
( hAPP(X1,X5) = hAPP(X2,X5)
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),c_Map_Odom(X1,X3,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3970]) ).
cnf(c_0_3970_1,axiom,
( ~ c_Map_Omap__le(X1,X2,X3,X4)
| hAPP(X1,X5) = hAPP(X2,X5)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),c_Map_Odom(X1,X3,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3970]) ).
cnf(c_0_3970_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X5),c_Map_Odom(X1,X3,X4)))
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| hAPP(X1,X5) = hAPP(X2,X5) ),
inference(literals_permutation,[status(thm)],[c_0_3970]) ).
cnf(c_0_3971_0,axiom,
( X3 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3971]) ).
cnf(c_0_3971_1,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X3))
| X3 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) ),
inference(literals_permutation,[status(thm)],[c_0_3971]) ).
cnf(c_0_3972_0,axiom,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3972]) ).
cnf(c_0_3972_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3972]) ).
cnf(c_0_3972_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_3972]) ).
cnf(c_0_3973_0,axiom,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3973]) ).
cnf(c_0_3973_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3973]) ).
cnf(c_0_3973_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_3973]) ).
cnf(c_0_3974_0,axiom,
( hBOOL(hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X5)),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X2,X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_3974]) ).
cnf(c_0_3974_1,axiom,
( ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X5)),X6))
| ~ hBOOL(hAPP(hAPP(X2,X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_3974]) ).
cnf(c_0_3974_2,axiom,
( ~ hBOOL(hAPP(hAPP(X2,X5),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X2,hAPP(hAPP(X3,X7),X5)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_3974]) ).
cnf(c_0_3975_0,axiom,
( hBOOL(hAPP(hAPP(X2,hAPP(hAPP(X3,X5),X7)),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X2,X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_3975]) ).
cnf(c_0_3975_1,axiom,
( ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X2,hAPP(hAPP(X3,X5),X7)),X6))
| ~ hBOOL(hAPP(hAPP(X2,X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_3975]) ).
cnf(c_0_3975_2,axiom,
( ~ hBOOL(hAPP(hAPP(X2,X5),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X2,hAPP(hAPP(X3,X5),X7)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_3975]) ).
cnf(c_0_3976_0,axiom,
( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(X3,X5),X7)),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_3976]) ).
cnf(c_0_3976_1,axiom,
( ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,hAPP(hAPP(X3,X5),X7)),X6))
| ~ hBOOL(hAPP(hAPP(X1,X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_3976]) ).
cnf(c_0_3976_2,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X5),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,hAPP(hAPP(X3,X5),X7)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_3976]) ).
cnf(c_0_3977_0,axiom,
( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(X3,X7),X5)),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_3977]) ).
cnf(c_0_3977_1,axiom,
( ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,hAPP(hAPP(X3,X7),X5)),X6))
| ~ hBOOL(hAPP(hAPP(X1,X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_3977]) ).
cnf(c_0_3977_2,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X5),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,hAPP(hAPP(X3,X7),X5)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_3977]) ).
cnf(c_0_3978_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X1)),X4))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X3),X4))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3978]) ).
cnf(c_0_3978_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X1)),X4))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X3),X4))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3978]) ).
cnf(c_0_3978_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X1)),X4))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X3),X4))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3978]) ).
cnf(c_0_3978_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X1)),X4))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X3),X4))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3978]) ).
cnf(c_0_3978_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X1)),X4))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3978]) ).
cnf(c_0_3978_5,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X1)),X4))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_3978]) ).
cnf(c_0_3979_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X1)),X4))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X3),X4))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3979]) ).
cnf(c_0_3979_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X1)),X4))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X3),X4))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3979]) ).
cnf(c_0_3979_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X1)),X4))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X3),X4))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3979]) ).
cnf(c_0_3979_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X1)),X4))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X3),X4))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3979]) ).
cnf(c_0_3979_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X1)),X4))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3979]) ).
cnf(c_0_3979_5,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X1)),X4))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_3979]) ).
cnf(c_0_3980_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3980]) ).
cnf(c_0_3980_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3980]) ).
cnf(c_0_3980_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3980]) ).
cnf(c_0_3980_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3980]) ).
cnf(c_0_3981_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3981]) ).
cnf(c_0_3981_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3981]) ).
cnf(c_0_3981_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3981]) ).
cnf(c_0_3981_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3981]) ).
cnf(c_0_3982_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3982]) ).
cnf(c_0_3982_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3982]) ).
cnf(c_0_3982_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3982]) ).
cnf(c_0_3982_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3982]) ).
cnf(c_0_3983_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3983]) ).
cnf(c_0_3983_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3983]) ).
cnf(c_0_3983_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3983]) ).
cnf(c_0_3983_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),c_HOL_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_3983]) ).
cnf(c_0_3984_0,axiom,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Option_Othe(hAPP(c_Com_Obody,X1),tc_Com_Ocom)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OBODY(X1)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3984]) ).
cnf(c_0_3984_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OBODY(X1)),X2),X3))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Option_Othe(hAPP(c_Com_Obody,X1),tc_Com_Ocom)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3984]) ).
cnf(c_0_3985_0,axiom,
( hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(X5,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(c_Map_Omap__add(X5,X1,X6,X3),X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_3985]) ).
cnf(c_0_3985_1,axiom,
( hAPP(X5,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(c_Map_Omap__add(X5,X1,X6,X3),X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_3985]) ).
cnf(c_0_3985_2,axiom,
( hAPP(c_Map_Omap__add(X5,X1,X6,X3),X2) != hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(X5,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_3985]) ).
cnf(c_0_3986_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3986]) ).
cnf(c_0_3986_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3986]) ).
cnf(c_0_3986_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3986]) ).
cnf(c_0_3987_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3987]) ).
cnf(c_0_3987_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3987]) ).
cnf(c_0_3987_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3987]) ).
cnf(c_0_3988_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3988]) ).
cnf(c_0_3988_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3988]) ).
cnf(c_0_3988_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3988]) ).
cnf(c_0_3989_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3989]) ).
cnf(c_0_3989_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3989]) ).
cnf(c_0_3989_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3989]) ).
cnf(c_0_3990_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3990]) ).
cnf(c_0_3990_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3990]) ).
cnf(c_0_3990_2,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3990]) ).
cnf(c_0_3991_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3991]) ).
cnf(c_0_3991_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3991]) ).
cnf(c_0_3991_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_3991]) ).
cnf(c_0_3992_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3992]) ).
cnf(c_0_3992_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3992]) ).
cnf(c_0_3992_2,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3992]) ).
cnf(c_0_3993_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3993]) ).
cnf(c_0_3993_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3993]) ).
cnf(c_0_3993_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_3993]) ).
cnf(c_0_3994_0,axiom,
( hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7)))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),X6))
| ~ hBOOL(hAPP(hAPP(X1,X5),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_3994]) ).
cnf(c_0_3994_1,axiom,
( ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7)))
| ~ hBOOL(hAPP(hAPP(X1,X5),X6))
| ~ hBOOL(hAPP(hAPP(X1,X5),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_3994]) ).
cnf(c_0_3994_2,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X5),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7)))
| ~ hBOOL(hAPP(hAPP(X1,X5),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_3994]) ).
cnf(c_0_3994_3,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X5),X7))
| ~ hBOOL(hAPP(hAPP(X1,X5),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7))) ),
inference(literals_permutation,[status(thm)],[c_0_3994]) ).
cnf(c_0_3995_0,axiom,
( hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7)))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),X6))
| ~ hBOOL(hAPP(hAPP(X1,X5),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_3995]) ).
cnf(c_0_3995_1,axiom,
( ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7)))
| ~ hBOOL(hAPP(hAPP(X1,X5),X6))
| ~ hBOOL(hAPP(hAPP(X1,X5),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_3995]) ).
cnf(c_0_3995_2,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X5),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7)))
| ~ hBOOL(hAPP(hAPP(X1,X5),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_3995]) ).
cnf(c_0_3995_3,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X5),X7))
| ~ hBOOL(hAPP(hAPP(X1,X5),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7))) ),
inference(literals_permutation,[status(thm)],[c_0_3995]) ).
cnf(c_0_3996_0,axiom,
( hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7)))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),X6))
| ~ hBOOL(hAPP(hAPP(X1,X5),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_3996]) ).
cnf(c_0_3996_1,axiom,
( ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7)))
| ~ hBOOL(hAPP(hAPP(X1,X5),X6))
| ~ hBOOL(hAPP(hAPP(X1,X5),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_3996]) ).
cnf(c_0_3996_2,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X5),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7)))
| ~ hBOOL(hAPP(hAPP(X1,X5),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_3996]) ).
cnf(c_0_3996_3,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X5),X7))
| ~ hBOOL(hAPP(hAPP(X1,X5),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7))) ),
inference(literals_permutation,[status(thm)],[c_0_3996]) ).
cnf(c_0_3997_0,axiom,
( hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X5,X1,X6,X3),X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_3997]) ).
cnf(c_0_3997_1,axiom,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(c_Map_Omap__add(X5,X1,X6,X3),X2) != hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_3997]) ).
cnf(c_0_3997_2,axiom,
( hAPP(c_Map_Omap__add(X5,X1,X6,X3),X2) != hAPP(c_Option_Ooption_OSome(X3),X4)
| hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(X1,X2) = hAPP(c_Option_Ooption_OSome(X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_3997]) ).
cnf(c_0_3998_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3998]) ).
cnf(c_0_3998_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3998]) ).
cnf(c_0_3998_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3998]) ).
cnf(c_0_3998_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_3998]) ).
cnf(c_0_3999_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3999]) ).
cnf(c_0_3999_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3999]) ).
cnf(c_0_3999_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3999]) ).
cnf(c_0_3999_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_3999]) ).
cnf(c_0_4000_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4000]) ).
cnf(c_0_4000_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4000]) ).
cnf(c_0_4000_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4000]) ).
cnf(c_0_4000_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4000]) ).
cnf(c_0_4001_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4001]) ).
cnf(c_0_4001_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4001]) ).
cnf(c_0_4001_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4001]) ).
cnf(c_0_4001_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4001]) ).
cnf(c_0_4002_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4002]) ).
cnf(c_0_4002_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4002]) ).
cnf(c_0_4002_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4002]) ).
cnf(c_0_4002_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4002]) ).
cnf(c_0_4003_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4003]) ).
cnf(c_0_4003_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4003]) ).
cnf(c_0_4003_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4003]) ).
cnf(c_0_4003_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4003]) ).
cnf(c_0_4004_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4004]) ).
cnf(c_0_4004_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4004]) ).
cnf(c_0_4004_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4004]) ).
cnf(c_0_4004_3,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4004]) ).
cnf(c_0_4005_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4005]) ).
cnf(c_0_4005_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4005]) ).
cnf(c_0_4005_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4005]) ).
cnf(c_0_4005_3,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4005]) ).
cnf(c_0_4006_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4006]) ).
cnf(c_0_4006_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4006]) ).
cnf(c_0_4006_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4006]) ).
cnf(c_0_4006_3,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4006]) ).
cnf(c_0_4007_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),X4),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4007]) ).
cnf(c_0_4007_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),X4),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4007]) ).
cnf(c_0_4007_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4007]) ).
cnf(c_0_4008_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4008]) ).
cnf(c_0_4008_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4008]) ).
cnf(c_0_4009_0,axiom,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X2)),hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4009]) ).
cnf(c_0_4009_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X2)),hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X3)))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4009]) ).
cnf(c_0_4009_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X2)),hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X3)))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4009]) ).
cnf(c_0_4009_3,axiom,
( ~ c_Finite__Set_Ofinite(X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X2)),hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X3)))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4009]) ).
cnf(c_0_4009_4,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X2)),hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X3)))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4009]) ).
cnf(c_0_4010_0,axiom,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_Finite__Set_Olinorder__class_OMin(X1),X3)),hAPP(c_Finite__Set_Olinorder__class_OMin(X1),X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4010]) ).
cnf(c_0_4010_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_Finite__Set_Olinorder__class_OMin(X1),X3)),hAPP(c_Finite__Set_Olinorder__class_OMin(X1),X2)))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4010]) ).
cnf(c_0_4010_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_Finite__Set_Olinorder__class_OMin(X1),X3)),hAPP(c_Finite__Set_Olinorder__class_OMin(X1),X2)))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4010]) ).
cnf(c_0_4010_3,axiom,
( ~ c_Finite__Set_Ofinite(X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_Finite__Set_Olinorder__class_OMin(X1),X3)),hAPP(c_Finite__Set_Olinorder__class_OMin(X1),X2)))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4010]) ).
cnf(c_0_4010_4,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_Finite__Set_Olinorder__class_OMin(X1),X3)),hAPP(c_Finite__Set_Olinorder__class_OMin(X1),X2)))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4010]) ).
cnf(c_0_4011_0,axiom,
( hBOOL(hAPP(hAPP(X1,X5),X7))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7))) ),
inference(literals_permutation,[status(thm)],[c_0_4011]) ).
cnf(c_0_4011_1,axiom,
( ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,X5),X7))
| ~ hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7))) ),
inference(literals_permutation,[status(thm)],[c_0_4011]) ).
cnf(c_0_4011_2,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7)))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,X5),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_4011]) ).
cnf(c_0_4012_0,axiom,
( hBOOL(hAPP(hAPP(X1,X5),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7))) ),
inference(literals_permutation,[status(thm)],[c_0_4012]) ).
cnf(c_0_4012_1,axiom,
( ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,X5),X6))
| ~ hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7))) ),
inference(literals_permutation,[status(thm)],[c_0_4012]) ).
cnf(c_0_4012_2,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7)))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_4012]) ).
cnf(c_0_4013_0,axiom,
( hBOOL(hAPP(hAPP(X1,X5),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7))) ),
inference(literals_permutation,[status(thm)],[c_0_4013]) ).
cnf(c_0_4013_1,axiom,
( ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,X5),X6))
| ~ hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7))) ),
inference(literals_permutation,[status(thm)],[c_0_4013]) ).
cnf(c_0_4013_2,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7)))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_4013]) ).
cnf(c_0_4014_0,axiom,
( hBOOL(hAPP(hAPP(X1,X5),X7))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7))) ),
inference(literals_permutation,[status(thm)],[c_0_4014]) ).
cnf(c_0_4014_1,axiom,
( ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,X5),X7))
| ~ hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7))) ),
inference(literals_permutation,[status(thm)],[c_0_4014]) ).
cnf(c_0_4014_2,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X5),hAPP(hAPP(X3,X6),X7)))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,X5),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_4014]) ).
cnf(c_0_4015_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4015]) ).
cnf(c_0_4015_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_4015]) ).
cnf(c_0_4016_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4016]) ).
cnf(c_0_4016_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_4016]) ).
cnf(c_0_4017_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Map_Odom(X3,X1,X4)))
| hAPP(c_Map_Omap__add(X5,X3,X1,X4),X2) = hAPP(X5,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4017]) ).
cnf(c_0_4017_1,axiom,
( hAPP(c_Map_Omap__add(X5,X3,X1,X4),X2) = hAPP(X5,X2)
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_Map_Odom(X3,X1,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_4017]) ).
cnf(c_0_4018_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Map_Odom(X3,X1,X4)))
| hAPP(c_Map_Omap__add(X3,X5,X1,X4),X2) = hAPP(X5,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4018]) ).
cnf(c_0_4018_1,axiom,
( hAPP(c_Map_Omap__add(X3,X5,X1,X4),X2) = hAPP(X5,X2)
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_Map_Odom(X3,X1,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_4018]) ).
cnf(c_0_4019_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4019]) ).
cnf(c_0_4019_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_4019]) ).
cnf(c_0_4020_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X3),X4))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X3),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4020]) ).
cnf(c_0_4020_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X3),X4))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X3),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4020]) ).
cnf(c_0_4020_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X3),X4))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X3),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4020]) ).
cnf(c_0_4020_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X3),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X1)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X3),X4))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4020]) ).
cnf(c_0_4020_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X2),X4),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X3),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X1)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X3),X4))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4020]) ).
cnf(c_0_4020_5,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X3),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X2),X2),X1)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X3),X4))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4020]) ).
cnf(c_0_4021_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X2),X3),X4))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X3),hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),X1))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4021]) ).
cnf(c_0_4021_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X2),X3),X4))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X3),hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),X1))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4021]) ).
cnf(c_0_4021_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),X3),X4))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X3),hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),X1))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4021]) ).
cnf(c_0_4021_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X3),hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X2),X1)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),X3),X4))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),X1))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4021]) ).
cnf(c_0_4021_4,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X2),X4),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X3),hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X2),X1)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),X3),X4))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4021]) ).
cnf(c_0_4021_5,axiom,
( ~ class_Lattices_Olower__semilattice(X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X4),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X3),hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X2),X1)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),X3),X4))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4021]) ).
cnf(c_0_4022_0,axiom,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X4,X1,X5,X3),X2) != c_Option_Ooption_ONone(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4022]) ).
cnf(c_0_4022_1,axiom,
( hAPP(c_Map_Omap__add(X4,X1,X5,X3),X2) != c_Option_Ooption_ONone(X3)
| hAPP(X1,X2) = c_Option_Ooption_ONone(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4022]) ).
cnf(c_0_4023_0,axiom,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X1,X4,X5,X3),X2) != c_Option_Ooption_ONone(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4023]) ).
cnf(c_0_4023_1,axiom,
( hAPP(c_Map_Omap__add(X1,X4,X5,X3),X2) != c_Option_Ooption_ONone(X3)
| hAPP(X1,X2) = c_Option_Ooption_ONone(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4023]) ).
cnf(c_0_4024_0,axiom,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))))) ),
inference(literals_permutation,[status(thm)],[c_0_4024]) ).
cnf(c_0_4024_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_4024]) ).
cnf(c_0_4025_0,axiom,
( X1 = X2
| X1 = X3
| hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X3),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_4025]) ).
cnf(c_0_4025_1,axiom,
( X1 = X3
| X1 = X2
| hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X3),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_4025]) ).
cnf(c_0_4025_2,axiom,
( hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X3),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))))
| X1 = X3
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4025]) ).
cnf(c_0_4026_0,axiom,
( X1 = X2
| X3 = X2
| hAPP(hAPP(c_Set_Oinsert(X4),X3),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_4026]) ).
cnf(c_0_4026_1,axiom,
( X3 = X2
| X1 = X2
| hAPP(hAPP(c_Set_Oinsert(X4),X3),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_4026]) ).
cnf(c_0_4026_2,axiom,
( hAPP(hAPP(c_Set_Oinsert(X4),X3),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))))
| X3 = X2
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4026]) ).
cnf(c_0_4027_0,axiom,
( X1 = X2
| X3 = X2
| hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X2),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_4027]) ).
cnf(c_0_4027_1,axiom,
( X3 = X2
| X1 = X2
| hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X2),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_4027]) ).
cnf(c_0_4027_2,axiom,
( hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X2),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))))
| X3 = X2
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4027]) ).
cnf(c_0_4028_0,axiom,
( X1 = X2
| X1 = X3
| hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X2),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_4028]) ).
cnf(c_0_4028_1,axiom,
( X1 = X3
| X1 = X2
| hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X2),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_4028]) ).
cnf(c_0_4028_2,axiom,
( hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X2),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))))
| X1 = X3
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4028]) ).
cnf(c_0_4029_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))
| ~ class_HOL_Oord(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4029]) ).
cnf(c_0_4029_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X3),X4))
| ~ class_HOL_Oord(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4029]) ).
cnf(c_0_4029_2,axiom,
( ~ class_HOL_Oord(X2)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,X2)),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4029]) ).
cnf(c_0_4030_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_4030]) ).
cnf(c_0_4030_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_4030]) ).
cnf(c_0_4031_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OlessThan(X2,X1)),c_SetInterval_Oord__class_OlessThan(X3,X1)))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4031]) ).
cnf(c_0_4031_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OlessThan(X2,X1)),c_SetInterval_Oord__class_OlessThan(X3,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4031]) ).
cnf(c_0_4031_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OlessThan(X2,X1)),c_SetInterval_Oord__class_OlessThan(X3,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4031]) ).
cnf(c_0_4032_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),X1)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),X3)) = hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4032]) ).
cnf(c_0_4032_1,axiom,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),X1)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),X3)) = hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4032]) ).
cnf(c_0_4032_2,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),X1)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),X3)) = hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4032]) ).
cnf(c_0_4032_3,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),X1)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),X3)) = hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4032]) ).
cnf(c_0_4032_4,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),X1)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),X3)) = hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4032]) ).
cnf(c_0_4032_5,axiom,
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),X1)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),X3)) = hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3))
| X3 = 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_4032]) ).
cnf(c_0_4033_0,axiom,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))) = X3
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4033]) ).
cnf(c_0_4033_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hAPP(hAPP(c_Set_Oinsert(X1),X2),c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool))) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_4033]) ).
cnf(c_0_4034_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4034]) ).
cnf(c_0_4034_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4034]) ).
cnf(c_0_4034_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4034]) ).
cnf(c_0_4034_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4034]) ).
cnf(c_0_4035_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4035]) ).
cnf(c_0_4035_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4035]) ).
cnf(c_0_4035_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4035]) ).
cnf(c_0_4035_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4035]) ).
cnf(c_0_4036_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4036]) ).
cnf(c_0_4036_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4036]) ).
cnf(c_0_4036_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4036]) ).
cnf(c_0_4036_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4036]) ).
cnf(c_0_4037_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4037]) ).
cnf(c_0_4037_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4037]) ).
cnf(c_0_4037_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4037]) ).
cnf(c_0_4037_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4037]) ).
cnf(c_0_4038_0,axiom,
( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(X3,X5),X6)),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4038]) ).
cnf(c_0_4038_1,axiom,
( ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,hAPP(hAPP(X3,X5),X6)),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_4038]) ).
cnf(c_0_4039_0,axiom,
( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(X3,X5),X6)),X5))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4039]) ).
cnf(c_0_4039_1,axiom,
( ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hBOOL(hAPP(hAPP(X1,hAPP(hAPP(X3,X5),X6)),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_4039]) ).
cnf(c_0_4040_0,axiom,
( X1 = X2
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| ~ c_Map_Omap__le(X2,X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4040]) ).
cnf(c_0_4040_1,axiom,
( ~ c_Map_Omap__le(X1,X2,X3,X4)
| X1 = X2
| ~ c_Map_Omap__le(X2,X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4040]) ).
cnf(c_0_4040_2,axiom,
( ~ c_Map_Omap__le(X2,X1,X3,X4)
| ~ c_Map_Omap__le(X1,X2,X3,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4040]) ).
cnf(c_0_4041_0,axiom,
( X1 = X2
| c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X1,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X6,X7,X2,X5) ),
inference(literals_permutation,[status(thm)],[c_0_4041]) ).
cnf(c_0_4041_1,axiom,
( c_Hoare__Mirabelle_Otriple_Otriple(X3,X4,X1,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X6,X7,X2,X5)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4041]) ).
cnf(c_0_4042_0,axiom,
( X1 = X2
| c_Hoare__Mirabelle_Otriple_Otriple(X3,X1,X4,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X6,X2,X7,X5) ),
inference(literals_permutation,[status(thm)],[c_0_4042]) ).
cnf(c_0_4042_1,axiom,
( c_Hoare__Mirabelle_Otriple_Otriple(X3,X1,X4,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X6,X2,X7,X5)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4042]) ).
cnf(c_0_4043_0,axiom,
( X1 = X2
| c_Hoare__Mirabelle_Otriple_Otriple(X1,X3,X4,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X2,X6,X7,X5) ),
inference(literals_permutation,[status(thm)],[c_0_4043]) ).
cnf(c_0_4043_1,axiom,
( c_Hoare__Mirabelle_Otriple_Otriple(X1,X3,X4,X5) != c_Hoare__Mirabelle_Otriple_Otriple(X2,X6,X7,X5)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4043]) ).
cnf(c_0_4044_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(X3,X5)),hAPP(X4,X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X3),X4))
| ~ class_HOL_Oord(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4044]) ).
cnf(c_0_4044_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(X3,X5)),hAPP(X4,X5)))
| ~ class_HOL_Oord(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4044]) ).
cnf(c_0_4044_2,axiom,
( ~ class_HOL_Oord(X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,X2)),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(X3,X5)),hAPP(X4,X5))) ),
inference(literals_permutation,[status(thm)],[c_0_4044]) ).
cnf(c_0_4045_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4045]) ).
cnf(c_0_4045_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4045]) ).
cnf(c_0_4045_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4045]) ).
cnf(c_0_4045_3,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_4045]) ).
cnf(c_0_4046_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4046]) ).
cnf(c_0_4046_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4046]) ).
cnf(c_0_4046_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4046]) ).
cnf(c_0_4046_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_4046]) ).
cnf(c_0_4047_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4047]) ).
cnf(c_0_4047_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4047]) ).
cnf(c_0_4047_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4047]) ).
cnf(c_0_4047_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_4047]) ).
cnf(c_0_4048_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4048]) ).
cnf(c_0_4048_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4048]) ).
cnf(c_0_4048_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4048]) ).
cnf(c_0_4048_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_4048]) ).
cnf(c_0_4049_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4049]) ).
cnf(c_0_4049_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4049]) ).
cnf(c_0_4049_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4049]) ).
cnf(c_0_4049_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_4049]) ).
cnf(c_0_4050_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4050]) ).
cnf(c_0_4050_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4050]) ).
cnf(c_0_4050_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4050]) ).
cnf(c_0_4050_3,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_4050]) ).
cnf(c_0_4051_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4051]) ).
cnf(c_0_4051_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4051]) ).
cnf(c_0_4051_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4051]) ).
cnf(c_0_4051_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_4051]) ).
cnf(c_0_4052_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4052]) ).
cnf(c_0_4052_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4052]) ).
cnf(c_0_4052_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4052]) ).
cnf(c_0_4052_3,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_4052]) ).
cnf(c_0_4053_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_4053]) ).
cnf(c_0_4053_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_4053]) ).
cnf(c_0_4054_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(X1,X3,X2)),X1))
| hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1) = X3
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4054]) ).
cnf(c_0_4054_1,axiom,
( hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1) = X3
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(X1,X3,X2)),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4054]) ).
cnf(c_0_4054_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1) = X3
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(X1,X3,X2)),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4054]) ).
cnf(c_0_4054_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1) = X3
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(X1,X3,X2)),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4054]) ).
cnf(c_0_4054_4,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1) = X3
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(X1,X3,X2)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4054]) ).
cnf(c_0_4055_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(X1,X3,X2)),X1))
| hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1) = X3
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4055]) ).
cnf(c_0_4055_1,axiom,
( hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1) = X3
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(X1,X3,X2)),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4055]) ).
cnf(c_0_4055_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1) = X3
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(X1,X3,X2)),X1))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4055]) ).
cnf(c_0_4055_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1) = X3
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(X1,X3,X2)),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4055]) ).
cnf(c_0_4055_4,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1) = X3
| hBOOL(hAPP(hAPP(c_in(X2),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(X1,X3,X2)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4055]) ).
cnf(c_0_4056_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X1,tc_bool))) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4056]) ).
cnf(c_0_4056_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X1,tc_bool))) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_4056]) ).
cnf(c_0_4057_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4057]) ).
cnf(c_0_4057_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4057]) ).
cnf(c_0_4058_0,axiom,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4058]) ).
cnf(c_0_4058_1,axiom,
( ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),X4),tc_fun(X2,tc_bool)),X2)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X4,tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4058]) ).
cnf(c_0_4059_0,axiom,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4059]) ).
cnf(c_0_4059_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4059]) ).
cnf(c_0_4059_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_4059]) ).
cnf(c_0_4060_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4060]) ).
cnf(c_0_4060_1,axiom,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4060]) ).
cnf(c_0_4060_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4060]) ).
cnf(c_0_4061_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4061]) ).
cnf(c_0_4061_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4061]) ).
cnf(c_0_4062_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4062]) ).
cnf(c_0_4062_1,axiom,
( ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4062]) ).
cnf(c_0_4062_2,axiom,
( ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4062]) ).
cnf(c_0_4063_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4063]) ).
cnf(c_0_4063_1,axiom,
( ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4063]) ).
cnf(c_0_4063_2,axiom,
( ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4063]) ).
cnf(c_0_4064_0,axiom,
( c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X5),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4064]) ).
cnf(c_0_4064_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X5),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4064]) ).
cnf(c_0_4065_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4065]) ).
cnf(c_0_4065_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4065]) ).
cnf(c_0_4065_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4065]) ).
cnf(c_0_4066_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4066]) ).
cnf(c_0_4066_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4066]) ).
cnf(c_0_4066_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4066]) ).
cnf(c_0_4067_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4067]) ).
cnf(c_0_4067_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4067]) ).
cnf(c_0_4067_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4067]) ).
cnf(c_0_4068_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4068]) ).
cnf(c_0_4068_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4068]) ).
cnf(c_0_4068_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4068]) ).
cnf(c_0_4069_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4069]) ).
cnf(c_0_4069_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4069]) ).
cnf(c_0_4069_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4069]) ).
cnf(c_0_4070_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(X3,X2)),c_Finite__Set_Ocard(X1,X2)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X2,tc_bool)),X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4070]) ).
cnf(c_0_4070_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(X3,X2)),c_Finite__Set_Ocard(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X2,tc_bool)),X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4070]) ).
cnf(c_0_4070_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X2,tc_bool)),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(X3,X2)),c_Finite__Set_Ocard(X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_4070]) ).
cnf(c_0_4071_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4071]) ).
cnf(c_0_4071_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_4071]) ).
cnf(c_0_4072_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4072]) ).
cnf(c_0_4072_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5))) ),
inference(literals_permutation,[status(thm)],[c_0_4072]) ).
cnf(c_0_4073_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4073]) ).
cnf(c_0_4073_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_4073]) ).
cnf(c_0_4074_0,axiom,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(X1,hAPP(c_Finite__Set_Ofold1(X1,X2),X3)),hAPP(c_Finite__Set_Ofold1(X1,X2),X4)) = hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4))
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4074]) ).
cnf(c_0_4074_1,axiom,
( X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(X1,hAPP(c_Finite__Set_Ofold1(X1,X2),X3)),hAPP(c_Finite__Set_Ofold1(X1,X2),X4)) = hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4))
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4074]) ).
cnf(c_0_4074_2,axiom,
( hAPP(hAPP(X1,hAPP(c_Finite__Set_Ofold1(X1,X2),X3)),hAPP(c_Finite__Set_Ofold1(X1,X2),X4)) = hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4074]) ).
cnf(c_0_4074_3,axiom,
( ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2)
| hAPP(hAPP(X1,hAPP(c_Finite__Set_Ofold1(X1,X2),X3)),hAPP(c_Finite__Set_Ofold1(X1,X2),X4)) = hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4074]) ).
cnf(c_0_4074_4,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2)
| hAPP(hAPP(X1,hAPP(c_Finite__Set_Ofold1(X1,X2),X3)),hAPP(c_Finite__Set_Ofold1(X1,X2),X4)) = hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4074]) ).
cnf(c_0_4074_5,axiom,
( ~ c_Finite__Set_Ofinite(X4,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2)
| hAPP(hAPP(X1,hAPP(c_Finite__Set_Ofold1(X1,X2),X3)),hAPP(c_Finite__Set_Ofold1(X1,X2),X4)) = hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4074]) ).
cnf(c_0_4075_0,axiom,
( hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1) = X3
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X3),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(X1,X3,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4075]) ).
cnf(c_0_4075_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X3),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(X1,X3,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4075]) ).
cnf(c_0_4075_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X3),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(X1,X3,X2)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1) = X3
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4075]) ).
cnf(c_0_4075_3,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X3),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(X1,X3,X2)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1) = X3
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4075]) ).
cnf(c_0_4075_4,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),X3),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(X1,X3,X2)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_4075]) ).
cnf(c_0_4076_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2) = c_Finite__Set_Ocard(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4076]) ).
cnf(c_0_4076_1,axiom,
( c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2) = c_Finite__Set_Ocard(X1,X2)
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4076]) ).
cnf(c_0_4076_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),X2) = c_Finite__Set_Ocard(X1,X2)
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4076]) ).
cnf(c_0_4077_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4077]) ).
cnf(c_0_4077_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4077]) ).
cnf(c_0_4077_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_4077]) ).
cnf(c_0_4078_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4078]) ).
cnf(c_0_4078_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4078]) ).
cnf(c_0_4078_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_4078]) ).
cnf(c_0_4079_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4079]) ).
cnf(c_0_4079_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4079]) ).
cnf(c_0_4079_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)),c_HOL_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_4079]) ).
cnf(c_0_4080_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4080]) ).
cnf(c_0_4080_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4080]) ).
cnf(c_0_4080_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),c_HOL_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_4080]) ).
cnf(c_0_4081_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4081]) ).
cnf(c_0_4081_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4081]) ).
cnf(c_0_4081_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),c_HOL_Ozero__class_Ozero(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_4081]) ).
cnf(c_0_4082_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4082]) ).
cnf(c_0_4082_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4082]) ).
cnf(c_0_4082_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4082]) ).
cnf(c_0_4082_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_4082]) ).
cnf(c_0_4083_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4083]) ).
cnf(c_0_4083_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4083]) ).
cnf(c_0_4083_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4083]) ).
cnf(c_0_4083_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_4083]) ).
cnf(c_0_4084_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4084]) ).
cnf(c_0_4084_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4084]) ).
cnf(c_0_4084_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4084]) ).
cnf(c_0_4084_3,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_4084]) ).
cnf(c_0_4085_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4085]) ).
cnf(c_0_4085_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4085]) ).
cnf(c_0_4085_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)))
| ~ class_Ring__and__Field_Opordered__ring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4085]) ).
cnf(c_0_4085_3,axiom,
( ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_HOL_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_4085]) ).
cnf(c_0_4086_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X2),X1)),X3))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4086]) ).
cnf(c_0_4086_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X2),X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4086]) ).
cnf(c_0_4086_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X2),X1)),X3))
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4086]) ).
cnf(c_0_4086_3,axiom,
( ~ class_Lattices_Olower__semilattice(X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X2),X2),X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4086]) ).
cnf(c_0_4087_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4087]) ).
cnf(c_0_4087_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4087]) ).
cnf(c_0_4087_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4087]) ).
cnf(c_0_4087_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4087]) ).
cnf(c_0_4088_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4088]) ).
cnf(c_0_4088_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4088]) ).
cnf(c_0_4088_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4088]) ).
cnf(c_0_4088_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4088]) ).
cnf(c_0_4089_0,axiom,
( hAPP(hAPP(X3,hAPP(hAPP(X3,X5),X6)),X7) = hAPP(hAPP(X3,X5),hAPP(hAPP(X3,X6),X7))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4089]) ).
cnf(c_0_4089_1,axiom,
( ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hAPP(hAPP(X3,hAPP(hAPP(X3,X5),X6)),X7) = hAPP(hAPP(X3,X5),hAPP(hAPP(X3,X6),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_4089]) ).
cnf(c_0_4090_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4090]) ).
cnf(c_0_4090_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4090]) ).
cnf(c_0_4090_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2)))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4090]) ).
cnf(c_0_4090_3,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4090]) ).
cnf(c_0_4090_4,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_4090]) ).
cnf(c_0_4091_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4091]) ).
cnf(c_0_4091_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4091]) ).
cnf(c_0_4091_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4091]) ).
cnf(c_0_4091_3,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4091]) ).
cnf(c_0_4091_4,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_4091]) ).
cnf(c_0_4092_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4092]) ).
cnf(c_0_4092_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4092]) ).
cnf(c_0_4092_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4092]) ).
cnf(c_0_4092_3,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4092]) ).
cnf(c_0_4092_4,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_4092]) ).
cnf(c_0_4093_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4093]) ).
cnf(c_0_4093_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4093]) ).
cnf(c_0_4093_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4093]) ).
cnf(c_0_4093_3,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4093]) ).
cnf(c_0_4093_4,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_4093]) ).
cnf(c_0_4094_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X1),X3),X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4094]) ).
cnf(c_0_4094_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X1),X3),X2))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4094]) ).
cnf(c_0_4094_2,axiom,
( ~ hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4094]) ).
cnf(c_0_4095_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4095]) ).
cnf(c_0_4095_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4095]) ).
cnf(c_0_4095_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4095]) ).
cnf(c_0_4095_3,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_4095]) ).
cnf(c_0_4096_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4096]) ).
cnf(c_0_4096_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4096]) ).
cnf(c_0_4096_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4096]) ).
cnf(c_0_4097_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4097]) ).
cnf(c_0_4097_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4097]) ).
cnf(c_0_4097_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4097]) ).
cnf(c_0_4098_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4098]) ).
cnf(c_0_4098_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4098]) ).
cnf(c_0_4098_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4098]) ).
cnf(c_0_4099_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4099]) ).
cnf(c_0_4099_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4099]) ).
cnf(c_0_4099_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4099]) ).
cnf(c_0_4100_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4100]) ).
cnf(c_0_4100_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X4),X2)),X3))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4100]) ).
cnf(c_0_4100_2,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X4),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4100]) ).
cnf(c_0_4101_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4101]) ).
cnf(c_0_4101_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)),X3))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4101]) ).
cnf(c_0_4101_2,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4101]) ).
cnf(c_0_4102_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4102]) ).
cnf(c_0_4102_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4102]) ).
cnf(c_0_4102_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4102]) ).
cnf(c_0_4103_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4103]) ).
cnf(c_0_4103_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4103]) ).
cnf(c_0_4103_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4103]) ).
cnf(c_0_4104_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4104]) ).
cnf(c_0_4104_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4104]) ).
cnf(c_0_4104_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4104]) ).
cnf(c_0_4105_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4105]) ).
cnf(c_0_4105_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4105]) ).
cnf(c_0_4105_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4105]) ).
cnf(c_0_4106_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4106]) ).
cnf(c_0_4106_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)),X3))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4106]) ).
cnf(c_0_4106_2,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4106]) ).
cnf(c_0_4107_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4107]) ).
cnf(c_0_4107_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X4),X2)),X3))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4107]) ).
cnf(c_0_4107_2,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X4),X2)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4107]) ).
cnf(c_0_4108_0,axiom,
( hAPP(c_Map_Orestrict__map(X4,X3,X1,X5),X2) = hAPP(X4,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4108]) ).
cnf(c_0_4108_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hAPP(c_Map_Orestrict__map(X4,X3,X1,X5),X2) = hAPP(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4108]) ).
cnf(c_0_4109_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_4109]) ).
cnf(c_0_4109_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_4109]) ).
cnf(c_0_4109_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_4109]) ).
cnf(c_0_4110_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_4110]) ).
cnf(c_0_4110_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_4110]) ).
cnf(c_0_4110_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_4110]) ).
cnf(c_0_4111_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4111]) ).
cnf(c_0_4111_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),X4),X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool))),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4111]) ).
cnf(c_0_4112_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4112]) ).
cnf(c_0_4112_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4112]) ).
cnf(c_0_4112_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4112]) ).
cnf(c_0_4113_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4113]) ).
cnf(c_0_4113_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4113]) ).
cnf(c_0_4113_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4113]) ).
cnf(c_0_4114_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4114]) ).
cnf(c_0_4114_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4114]) ).
cnf(c_0_4114_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4114]) ).
cnf(c_0_4114_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_4114]) ).
cnf(c_0_4115_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4115]) ).
cnf(c_0_4115_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4115]) ).
cnf(c_0_4115_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4115]) ).
cnf(c_0_4115_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_4115]) ).
cnf(c_0_4116_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4116]) ).
cnf(c_0_4116_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4116]) ).
cnf(c_0_4116_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4116]) ).
cnf(c_0_4116_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_4116]) ).
cnf(c_0_4117_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4117]) ).
cnf(c_0_4117_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4117]) ).
cnf(c_0_4117_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4117]) ).
cnf(c_0_4117_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_4117]) ).
cnf(c_0_4118_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4118]) ).
cnf(c_0_4118_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4118]) ).
cnf(c_0_4118_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4118]) ).
cnf(c_0_4118_3,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_4118]) ).
cnf(c_0_4119_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4119]) ).
cnf(c_0_4119_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4119]) ).
cnf(c_0_4119_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4119]) ).
cnf(c_0_4119_3,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_4119]) ).
cnf(c_0_4120_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4120]) ).
cnf(c_0_4120_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4120]) ).
cnf(c_0_4120_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4120]) ).
cnf(c_0_4120_3,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_4120]) ).
cnf(c_0_4121_0,axiom,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X1,X4)),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X4),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_4121]) ).
cnf(c_0_4121_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X1,X4)),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X4),X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_4121]) ).
cnf(c_0_4121_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X4),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(X1,X4)),X2),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_4121]) ).
cnf(c_0_4122_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X1),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4122]) ).
cnf(c_0_4122_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4122]) ).
cnf(c_0_4123_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4123]) ).
cnf(c_0_4123_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4123]) ).
cnf(c_0_4124_0,axiom,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_4124]) ).
cnf(c_0_4124_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4124]) ).
cnf(c_0_4125_0,axiom,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X3),X4),X2),tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4125]) ).
cnf(c_0_4125_1,axiom,
( ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X3)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,hAPP(hAPP(c_Set_Oinsert(X3),X4),X2),tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4125]) ).
cnf(c_0_4126_0,axiom,
( hAPP(hAPP(X3,X5),hAPP(hAPP(X3,X6),X7)) = hAPP(hAPP(X3,X6),hAPP(hAPP(X3,X5),X7))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4126]) ).
cnf(c_0_4126_1,axiom,
( ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hAPP(hAPP(X3,X5),hAPP(hAPP(X3,X6),X7)) = hAPP(hAPP(X3,X6),hAPP(hAPP(X3,X5),X7)) ),
inference(literals_permutation,[status(thm)],[c_0_4126]) ).
cnf(c_0_4127_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4127]) ).
cnf(c_0_4127_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4127]) ).
cnf(c_0_4128_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4)
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4128]) ).
cnf(c_0_4128_1,axiom,
( ~ class_Lattices_Odistrib__lattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4128]) ).
cnf(c_0_4129_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4)
| ~ class_OrderedGroup_Olordered__ab__group__add__join(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4129]) ).
cnf(c_0_4129_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add__join(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4129]) ).
cnf(c_0_4130_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4130]) ).
cnf(c_0_4130_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4130]) ).
cnf(c_0_4131_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4)
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4131]) ).
cnf(c_0_4131_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4131]) ).
cnf(c_0_4132_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4132]) ).
cnf(c_0_4132_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4132]) ).
cnf(c_0_4133_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4)
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4133]) ).
cnf(c_0_4133_1,axiom,
( ~ class_Lattices_Odistrib__lattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4133]) ).
cnf(c_0_4134_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4134]) ).
cnf(c_0_4134_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4134]) ).
cnf(c_0_4135_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4135]) ).
cnf(c_0_4135_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4135]) ).
cnf(c_0_4136_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4136]) ).
cnf(c_0_4136_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4136]) ).
cnf(c_0_4137_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4137]) ).
cnf(c_0_4137_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4137]) ).
cnf(c_0_4138_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4138]) ).
cnf(c_0_4138_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4138]) ).
cnf(c_0_4139_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4139]) ).
cnf(c_0_4139_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4139]) ).
cnf(c_0_4140_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OlessThan(X2,X1)),c_SetInterval_Oord__class_OlessThan(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4140]) ).
cnf(c_0_4140_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OlessThan(X2,X1)),c_SetInterval_Oord__class_OlessThan(X3,X1)))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4140]) ).
cnf(c_0_4140_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OlessThan(X2,X1)),c_SetInterval_Oord__class_OlessThan(X3,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_4140]) ).
cnf(c_0_4141_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hAPP(c_Map_Orestrict__map(X4,X3,X1,X5),X2) = c_Option_Ooption_ONone(X5) ),
inference(literals_permutation,[status(thm)],[c_0_4141]) ).
cnf(c_0_4141_1,axiom,
( hAPP(c_Map_Orestrict__map(X4,X3,X1,X5),X2) = c_Option_Ooption_ONone(X5)
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4141]) ).
cnf(c_0_4142_0,axiom,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(c_Option_Ooption_OSome(X4),X6)
| hAPP(X2,X5) != c_Option_Ooption_ONone(X4)
| hAPP(X1,X5) != hAPP(c_Option_Ooption_OSome(X4),X6) ),
inference(literals_permutation,[status(thm)],[c_0_4142]) ).
cnf(c_0_4142_1,axiom,
( hAPP(X2,X5) != c_Option_Ooption_ONone(X4)
| hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(c_Option_Ooption_OSome(X4),X6)
| hAPP(X1,X5) != hAPP(c_Option_Ooption_OSome(X4),X6) ),
inference(literals_permutation,[status(thm)],[c_0_4142]) ).
cnf(c_0_4142_2,axiom,
( hAPP(X1,X5) != hAPP(c_Option_Ooption_OSome(X4),X6)
| hAPP(X2,X5) != c_Option_Ooption_ONone(X4)
| hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(c_Option_Ooption_OSome(X4),X6) ),
inference(literals_permutation,[status(thm)],[c_0_4142]) ).
cnf(c_0_4143_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4143]) ).
cnf(c_0_4143_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4143]) ).
cnf(c_0_4143_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4143]) ).
cnf(c_0_4144_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4144]) ).
cnf(c_0_4144_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4144]) ).
cnf(c_0_4144_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4144]) ).
cnf(c_0_4145_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4145]) ).
cnf(c_0_4145_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4145]) ).
cnf(c_0_4145_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4145]) ).
cnf(c_0_4146_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4146]) ).
cnf(c_0_4146_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4146]) ).
cnf(c_0_4146_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4146]) ).
cnf(c_0_4147_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4147]) ).
cnf(c_0_4147_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4147]) ).
cnf(c_0_4147_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4147]) ).
cnf(c_0_4148_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4148]) ).
cnf(c_0_4148_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4148]) ).
cnf(c_0_4148_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4148]) ).
cnf(c_0_4149_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4149]) ).
cnf(c_0_4149_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4149]) ).
cnf(c_0_4149_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4149]) ).
cnf(c_0_4150_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4150]) ).
cnf(c_0_4150_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4150]) ).
cnf(c_0_4150_2,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4150]) ).
cnf(c_0_4151_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4151]) ).
cnf(c_0_4151_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4151]) ).
cnf(c_0_4151_2,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4151]) ).
cnf(c_0_4152_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4152]) ).
cnf(c_0_4152_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4152]) ).
cnf(c_0_4152_2,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4152]) ).
cnf(c_0_4153_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4153]) ).
cnf(c_0_4153_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4153]) ).
cnf(c_0_4153_2,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4153]) ).
cnf(c_0_4154_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4154]) ).
cnf(c_0_4154_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_4154]) ).
cnf(c_0_4155_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X2) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4155]) ).
cnf(c_0_4155_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_4155]) ).
cnf(c_0_4156_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4156]) ).
cnf(c_0_4156_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4156]) ).
cnf(c_0_4157_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X2) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4157]) ).
cnf(c_0_4157_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4157]) ).
cnf(c_0_4158_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4158]) ).
cnf(c_0_4158_1,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X3)
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4158]) ).
cnf(c_0_4159_0,axiom,
( X2 = X3
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_4159]) ).
cnf(c_0_4159_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_4159]) ).
cnf(c_0_4159_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_4159]) ).
cnf(c_0_4160_0,axiom,
( c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4160]) ).
cnf(c_0_4160_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4160]) ).
cnf(c_0_4161_0,axiom,
( c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4161]) ).
cnf(c_0_4161_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4161]) ).
cnf(c_0_4162_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4162]) ).
cnf(c_0_4162_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4162]) ).
cnf(c_0_4162_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4162]) ).
cnf(c_0_4163_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4163]) ).
cnf(c_0_4163_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oordered__ring__strict(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4163]) ).
cnf(c_0_4163_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X3)) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4163]) ).
cnf(c_0_4164_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1)),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X3)) = hAPP(c_Finite__Set_Olinorder__class_OMax(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4164]) ).
cnf(c_0_4164_1,axiom,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1)),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X3)) = hAPP(c_Finite__Set_Olinorder__class_OMax(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4164]) ).
cnf(c_0_4164_2,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1)),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X3)) = hAPP(c_Finite__Set_Olinorder__class_OMax(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4164]) ).
cnf(c_0_4164_3,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1)),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X3)) = hAPP(c_Finite__Set_Olinorder__class_OMax(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4164]) ).
cnf(c_0_4164_4,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1)),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X3)) = hAPP(c_Finite__Set_Olinorder__class_OMax(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4164]) ).
cnf(c_0_4164_5,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1)),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X3)) = hAPP(c_Finite__Set_Olinorder__class_OMax(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3))
| X3 = 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_4164]) ).
cnf(c_0_4165_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X2),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1)),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X3)) = hAPP(c_Finite__Set_Olinorder__class_OMin(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4165]) ).
cnf(c_0_4165_1,axiom,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X2),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1)),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X3)) = hAPP(c_Finite__Set_Olinorder__class_OMin(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4165]) ).
cnf(c_0_4165_2,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X2),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1)),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X3)) = hAPP(c_Finite__Set_Olinorder__class_OMin(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4165]) ).
cnf(c_0_4165_3,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X2),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1)),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X3)) = hAPP(c_Finite__Set_Olinorder__class_OMin(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4165]) ).
cnf(c_0_4165_4,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X2),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1)),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X3)) = hAPP(c_Finite__Set_Olinorder__class_OMin(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4165]) ).
cnf(c_0_4165_5,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X2),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1)),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X3)) = hAPP(c_Finite__Set_Olinorder__class_OMin(X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3))
| X3 = 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_4165]) ).
cnf(c_0_4166_0,axiom,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(c_Option_Ooption_OSome(X4),X6)
| hAPP(X2,X5) != hAPP(c_Option_Ooption_OSome(X4),X6) ),
inference(literals_permutation,[status(thm)],[c_0_4166]) ).
cnf(c_0_4166_1,axiom,
( hAPP(X2,X5) != hAPP(c_Option_Ooption_OSome(X4),X6)
| hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(c_Option_Ooption_OSome(X4),X6) ),
inference(literals_permutation,[status(thm)],[c_0_4166]) ).
cnf(c_0_4167_0,axiom,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(c_Option_Ooption_OSome(X4),X6)
| hAPP(X2,X5) != hAPP(c_Option_Ooption_OSome(X4),X6) ),
inference(literals_permutation,[status(thm)],[c_0_4167]) ).
cnf(c_0_4167_1,axiom,
( hAPP(X2,X5) != hAPP(c_Option_Ooption_OSome(X4),X6)
| hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = hAPP(c_Option_Ooption_OSome(X4),X6) ),
inference(literals_permutation,[status(thm)],[c_0_4167]) ).
cnf(c_0_4168_0,axiom,
( hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = c_Option_Ooption_ONone(X4)
| hAPP(X2,X5) != c_Option_Ooption_ONone(X4)
| hAPP(X1,X5) != c_Option_Ooption_ONone(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4168]) ).
cnf(c_0_4168_1,axiom,
( hAPP(X2,X5) != c_Option_Ooption_ONone(X4)
| hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = c_Option_Ooption_ONone(X4)
| hAPP(X1,X5) != c_Option_Ooption_ONone(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4168]) ).
cnf(c_0_4168_2,axiom,
( hAPP(X1,X5) != c_Option_Ooption_ONone(X4)
| hAPP(X2,X5) != c_Option_Ooption_ONone(X4)
| hAPP(c_Map_Omap__add(X1,X2,X3,X4),X5) = c_Option_Ooption_ONone(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4168]) ).
cnf(c_0_4169_0,axiom,
( c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) ),
inference(literals_permutation,[status(thm)],[c_0_4169]) ).
cnf(c_0_4169_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))))
| c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4169]) ).
cnf(c_0_4170_0,axiom,
( hAPP(hAPP(X3,X6),X5) = X5
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_4170]) ).
cnf(c_0_4170_1,axiom,
( ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hAPP(hAPP(X3,X6),X5) = X5
| ~ hBOOL(hAPP(hAPP(X1,X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_4170]) ).
cnf(c_0_4170_2,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X5),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hAPP(hAPP(X3,X6),X5) = X5 ),
inference(literals_permutation,[status(thm)],[c_0_4170]) ).
cnf(c_0_4171_0,axiom,
( hAPP(hAPP(X3,X5),X6) = X5
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(X1,X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_4171]) ).
cnf(c_0_4171_1,axiom,
( ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hAPP(hAPP(X3,X5),X6) = X5
| ~ hBOOL(hAPP(hAPP(X1,X5),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_4171]) ).
cnf(c_0_4171_2,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X5),X6))
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hAPP(hAPP(X3,X5),X6) = X5 ),
inference(literals_permutation,[status(thm)],[c_0_4171]) ).
cnf(c_0_4172_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4172]) ).
cnf(c_0_4172_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4172]) ).
cnf(c_0_4172_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_4172]) ).
cnf(c_0_4173_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4173]) ).
cnf(c_0_4173_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4173]) ).
cnf(c_0_4173_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_4173]) ).
cnf(c_0_4174_0,axiom,
( hAPP(hAPP(X3,X5),hAPP(hAPP(X3,X5),X6)) = hAPP(hAPP(X3,X5),X6)
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4174]) ).
cnf(c_0_4174_1,axiom,
( ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hAPP(hAPP(X3,X5),hAPP(hAPP(X3,X5),X6)) = hAPP(hAPP(X3,X5),X6) ),
inference(literals_permutation,[status(thm)],[c_0_4174]) ).
cnf(c_0_4175_0,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ c_Lattices_Olower__semilattice(X1,X4,X5,X6)
| hAPP(hAPP(X5,X2),X3) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_4175]) ).
cnf(c_0_4175_1,axiom,
( ~ c_Lattices_Olower__semilattice(X1,X4,X5,X6)
| hBOOL(hAPP(hAPP(X1,X2),X3))
| hAPP(hAPP(X5,X2),X3) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_4175]) ).
cnf(c_0_4175_2,axiom,
( hAPP(hAPP(X5,X2),X3) != X2
| ~ c_Lattices_Olower__semilattice(X1,X4,X5,X6)
| hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4175]) ).
cnf(c_0_4176_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_HOL_Ominus__class_Ominus(X2,X4,X1)),c_HOL_Ominus__class_Ominus(X3,X4,X1)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3),X4,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4176]) ).
cnf(c_0_4176_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_HOL_Ominus__class_Ominus(X2,X4,X1)),c_HOL_Ominus__class_Ominus(X3,X4,X1)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3),X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_4176]) ).
cnf(c_0_4177_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_HOL_Ominus__class_Ominus(X2,X4,X1)),c_HOL_Ominus__class_Ominus(X3,X4,X1)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3),X4,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4177]) ).
cnf(c_0_4177_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),c_HOL_Ominus__class_Ominus(X2,X4,X1)),c_HOL_Ominus__class_Ominus(X3,X4,X1)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3),X4,X1) ),
inference(literals_permutation,[status(thm)],[c_0_4177]) ).
cnf(c_0_4178_0,axiom,
( hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4178]) ).
cnf(c_0_4178_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4178]) ).
cnf(c_0_4178_2,axiom,
( ~ hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4178]) ).
cnf(c_0_4179_0,axiom,
( hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4179]) ).
cnf(c_0_4179_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X4,X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4179]) ).
cnf(c_0_4179_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X4))
| ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4179]) ).
cnf(c_0_4180_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4180]) ).
cnf(c_0_4180_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)))
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4180]) ).
cnf(c_0_4180_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4180]) ).
cnf(c_0_4180_3,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4180]) ).
cnf(c_0_4181_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Map_Odom(X3,X1,X4)))
| hAPP(X3,X2) != c_Option_Ooption_ONone(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4181]) ).
cnf(c_0_4181_1,axiom,
( hAPP(X3,X2) != c_Option_Ooption_ONone(X4)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Map_Odom(X3,X1,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_4181]) ).
cnf(c_0_4182_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4182]) ).
cnf(c_0_4182_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4182]) ).
cnf(c_0_4183_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4183]) ).
cnf(c_0_4183_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4183]) ).
cnf(c_0_4184_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X2))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4184]) ).
cnf(c_0_4184_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4184]) ).
cnf(c_0_4185_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X3))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4185]) ).
cnf(c_0_4185_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4185]) ).
cnf(c_0_4186_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X3))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4186]) ).
cnf(c_0_4186_1,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4186]) ).
cnf(c_0_4187_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X2))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4187]) ).
cnf(c_0_4187_1,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4187]) ).
cnf(c_0_4188_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4188]) ).
cnf(c_0_4188_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4188]) ).
cnf(c_0_4189_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4189]) ).
cnf(c_0_4189_1,axiom,
( ~ class_Lattices_Odistrib__lattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4189]) ).
cnf(c_0_4190_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
| ~ class_OrderedGroup_Olordered__ab__group__add__join(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4190]) ).
cnf(c_0_4190_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add__join(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4190]) ).
cnf(c_0_4191_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4191]) ).
cnf(c_0_4191_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4191]) ).
cnf(c_0_4192_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4192]) ).
cnf(c_0_4192_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4192]) ).
cnf(c_0_4193_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4193]) ).
cnf(c_0_4193_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4193]) ).
cnf(c_0_4194_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4194]) ).
cnf(c_0_4194_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4194]) ).
cnf(c_0_4195_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4195]) ).
cnf(c_0_4195_1,axiom,
( ~ class_Lattices_Odistrib__lattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4195]) ).
cnf(c_0_4196_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4196]) ).
cnf(c_0_4196_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4196]) ).
cnf(c_0_4197_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4197]) ).
cnf(c_0_4197_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4197]) ).
cnf(c_0_4198_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4198]) ).
cnf(c_0_4198_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4198]) ).
cnf(c_0_4199_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) != X3 ),
inference(literals_permutation,[status(thm)],[c_0_4199]) ).
cnf(c_0_4199_1,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) != X3
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4199]) ).
cnf(c_0_4200_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_HOL_Ozero__class_Ozero(X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_HOL_Ozero__class_Ozero(X2)),X1))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4200]) ).
cnf(c_0_4200_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_HOL_Ozero__class_Ozero(X2)),X3))
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_HOL_Ozero__class_Ozero(X2)),X1))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4200]) ).
cnf(c_0_4200_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_HOL_Ozero__class_Ozero(X2)),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_HOL_Ozero__class_Ozero(X2)),X3))
| X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4200]) ).
cnf(c_0_4200_3,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_HOL_Ozero__class_Ozero(X2)),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_HOL_Ozero__class_Ozero(X2)),X3))
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4200]) ).
cnf(c_0_4200_4,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_HOL_Ozero__class_Ozero(X2)),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_HOL_Ozero__class_Ozero(X2)),X3))
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4200]) ).
cnf(c_0_4201_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_HOL_Ozero__class_Ozero(X2)),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_HOL_Ozero__class_Ozero(X2)),X3))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4201]) ).
cnf(c_0_4201_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_HOL_Ozero__class_Ozero(X2)),X1))
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_HOL_Ozero__class_Ozero(X2)),X3))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4201]) ).
cnf(c_0_4201_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_HOL_Ozero__class_Ozero(X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_HOL_Ozero__class_Ozero(X2)),X1))
| X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4201]) ).
cnf(c_0_4201_3,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_HOL_Ozero__class_Ozero(X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_HOL_Ozero__class_Ozero(X2)),X1))
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4201]) ).
cnf(c_0_4201_4,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_HOL_Ozero__class_Ozero(X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X2),c_HOL_Ozero__class_Ozero(X2)),X1))
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4201]) ).
cnf(c_0_4202_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X1,X2),c_ATP__Linkup_Osko__Finite__Set__Xfinite__nonempty__imp__fold1Set__1__1(X1,X3,X2)))
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4202]) ).
cnf(c_0_4202_1,axiom,
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X1,X2),c_ATP__Linkup_Osko__Finite__Set__Xfinite__nonempty__imp__fold1Set__1__1(X1,X3,X2)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4202]) ).
cnf(c_0_4202_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X1,X2),c_ATP__Linkup_Osko__Finite__Set__Xfinite__nonempty__imp__fold1Set__1__1(X1,X3,X2)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4202]) ).
cnf(c_0_4203_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4))
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4203]) ).
cnf(c_0_4203_1,axiom,
( X3 = X4
| X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4))
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4203]) ).
cnf(c_0_4203_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4))
| X3 = X4
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4203]) ).
cnf(c_0_4203_3,axiom,
( ~ class_Int_Onumber__ring(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4))
| X3 = X4
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4203]) ).
cnf(c_0_4203_4,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X4))
| X3 = X4
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4203]) ).
cnf(c_0_4204_0,axiom,
( c_HOL_Ominus__class_Ominus(c_Map_Odom(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X2),X4),X5),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Map_Odom(X1,X2,X3),X5,tc_fun(X2,tc_bool))
| hAPP(X1,X4) != c_Option_Ooption_ONone(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4204]) ).
cnf(c_0_4204_1,axiom,
( hAPP(X1,X4) != c_Option_Ooption_ONone(X3)
| c_HOL_Ominus__class_Ominus(c_Map_Odom(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X2),X4),X5),tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Map_Odom(X1,X2,X3),X5,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4204]) ).
cnf(c_0_4205_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4205]) ).
cnf(c_0_4205_1,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4205]) ).
cnf(c_0_4206_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool)) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_4206]) ).
cnf(c_0_4206_1,axiom,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),tc_fun(X1,tc_bool)) = X3
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4206]) ).
cnf(c_0_4207_0,axiom,
( c_Finite__Set_Ofinite(X2,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ c_Finite__Set_Ofinite(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_4207]) ).
cnf(c_0_4207_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_4207]) ).
cnf(c_0_4207_2,axiom,
( ~ c_Finite__Set_Ofinite(X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| c_Finite__Set_Ofinite(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_4207]) ).
cnf(c_0_4208_0,axiom,
( c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4208]) ).
cnf(c_0_4208_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X3,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4208]) ).
cnf(c_0_4208_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4208]) ).
cnf(c_0_4209_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X1),X2),X4),X3,tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_HOL_Ominus__class_Ominus(X4,X3,tc_fun(X1,tc_bool))) ),
inference(literals_permutation,[status(thm)],[c_0_4209]) ).
cnf(c_0_4209_1,axiom,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X1),X2),X4),X3,tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),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_4209]) ).
cnf(c_0_4210_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_4210]) ).
cnf(c_0_4210_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_4210]) ).
cnf(c_0_4211_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4211]) ).
cnf(c_0_4211_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3)))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4211]) ).
cnf(c_0_4211_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_4211]) ).
cnf(c_0_4212_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4212]) ).
cnf(c_0_4212_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4212]) ).
cnf(c_0_4212_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_4212]) ).
cnf(c_0_4213_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4213]) ).
cnf(c_0_4213_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3)))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4213]) ).
cnf(c_0_4213_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_4213]) ).
cnf(c_0_4214_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4214]) ).
cnf(c_0_4214_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4214]) ).
cnf(c_0_4214_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_4214]) ).
cnf(c_0_4215_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4215]) ).
cnf(c_0_4215_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4215]) ).
cnf(c_0_4215_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_4215]) ).
cnf(c_0_4216_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4216]) ).
cnf(c_0_4216_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3)))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4216]) ).
cnf(c_0_4216_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_4216]) ).
cnf(c_0_4217_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4217]) ).
cnf(c_0_4217_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4217]) ).
cnf(c_0_4217_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_4217]) ).
cnf(c_0_4218_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4218]) ).
cnf(c_0_4218_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3)))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4218]) ).
cnf(c_0_4218_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_4218]) ).
cnf(c_0_4219_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4219]) ).
cnf(c_0_4219_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X4),X3)))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4219]) ).
cnf(c_0_4219_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_4219]) ).
cnf(c_0_4220_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4220]) ).
cnf(c_0_4220_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4220]) ).
cnf(c_0_4220_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_4220]) ).
cnf(c_0_4221_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4221]) ).
cnf(c_0_4221_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4221]) ).
cnf(c_0_4221_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))) ),
inference(literals_permutation,[status(thm)],[c_0_4221]) ).
cnf(c_0_4222_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4222]) ).
cnf(c_0_4222_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X4),X3)))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4222]) ).
cnf(c_0_4222_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_4222]) ).
cnf(c_0_4223_0,axiom,
( c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4223]) ).
cnf(c_0_4223_1,axiom,
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X1)
| c_Finite__Set_Ofinite(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_4223]) ).
cnf(c_0_4224_0,axiom,
( c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4224]) ).
cnf(c_0_4224_1,axiom,
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X1)
| c_Finite__Set_Ofinite(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_4224]) ).
cnf(c_0_4225_0,axiom,
( c_Finite__Set_Osetprod(X1,X2,X3,X4) = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2))
| hAPP(X1,X5) != c_HOL_Ozero__class_Ozero(X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| ~ class_Ring__and__Field_Ono__zero__divisors(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4225]) ).
cnf(c_0_4225_1,axiom,
( ~ c_Finite__Set_Ofinite(X2,X3)
| c_Finite__Set_Osetprod(X1,X2,X3,X4) = c_HOL_Ozero__class_Ozero(X4)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2))
| hAPP(X1,X5) != c_HOL_Ozero__class_Ozero(X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| ~ class_Ring__and__Field_Ono__zero__divisors(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4225]) ).
cnf(c_0_4225_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2))
| ~ c_Finite__Set_Ofinite(X2,X3)
| c_Finite__Set_Osetprod(X1,X2,X3,X4) = c_HOL_Ozero__class_Ozero(X4)
| hAPP(X1,X5) != c_HOL_Ozero__class_Ozero(X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| ~ class_Ring__and__Field_Ono__zero__divisors(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4225]) ).
cnf(c_0_4225_3,axiom,
( hAPP(X1,X5) != c_HOL_Ozero__class_Ozero(X4)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2))
| ~ c_Finite__Set_Ofinite(X2,X3)
| c_Finite__Set_Osetprod(X1,X2,X3,X4) = c_HOL_Ozero__class_Ozero(X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| ~ class_Ring__and__Field_Ono__zero__divisors(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4225]) ).
cnf(c_0_4225_4,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| hAPP(X1,X5) != c_HOL_Ozero__class_Ozero(X4)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2))
| ~ c_Finite__Set_Ofinite(X2,X3)
| c_Finite__Set_Osetprod(X1,X2,X3,X4) = c_HOL_Ozero__class_Ozero(X4)
| ~ class_Ring__and__Field_Ono__zero__divisors(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4225]) ).
cnf(c_0_4225_5,axiom,
( ~ class_Ring__and__Field_Ono__zero__divisors(X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| hAPP(X1,X5) != c_HOL_Ozero__class_Ozero(X4)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2))
| ~ c_Finite__Set_Ofinite(X2,X3)
| c_Finite__Set_Osetprod(X1,X2,X3,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4225]) ).
cnf(c_0_4226_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4226]) ).
cnf(c_0_4226_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4226]) ).
cnf(c_0_4227_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4227]) ).
cnf(c_0_4227_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_4227]) ).
cnf(c_0_4228_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4228]) ).
cnf(c_0_4228_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_4228]) ).
cnf(c_0_4229_0,axiom,
( c_Finite__Set_Osetprod(X1,X2,X3,X4) = c_HOL_Ozero__class_Ozero(X4)
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2))
| hAPP(X1,X5) != c_HOL_Ozero__class_Ozero(X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4229]) ).
cnf(c_0_4229_1,axiom,
( ~ c_Finite__Set_Ofinite(X2,X3)
| c_Finite__Set_Osetprod(X1,X2,X3,X4) = c_HOL_Ozero__class_Ozero(X4)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2))
| hAPP(X1,X5) != c_HOL_Ozero__class_Ozero(X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4229]) ).
cnf(c_0_4229_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2))
| ~ c_Finite__Set_Ofinite(X2,X3)
| c_Finite__Set_Osetprod(X1,X2,X3,X4) = c_HOL_Ozero__class_Ozero(X4)
| hAPP(X1,X5) != c_HOL_Ozero__class_Ozero(X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4229]) ).
cnf(c_0_4229_3,axiom,
( hAPP(X1,X5) != c_HOL_Ozero__class_Ozero(X4)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2))
| ~ c_Finite__Set_Ofinite(X2,X3)
| c_Finite__Set_Osetprod(X1,X2,X3,X4) = c_HOL_Ozero__class_Ozero(X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4229]) ).
cnf(c_0_4229_4,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X4)
| hAPP(X1,X5) != c_HOL_Ozero__class_Ozero(X4)
| ~ hBOOL(hAPP(hAPP(c_in(X3),X5),X2))
| ~ c_Finite__Set_Ofinite(X2,X3)
| c_Finite__Set_Osetprod(X1,X2,X3,X4) = c_HOL_Ozero__class_Ozero(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4229]) ).
cnf(c_0_4230_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X2),X2),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4230]) ).
cnf(c_0_4230_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X2),X2),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4230]) ).
cnf(c_0_4230_2,axiom,
( hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X2),X2),X1))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4230]) ).
cnf(c_0_4230_3,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X2),X2),X1))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_OrderedGroup_Ocomm__monoid__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4230]) ).
cnf(c_0_4230_4,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X2),X2),X1))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4230]) ).
cnf(c_0_4231_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Oab__semigroup__mult(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4231]) ).
cnf(c_0_4231_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Oab__semigroup__mult(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4231]) ).
cnf(c_0_4231_2,axiom,
( hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),X1))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Oab__semigroup__mult(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4231]) ).
cnf(c_0_4231_3,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),X1))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_OrderedGroup_Oab__semigroup__mult(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4231]) ).
cnf(c_0_4231_4,axiom,
( ~ class_OrderedGroup_Oab__semigroup__mult(X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),X1))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4231]) ).
cnf(c_0_4232_0,axiom,
( hAPP(hAPP(X3,X5),X6) = hAPP(hAPP(X3,X6),X5)
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4232]) ).
cnf(c_0_4232_1,axiom,
( ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hAPP(hAPP(X3,X5),X6) = hAPP(hAPP(X3,X6),X5) ),
inference(literals_permutation,[status(thm)],[c_0_4232]) ).
cnf(c_0_4233_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1)),X3))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4233]) ).
cnf(c_0_4233_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4233]) ).
cnf(c_0_4233_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1)),X3))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4233]) ).
cnf(c_0_4233_3,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4233]) ).
cnf(c_0_4234_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(X3,X2,X1) != c_HOL_Ominus__class_Ominus(X5,X4,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4234]) ).
cnf(c_0_4234_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| c_HOL_Ominus__class_Ominus(X3,X2,X1) != c_HOL_Ominus__class_Ominus(X5,X4,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4234]) ).
cnf(c_0_4234_2,axiom,
( c_HOL_Ominus__class_Ominus(X3,X2,X1) != c_HOL_Ominus__class_Ominus(X5,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4234]) ).
cnf(c_0_4234_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X3,X2,X1) != c_HOL_Ominus__class_Ominus(X5,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_4234]) ).
cnf(c_0_4235_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(X5,X4,X1) != c_HOL_Ominus__class_Ominus(X3,X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4235]) ).
cnf(c_0_4235_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| c_HOL_Ominus__class_Ominus(X5,X4,X1) != c_HOL_Ominus__class_Ominus(X3,X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4235]) ).
cnf(c_0_4235_2,axiom,
( c_HOL_Ominus__class_Ominus(X5,X4,X1) != c_HOL_Ominus__class_Ominus(X3,X2,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4235]) ).
cnf(c_0_4235_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X5,X4,X1) != c_HOL_Ominus__class_Ominus(X3,X2,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_4235]) ).
cnf(c_0_4236_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4236]) ).
cnf(c_0_4236_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4236]) ).
cnf(c_0_4236_2,axiom,
( c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4236]) ).
cnf(c_0_4236_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_4236]) ).
cnf(c_0_4237_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(X4,X5,X1) != c_HOL_Ominus__class_Ominus(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4237]) ).
cnf(c_0_4237_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| c_HOL_Ominus__class_Ominus(X4,X5,X1) != c_HOL_Ominus__class_Ominus(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4237]) ).
cnf(c_0_4237_2,axiom,
( c_HOL_Ominus__class_Ominus(X4,X5,X1) != c_HOL_Ominus__class_Ominus(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4237]) ).
cnf(c_0_4237_3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X4,X5,X1) != c_HOL_Ominus__class_Ominus(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_4237]) ).
cnf(c_0_4238_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4238]) ).
cnf(c_0_4238_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4238]) ).
cnf(c_0_4238_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4238]) ).
cnf(c_0_4238_3,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4238]) ).
cnf(c_0_4239_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4239]) ).
cnf(c_0_4239_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4239]) ).
cnf(c_0_4239_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4239]) ).
cnf(c_0_4239_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4239]) ).
cnf(c_0_4240_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4240]) ).
cnf(c_0_4240_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4240]) ).
cnf(c_0_4240_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4240]) ).
cnf(c_0_4240_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4240]) ).
cnf(c_0_4241_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4241]) ).
cnf(c_0_4241_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4241]) ).
cnf(c_0_4241_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4241]) ).
cnf(c_0_4241_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4241]) ).
cnf(c_0_4242_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4242]) ).
cnf(c_0_4242_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4242]) ).
cnf(c_0_4242_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4242]) ).
cnf(c_0_4242_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4242]) ).
cnf(c_0_4243_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4243]) ).
cnf(c_0_4243_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4243]) ).
cnf(c_0_4243_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4243]) ).
cnf(c_0_4243_3,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4243]) ).
cnf(c_0_4244_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4244]) ).
cnf(c_0_4244_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4244]) ).
cnf(c_0_4244_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4244]) ).
cnf(c_0_4244_3,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4244]) ).
cnf(c_0_4245_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4245]) ).
cnf(c_0_4245_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4245]) ).
cnf(c_0_4245_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4245]) ).
cnf(c_0_4245_3,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4245]) ).
cnf(c_0_4246_0,axiom,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),X4),X3))
| hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = hAPP(hAPP(X1,X4),hAPP(c_Finite__Set_Ofold1(X1,X2),X3))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4246]) ).
cnf(c_0_4246_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),X4),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = hAPP(hAPP(X1,X4),hAPP(c_Finite__Set_Ofold1(X1,X2),X3))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4246]) ).
cnf(c_0_4246_2,axiom,
( hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = hAPP(hAPP(X1,X4),hAPP(c_Finite__Set_Ofold1(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_in(X2),X4),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4246]) ).
cnf(c_0_4246_3,axiom,
( ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = hAPP(hAPP(X1,X4),hAPP(c_Finite__Set_Ofold1(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_in(X2),X4),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4246]) ).
cnf(c_0_4246_4,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = hAPP(hAPP(X1,X4),hAPP(c_Finite__Set_Ofold1(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_in(X2),X4),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4246]) ).
cnf(c_0_4247_0,axiom,
( hAPP(hAPP(X3,X5),X5) = X5
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4247]) ).
cnf(c_0_4247_1,axiom,
( ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| hAPP(hAPP(X3,X5),X5) = X5 ),
inference(literals_permutation,[status(thm)],[c_0_4247]) ).
cnf(c_0_4248_0,axiom,
( hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,X1)),X2),X3),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(X2,v_x)),hAPP(X3,v_x))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4248]) ).
cnf(c_0_4248_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,X1)),X2),X3),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(X2,v_x)),hAPP(X3,v_x)) ),
inference(literals_permutation,[status(thm)],[c_0_4248]) ).
cnf(c_0_4249_0,axiom,
( hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,X1)),X2),X3),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(X2,v_x)),hAPP(X3,v_x))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4249]) ).
cnf(c_0_4249_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,X1)),X2),X3),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(X2,v_x)),hAPP(X3,v_x)) ),
inference(literals_permutation,[status(thm)],[c_0_4249]) ).
cnf(c_0_4250_0,axiom,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X1),X2),X4),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_4250]) ).
cnf(c_0_4250_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X1),X2),X4),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_4250]) ).
cnf(c_0_4251_0,axiom,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_SetInterval_Oord__class_OlessThan(X2,X1),tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4251]) ).
cnf(c_0_4251_1,axiom,
( ~ class_Orderings_Oorder(X1)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_SetInterval_Oord__class_OlessThan(X2,X1),tc_fun(X1,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) ),
inference(literals_permutation,[status(thm)],[c_0_4251]) ).
cnf(c_0_4252_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4252]) ).
cnf(c_0_4252_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4252]) ).
cnf(c_0_4253_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4253]) ).
cnf(c_0_4253_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4253]) ).
cnf(c_0_4254_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4254]) ).
cnf(c_0_4254_1,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4254]) ).
cnf(c_0_4255_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4255]) ).
cnf(c_0_4255_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4255]) ).
cnf(c_0_4256_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4256]) ).
cnf(c_0_4256_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4256]) ).
cnf(c_0_4257_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4257]) ).
cnf(c_0_4257_1,axiom,
( ~ class_OrderedGroup_Oab__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4257]) ).
cnf(c_0_4258_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4258]) ).
cnf(c_0_4258_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4258]) ).
cnf(c_0_4259_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4259]) ).
cnf(c_0_4259_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4259]) ).
cnf(c_0_4260_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4260]) ).
cnf(c_0_4260_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4260]) ).
cnf(c_0_4261_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4261]) ).
cnf(c_0_4261_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4261]) ).
cnf(c_0_4262_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4262]) ).
cnf(c_0_4262_1,axiom,
( ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4262]) ).
cnf(c_0_4263_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4263]) ).
cnf(c_0_4263_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4263]) ).
cnf(c_0_4264_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4264]) ).
cnf(c_0_4264_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4264]) ).
cnf(c_0_4265_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4265]) ).
cnf(c_0_4265_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4265]) ).
cnf(c_0_4266_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4266]) ).
cnf(c_0_4266_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4266]) ).
cnf(c_0_4267_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4267]) ).
cnf(c_0_4267_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4267]) ).
cnf(c_0_4268_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4268]) ).
cnf(c_0_4268_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4268]) ).
cnf(c_0_4268_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4268]) ).
cnf(c_0_4269_0,axiom,
( c_OrderedGroup_Oab__semigroup__idem__mult(X3,X4)
| ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4269]) ).
cnf(c_0_4269_1,axiom,
( ~ c_Lattices_Olower__semilattice(X1,X2,X3,X4)
| c_OrderedGroup_Oab__semigroup__idem__mult(X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4269]) ).
cnf(c_0_4270_0,axiom,
( X2 = X4
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4270]) ).
cnf(c_0_4270_1,axiom,
( hBOOL(hAPP(X3,X4))
| X2 = X4
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4270]) ).
cnf(c_0_4270_2,axiom,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4))
| hBOOL(hAPP(X3,X4))
| X2 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_4270]) ).
cnf(c_0_4271_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4271]) ).
cnf(c_0_4271_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4271]) ).
cnf(c_0_4271_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4271]) ).
cnf(c_0_4271_3,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4271]) ).
cnf(c_0_4272_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_Complete__Lattice_OInf__class_OInf(X3,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4272]) ).
cnf(c_0_4272_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_Complete__Lattice_OInf__class_OInf(X3,X1)),X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4272]) ).
cnf(c_0_4272_2,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_Complete__Lattice_OInf__class_OInf(X3,X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4272]) ).
cnf(c_0_4273_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X4)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4273]) ).
cnf(c_0_4273_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = X4
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4273]) ).
cnf(c_0_4273_2,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X3)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X5),X4)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = X4 ),
inference(literals_permutation,[status(thm)],[c_0_4273]) ).
cnf(c_0_4274_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X2),X3),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1)))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4274]) ).
cnf(c_0_4274_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),X3),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4274]) ).
cnf(c_0_4274_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),X3),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1)))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4274]) ).
cnf(c_0_4274_3,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_lessequals(X2),X3),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1))) ),
inference(literals_permutation,[status(thm)],[c_0_4274]) ).
cnf(c_0_4275_0,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| hAPP(hAPP(c_Set_Oinsert(X3),X4),X1) != hAPP(hAPP(c_Set_Oinsert(X3),X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4275]) ).
cnf(c_0_4275_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| X1 = X2
| hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| hAPP(hAPP(c_Set_Oinsert(X3),X4),X1) != hAPP(hAPP(c_Set_Oinsert(X3),X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4275]) ).
cnf(c_0_4275_2,axiom,
( hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| hBOOL(hAPP(hAPP(c_in(X3),X4),X1))
| X1 = X2
| hAPP(hAPP(c_Set_Oinsert(X3),X4),X1) != hAPP(hAPP(c_Set_Oinsert(X3),X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4275]) ).
cnf(c_0_4275_3,axiom,
( hAPP(hAPP(c_Set_Oinsert(X3),X4),X1) != hAPP(hAPP(c_Set_Oinsert(X3),X4),X2)
| 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_4275]) ).
cnf(c_0_4276_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_4276]) ).
cnf(c_0_4276_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_4276]) ).
cnf(c_0_4277_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),X4),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4277]) ).
cnf(c_0_4277_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),X3),X4),X2)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4277]) ).
cnf(c_0_4278_0,axiom,
( c_Finite__Set_Osetsum(c_COMBK(c_HOL_Ozero__class_Ozero(X1),X1,X2),X3,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4278]) ).
cnf(c_0_4278_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_Finite__Set_Osetsum(c_COMBK(c_HOL_Ozero__class_Ozero(X1),X1,X2),X3,X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4278]) ).
cnf(c_0_4279_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Map_Odom(X3,X1,X4)))
| hAPP(X3,X2) != hAPP(c_Option_Ooption_OSome(X4),X5) ),
inference(literals_permutation,[status(thm)],[c_0_4279]) ).
cnf(c_0_4279_1,axiom,
( hAPP(X3,X2) != hAPP(c_Option_Ooption_OSome(X4),X5)
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_Map_Odom(X3,X1,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_4279]) ).
cnf(c_0_4280_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4280]) ).
cnf(c_0_4280_1,axiom,
( hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),X1))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4280]) ).
cnf(c_0_4280_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),X1))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4280]) ).
cnf(c_0_4280_3,axiom,
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X2),X2),X1))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4280]) ).
cnf(c_0_4281_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord__class_OlessThan(X3,X1)))
| ~ class_HOL_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4281]) ).
cnf(c_0_4281_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord__class_OlessThan(X3,X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_HOL_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4281]) ).
cnf(c_0_4281_2,axiom,
( ~ class_HOL_Oord(X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord__class_OlessThan(X3,X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4281]) ).
cnf(c_0_4282_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_4282]) ).
cnf(c_0_4282_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_4282]) ).
cnf(c_0_4283_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = X1
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4283]) ).
cnf(c_0_4283_1,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_4283]) ).
cnf(c_0_4284_0,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4284]) ).
cnf(c_0_4284_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4284]) ).
cnf(c_0_4284_2,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4284]) ).
cnf(c_0_4285_0,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4285]) ).
cnf(c_0_4285_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4285]) ).
cnf(c_0_4285_2,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4285]) ).
cnf(c_0_4286_0,axiom,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ hBOOL(hAPP(hAPP(X2,X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4286]) ).
cnf(c_0_4286_1,axiom,
( ~ hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X2,X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4286]) ).
cnf(c_0_4286_2,axiom,
( ~ hBOOL(hAPP(hAPP(X2,X5),X4))
| ~ hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4286]) ).
cnf(c_0_4287_0,axiom,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X5))
| ~ hBOOL(hAPP(hAPP(X2,X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4287]) ).
cnf(c_0_4287_1,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X2,X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4287]) ).
cnf(c_0_4287_2,axiom,
( ~ hBOOL(hAPP(hAPP(X2,X5),X4))
| ~ hBOOL(hAPP(hAPP(X1,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4287]) ).
cnf(c_0_4288_0,axiom,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ hBOOL(hAPP(hAPP(X1,X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4288]) ).
cnf(c_0_4288_1,axiom,
( ~ hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X5),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4288]) ).
cnf(c_0_4288_2,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4288]) ).
cnf(c_0_4289_0,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X2))
| ~ c_Orderings_Olinorder(X3,X1,X4)
| ~ hBOOL(hAPP(hAPP(X3,X2),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4289]) ).
cnf(c_0_4289_1,axiom,
( ~ c_Orderings_Olinorder(X3,X1,X4)
| ~ hBOOL(hAPP(hAPP(X1,X2),X2))
| ~ hBOOL(hAPP(hAPP(X3,X2),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4289]) ).
cnf(c_0_4289_2,axiom,
( ~ hBOOL(hAPP(hAPP(X3,X2),X2))
| ~ c_Orderings_Olinorder(X3,X1,X4)
| ~ hBOOL(hAPP(hAPP(X1,X2),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4289]) ).
cnf(c_0_4290_0,axiom,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4290]) ).
cnf(c_0_4290_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4290]) ).
cnf(c_0_4290_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| X2 = X3
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4290]) ).
cnf(c_0_4290_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_4290]) ).
cnf(c_0_4291_0,axiom,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4291]) ).
cnf(c_0_4291_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4291]) ).
cnf(c_0_4291_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| X2 = X3
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4291]) ).
cnf(c_0_4291_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_4291]) ).
cnf(c_0_4292_0,axiom,
( X3 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4292]) ).
cnf(c_0_4292_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| X3 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4292]) ).
cnf(c_0_4292_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| X3 = X2
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4292]) ).
cnf(c_0_4292_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| X3 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4292]) ).
cnf(c_0_4293_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4293]) ).
cnf(c_0_4293_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4293]) ).
cnf(c_0_4293_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4293]) ).
cnf(c_0_4294_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4294]) ).
cnf(c_0_4294_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4294]) ).
cnf(c_0_4294_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4294]) ).
cnf(c_0_4295_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4295]) ).
cnf(c_0_4295_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4295]) ).
cnf(c_0_4295_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4295]) ).
cnf(c_0_4296_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4296]) ).
cnf(c_0_4296_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4296]) ).
cnf(c_0_4296_2,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4296]) ).
cnf(c_0_4297_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4297]) ).
cnf(c_0_4297_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_HOL_Ozero__class_Ozero(X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_4297]) ).
cnf(c_0_4298_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4298]) ).
cnf(c_0_4298_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4298]) ).
cnf(c_0_4298_2,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4298]) ).
cnf(c_0_4299_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4299]) ).
cnf(c_0_4299_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4299]) ).
cnf(c_0_4299_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4299]) ).
cnf(c_0_4300_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4300]) ).
cnf(c_0_4300_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4300]) ).
cnf(c_0_4300_2,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4300]) ).
cnf(c_0_4301_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4301]) ).
cnf(c_0_4301_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4301]) ).
cnf(c_0_4301_2,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4301]) ).
cnf(c_0_4302_0,axiom,
( hAPP(X1,X2) = c_Option_Ooption_ONone(X3)
| hBOOL(hAPP(hAPP(c_in(X4),X2),c_Map_Odom(X1,X4,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_4302]) ).
cnf(c_0_4302_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X4),X2),c_Map_Odom(X1,X4,X3)))
| hAPP(X1,X2) = c_Option_Ooption_ONone(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4302]) ).
cnf(c_0_4303_0,axiom,
( X4 = X3
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4303]) ).
cnf(c_0_4303_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
| X4 = X3
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4303]) ).
cnf(c_0_4303_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
| X4 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_4303]) ).
cnf(c_0_4304_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OlessThan(X2,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4304]) ).
cnf(c_0_4304_1,axiom,
( ~ class_Orderings_Oorder(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OlessThan(X2,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4304]) ).
cnf(c_0_4305_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X3),X4)),X5) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4305]) ).
cnf(c_0_4305_1,axiom,
( ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hAPP(hAPP(X1,hAPP(hAPP(X1,X3),X4)),X5) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_4305]) ).
cnf(c_0_4306_0,axiom,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = hAPP(hAPP(X1,X4),hAPP(c_Finite__Set_Ofold1(X1,X2),X3))
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4306]) ).
cnf(c_0_4306_1,axiom,
( hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = hAPP(hAPP(X1,X4),hAPP(c_Finite__Set_Ofold1(X1,X2),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4306]) ).
cnf(c_0_4306_2,axiom,
( ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2)
| hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = hAPP(hAPP(X1,X4),hAPP(c_Finite__Set_Ofold1(X1,X2),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4306]) ).
cnf(c_0_4306_3,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2)
| hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = hAPP(hAPP(X1,X4),hAPP(c_Finite__Set_Ofold1(X1,X2),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4306]) ).
cnf(c_0_4307_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord__class_OlessThan(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_HOL_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4307]) ).
cnf(c_0_4307_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord__class_OlessThan(X3,X1)))
| ~ class_HOL_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4307]) ).
cnf(c_0_4307_2,axiom,
( ~ class_HOL_Oord(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord__class_OlessThan(X3,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_4307]) ).
cnf(c_0_4308_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Complete__Lattice_OSup__class_OSup(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4308]) ).
cnf(c_0_4308_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Complete__Lattice_OSup__class_OSup(X3,X1)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4308]) ).
cnf(c_0_4308_2,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Complete__Lattice_OSup__class_OSup(X3,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_4308]) ).
cnf(c_0_4309_0,axiom,
( hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))) = X3
| ~ c_Orderings_Olinorder(X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_4309]) ).
cnf(c_0_4309_1,axiom,
( ~ c_Orderings_Olinorder(X4,X5,X6)
| hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_4309]) ).
cnf(c_0_4310_0,axiom,
( X1 = X2
| hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) != hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) ),
inference(literals_permutation,[status(thm)],[c_0_4310]) ).
cnf(c_0_4310_1,axiom,
( hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) != hAPP(hAPP(c_Set_Oinsert(X3),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4310]) ).
cnf(c_0_4311_0,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X1),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4311]) ).
cnf(c_0_4311_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4311]) ).
cnf(c_0_4312_0,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4312]) ).
cnf(c_0_4312_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4312]) ).
cnf(c_0_4313_0,axiom,
( hAPP(hAPP(X1,X4),hAPP(hAPP(X1,X5),X6)) = hAPP(hAPP(X1,X5),hAPP(hAPP(X1,X4),X6))
| ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4313]) ).
cnf(c_0_4313_1,axiom,
( ~ c_Finite__Set_Ofun__left__comm(X1,X2,X3)
| hAPP(hAPP(X1,X4),hAPP(hAPP(X1,X5),X6)) = hAPP(hAPP(X1,X5),hAPP(hAPP(X1,X4),X6)) ),
inference(literals_permutation,[status(thm)],[c_0_4313]) ).
cnf(c_0_4314_0,axiom,
( c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2) = c_Finite__Set_Ocard(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4314]) ).
cnf(c_0_4314_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2) = c_Finite__Set_Ocard(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4314]) ).
cnf(c_0_4314_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2) = c_Finite__Set_Ocard(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4314]) ).
cnf(c_0_4315_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2)))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4315]) ).
cnf(c_0_4315_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_4315]) ).
cnf(c_0_4316_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4316]) ).
cnf(c_0_4316_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_4316]) ).
cnf(c_0_4317_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4317]) ).
cnf(c_0_4317_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_4317]) ).
cnf(c_0_4318_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4318]) ).
cnf(c_0_4318_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_4318]) ).
cnf(c_0_4319_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4319]) ).
cnf(c_0_4319_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2))) ),
inference(literals_permutation,[status(thm)],[c_0_4319]) ).
cnf(c_0_4320_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4320]) ).
cnf(c_0_4320_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3))) ),
inference(literals_permutation,[status(thm)],[c_0_4320]) ).
cnf(c_0_4321_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1)),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4321]) ).
cnf(c_0_4321_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1)),X1))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4321]) ).
cnf(c_0_4321_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_in(X2),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1)),X1))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4321]) ).
cnf(c_0_4321_3,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_in(X2),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1)),X1))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4321]) ).
cnf(c_0_4322_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1)),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4322]) ).
cnf(c_0_4322_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1)),X1))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4322]) ).
cnf(c_0_4322_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_in(X2),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1)),X1))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4322]) ).
cnf(c_0_4322_3,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| hBOOL(hAPP(hAPP(c_in(X2),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1)),X1))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4322]) ).
cnf(c_0_4323_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4323]) ).
cnf(c_0_4323_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_4323]) ).
cnf(c_0_4324_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4324]) ).
cnf(c_0_4324_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4324]) ).
cnf(c_0_4325_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4325]) ).
cnf(c_0_4325_1,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4325]) ).
cnf(c_0_4326_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4326]) ).
cnf(c_0_4326_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4326]) ).
cnf(c_0_4327_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4327]) ).
cnf(c_0_4327_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4327]) ).
cnf(c_0_4328_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4328]) ).
cnf(c_0_4328_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4328]) ).
cnf(c_0_4329_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4329]) ).
cnf(c_0_4329_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4329]) ).
cnf(c_0_4330_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4330]) ).
cnf(c_0_4330_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4330]) ).
cnf(c_0_4331_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4331]) ).
cnf(c_0_4331_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4331]) ).
cnf(c_0_4332_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4332]) ).
cnf(c_0_4332_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4332]) ).
cnf(c_0_4333_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4333]) ).
cnf(c_0_4333_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4333]) ).
cnf(c_0_4334_0,axiom,
( c_Finite__Set_Osetsum(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3) = c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4334]) ).
cnf(c_0_4334_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_Finite__Set_Osetsum(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3) = c_HOL_Ozero__class_Ozero(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4334]) ).
cnf(c_0_4335_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4335]) ).
cnf(c_0_4335_1,axiom,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4335]) ).
cnf(c_0_4335_2,axiom,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4335]) ).
cnf(c_0_4336_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4336]) ).
cnf(c_0_4336_1,axiom,
( c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4336]) ).
cnf(c_0_4336_2,axiom,
( ~ class_Orderings_Oorder(X1)
| c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4336]) ).
cnf(c_0_4337_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),c_Suc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_4337]) ).
cnf(c_0_4337_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),c_Suc(X2)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4337]) ).
cnf(c_0_4338_0,axiom,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| X4 = X5
| ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_4338]) ).
cnf(c_0_4338_1,axiom,
( X4 = X5
| hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_4338]) ).
cnf(c_0_4338_2,axiom,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| X4 = X5
| hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_4338]) ).
cnf(c_0_4338_3,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3)
| X4 = X5
| hBOOL(hAPP(hAPP(X2,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_4338]) ).
cnf(c_0_4339_0,axiom,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| X4 = X5
| ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_4339]) ).
cnf(c_0_4339_1,axiom,
( X4 = X5
| hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_4339]) ).
cnf(c_0_4339_2,axiom,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| X4 = X5
| hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ hBOOL(hAPP(hAPP(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_4339]) ).
cnf(c_0_4339_3,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3)
| X4 = X5
| hBOOL(hAPP(hAPP(X2,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_4339]) ).
cnf(c_0_4340_0,axiom,
( c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4340]) ).
cnf(c_0_4340_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4340]) ).
cnf(c_0_4340_2,axiom,
( ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4340]) ).
cnf(c_0_4341_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X1) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4341]) ).
cnf(c_0_4341_1,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X1) != 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_4341]) ).
cnf(c_0_4342_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4342]) ).
cnf(c_0_4342_1,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3) != 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_4342]) ).
cnf(c_0_4343_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),hAPP(c_Finite__Set_Olattice__class_OInf__fin(X2),X1)) = X3
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Lattices_Olattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4343]) ).
cnf(c_0_4343_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),hAPP(c_Finite__Set_Olattice__class_OInf__fin(X2),X1)) = X3
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ class_Lattices_Olattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4343]) ).
cnf(c_0_4343_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),hAPP(c_Finite__Set_Olattice__class_OInf__fin(X2),X1)) = X3
| ~ class_Lattices_Olattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4343]) ).
cnf(c_0_4343_3,axiom,
( ~ class_Lattices_Olattice(X2)
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),hAPP(c_Finite__Set_Olattice__class_OInf__fin(X2),X1)) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_4343]) ).
cnf(c_0_4344_0,axiom,
( X3 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4344]) ).
cnf(c_0_4344_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X3 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4344]) ).
cnf(c_0_4344_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X3 = X2
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4344]) ).
cnf(c_0_4344_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X3 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4344]) ).
cnf(c_0_4345_0,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4345]) ).
cnf(c_0_4345_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X2),X1))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4345]) ).
cnf(c_0_4345_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X2),X1))
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4345]) ).
cnf(c_0_4345_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X2),X1))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4345]) ).
cnf(c_0_4346_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4346]) ).
cnf(c_0_4346_1,axiom,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4346]) ).
cnf(c_0_4346_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4346]) ).
cnf(c_0_4346_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4346]) ).
cnf(c_0_4347_0,axiom,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4347]) ).
cnf(c_0_4347_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4347]) ).
cnf(c_0_4347_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4347]) ).
cnf(c_0_4347_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_4347]) ).
cnf(c_0_4348_0,axiom,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4348]) ).
cnf(c_0_4348_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4348]) ).
cnf(c_0_4348_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4348]) ).
cnf(c_0_4348_3,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_4348]) ).
cnf(c_0_4349_0,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4349]) ).
cnf(c_0_4349_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4349]) ).
cnf(c_0_4349_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X1),X2))
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4349]) ).
cnf(c_0_4349_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X3),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X1),X2))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4349]) ).
cnf(c_0_4350_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4350]) ).
cnf(c_0_4350_1,axiom,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4350]) ).
cnf(c_0_4350_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4350]) ).
cnf(c_0_4350_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4350]) ).
cnf(c_0_4351_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4351]) ).
cnf(c_0_4351_1,axiom,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4351]) ).
cnf(c_0_4351_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4351]) ).
cnf(c_0_4351_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4351]) ).
cnf(c_0_4352_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X4),X1),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4352]) ).
cnf(c_0_4352_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X4),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4352]) ).
cnf(c_0_4353_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4353]) ).
cnf(c_0_4353_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4353]) ).
cnf(c_0_4353_2,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4353]) ).
cnf(c_0_4354_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4354]) ).
cnf(c_0_4354_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4354]) ).
cnf(c_0_4354_2,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4354]) ).
cnf(c_0_4355_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4355]) ).
cnf(c_0_4355_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4355]) ).
cnf(c_0_4356_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),c_Suc(X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4356]) ).
cnf(c_0_4356_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),c_Suc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_4356]) ).
cnf(c_0_4357_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),c_Suc(X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4357]) ).
cnf(c_0_4357_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),c_Suc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_4357]) ).
cnf(c_0_4358_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2) = c_Suc(c_Finite__Set_Ocard(X1,X2))
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4358]) ).
cnf(c_0_4358_1,axiom,
( c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2) = c_Suc(c_Finite__Set_Ocard(X1,X2))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4358]) ).
cnf(c_0_4358_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2) = c_Suc(c_Finite__Set_Ocard(X1,X2))
| hBOOL(hAPP(hAPP(c_in(X2),X3),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4358]) ).
cnf(c_0_4359_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X3) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4359]) ).
cnf(c_0_4359_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ominus__class_Ominus(X2,X3,X1)),X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4359]) ).
cnf(c_0_4360_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1))
| hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4360]) ).
cnf(c_0_4360_1,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1))
| hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4360]) ).
cnf(c_0_4360_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1))
| X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| hBOOL(hAPP(hAPP(X3,X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4360]) ).
cnf(c_0_4360_3,axiom,
( hBOOL(hAPP(hAPP(X3,X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1))
| X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4360]) ).
cnf(c_0_4361_0,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Osetsum(X3,X1,X2,X4) = c_HOL_Ozero__class_Ozero(X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4361]) ).
cnf(c_0_4361_1,axiom,
( c_Finite__Set_Osetsum(X3,X1,X2,X4) = c_HOL_Ozero__class_Ozero(X4)
| c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4361]) ).
cnf(c_0_4361_2,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_Finite__Set_Osetsum(X3,X1,X2,X4) = c_HOL_Ozero__class_Ozero(X4)
| c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4361]) ).
cnf(c_0_4362_0,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Osetsum(X3,X1,X2,X4) = c_HOL_Ozero__class_Ozero(X4)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4362]) ).
cnf(c_0_4362_1,axiom,
( c_Finite__Set_Osetsum(X3,X1,X2,X4) = c_HOL_Ozero__class_Ozero(X4)
| c_Finite__Set_Ofinite(X1,X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X4) ),
inference(literals_permutation,[status(thm)],[c_0_4362]) ).
cnf(c_0_4362_2,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X4)
| c_Finite__Set_Osetsum(X3,X1,X2,X4) = c_HOL_Ozero__class_Ozero(X4)
| c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4362]) ).
cnf(c_0_4363_0,axiom,
( c_Suc(X1) = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4363]) ).
cnf(c_0_4363_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),X2))
| c_Suc(X1) = X2
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4363]) ).
cnf(c_0_4363_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),X2))
| c_Suc(X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4363]) ).
cnf(c_0_4364_0,axiom,
( c_HOL_Ominus__class_Ominus(hAPP(X1,v_x),hAPP(X2,v_x),X3) = hAPP(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(t_a,X3)),v_x)
| ~ class_HOL_Ominus(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4364]) ).
cnf(c_0_4364_1,axiom,
( ~ class_HOL_Ominus(X3)
| c_HOL_Ominus__class_Ominus(hAPP(X1,v_x),hAPP(X2,v_x),X3) = hAPP(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(t_a,X3)),v_x) ),
inference(literals_permutation,[status(thm)],[c_0_4364]) ).
cnf(c_0_4365_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X2),X3),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1)) = hAPP(c_Finite__Set_Olinorder__class_OMin(X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4365]) ).
cnf(c_0_4365_1,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X2),X3),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1)) = hAPP(c_Finite__Set_Olinorder__class_OMin(X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4365]) ).
cnf(c_0_4365_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X2),X3),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1)) = hAPP(c_Finite__Set_Olinorder__class_OMin(X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4365]) ).
cnf(c_0_4365_3,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X2),X3),hAPP(c_Finite__Set_Olinorder__class_OMin(X2),X1)) = hAPP(c_Finite__Set_Olinorder__class_OMin(X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4365]) ).
cnf(c_0_4366_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),X3),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1)) = hAPP(c_Finite__Set_Olinorder__class_OMax(X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4366]) ).
cnf(c_0_4366_1,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),X3),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1)) = hAPP(c_Finite__Set_Olinorder__class_OMax(X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4366]) ).
cnf(c_0_4366_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),X3),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1)) = hAPP(c_Finite__Set_Olinorder__class_OMax(X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_Orderings_Olinorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4366]) ).
cnf(c_0_4366_3,axiom,
( ~ class_Orderings_Olinorder(X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),X3),hAPP(c_Finite__Set_Olinorder__class_OMax(X2),X1)) = hAPP(c_Finite__Set_Olinorder__class_OMax(X2),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4366]) ).
cnf(c_0_4367_0,axiom,
( X3 = hAPP(c_Option_Ooption_OSome(X1),X2)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Option_Oset(X3,X1))) ),
inference(literals_permutation,[status(thm)],[c_0_4367]) ).
cnf(c_0_4367_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Option_Oset(X3,X1)))
| X3 = hAPP(c_Option_Ooption_OSome(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4367]) ).
cnf(c_0_4368_0,axiom,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Map_Odom(X3,X1,X4)) = c_Map_Odom(X3,X1,X4)
| hAPP(X3,X2) != hAPP(c_Option_Ooption_OSome(X4),X5) ),
inference(literals_permutation,[status(thm)],[c_0_4368]) ).
cnf(c_0_4368_1,axiom,
( hAPP(X3,X2) != hAPP(c_Option_Ooption_OSome(X4),X5)
| hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Map_Odom(X3,X1,X4)) = c_Map_Odom(X3,X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4368]) ).
cnf(c_0_4369_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_4369]) ).
cnf(c_0_4369_1,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_4369]) ).
cnf(c_0_4369_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2)))
| X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4369]) ).
cnf(c_0_4370_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| X2 = X1
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_4370]) ).
cnf(c_0_4370_1,axiom,
( X2 = X1
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_4370]) ).
cnf(c_0_4370_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2)))
| X2 = X1
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4370]) ).
cnf(c_0_4371_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_4371]) ).
cnf(c_0_4371_1,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_4371]) ).
cnf(c_0_4371_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2)))
| X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4371]) ).
cnf(c_0_4372_0,axiom,
( hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5)) = hAPP(hAPP(X1,X4),hAPP(hAPP(X1,X3),X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4372]) ).
cnf(c_0_4372_1,axiom,
( ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X4),X5)) = hAPP(hAPP(X1,X4),hAPP(hAPP(X1,X3),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_4372]) ).
cnf(c_0_4373_0,axiom,
( c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4373]) ).
cnf(c_0_4373_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4373]) ).
cnf(c_0_4373_2,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4373]) ).
cnf(c_0_4374_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4374]) ).
cnf(c_0_4374_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_4374]) ).
cnf(c_0_4375_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X3),X4),X5))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hAPP(hAPP(c_Set_Oinsert(X3),X4),X5) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4375]) ).
cnf(c_0_4375_1,axiom,
( ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hBOOL(hAPP(hAPP(c_in(X3),X4),X5))
| hAPP(hAPP(c_Set_Oinsert(X3),X4),X5) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4375]) ).
cnf(c_0_4375_2,axiom,
( hAPP(hAPP(c_Set_Oinsert(X3),X4),X5) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hBOOL(hAPP(hAPP(c_in(X3),X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_4375]) ).
cnf(c_0_4376_0,axiom,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| hBOOL(hAPP(hAPP(X2,X5),X4))
| X4 = X5
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4376]) ).
cnf(c_0_4376_1,axiom,
( hBOOL(hAPP(hAPP(X2,X5),X4))
| hBOOL(hAPP(hAPP(X2,X4),X5))
| X4 = X5
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4376]) ).
cnf(c_0_4376_2,axiom,
( X4 = X5
| hBOOL(hAPP(hAPP(X2,X5),X4))
| hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4376]) ).
cnf(c_0_4376_3,axiom,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| X4 = X5
| hBOOL(hAPP(hAPP(X2,X5),X4))
| hBOOL(hAPP(hAPP(X2,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_4376]) ).
cnf(c_0_4377_0,axiom,
( X4 = X5
| hBOOL(hAPP(hAPP(X2,X4),X5))
| hBOOL(hAPP(hAPP(X2,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4377]) ).
cnf(c_0_4377_1,axiom,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| X4 = X5
| hBOOL(hAPP(hAPP(X2,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4377]) ).
cnf(c_0_4377_2,axiom,
( hBOOL(hAPP(hAPP(X2,X5),X4))
| hBOOL(hAPP(hAPP(X2,X4),X5))
| X4 = X5
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4377]) ).
cnf(c_0_4377_3,axiom,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| hBOOL(hAPP(hAPP(X2,X5),X4))
| hBOOL(hAPP(hAPP(X2,X4),X5))
| X4 = X5 ),
inference(literals_permutation,[status(thm)],[c_0_4377]) ).
cnf(c_0_4378_0,axiom,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| X4 = X5
| hBOOL(hAPP(hAPP(X2,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4378]) ).
cnf(c_0_4378_1,axiom,
( X4 = X5
| hBOOL(hAPP(hAPP(X2,X4),X5))
| hBOOL(hAPP(hAPP(X2,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4378]) ).
cnf(c_0_4378_2,axiom,
( hBOOL(hAPP(hAPP(X2,X5),X4))
| X4 = X5
| hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4378]) ).
cnf(c_0_4378_3,axiom,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| hBOOL(hAPP(hAPP(X2,X5),X4))
| X4 = X5
| hBOOL(hAPP(hAPP(X2,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_4378]) ).
cnf(c_0_4379_0,axiom,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| hBOOL(hAPP(hAPP(X2,X5),X4))
| X5 = X4
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4379]) ).
cnf(c_0_4379_1,axiom,
( hBOOL(hAPP(hAPP(X2,X5),X4))
| hBOOL(hAPP(hAPP(X2,X4),X5))
| X5 = X4
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4379]) ).
cnf(c_0_4379_2,axiom,
( X5 = X4
| hBOOL(hAPP(hAPP(X2,X5),X4))
| hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4379]) ).
cnf(c_0_4379_3,axiom,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| X5 = X4
| hBOOL(hAPP(hAPP(X2,X5),X4))
| hBOOL(hAPP(hAPP(X2,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_4379]) ).
cnf(c_0_4380_0,axiom,
( hBOOL(hAPP(hAPP(X2,X4),X5))
| hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4380]) ).
cnf(c_0_4380_1,axiom,
( hBOOL(hAPP(hAPP(X1,X5),X4))
| hBOOL(hAPP(hAPP(X2,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4380]) ).
cnf(c_0_4380_2,axiom,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| hBOOL(hAPP(hAPP(X1,X5),X4))
| hBOOL(hAPP(hAPP(X2,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_4380]) ).
cnf(c_0_4381_0,axiom,
( hBOOL(hAPP(hAPP(X1,X4),X5))
| hBOOL(hAPP(hAPP(X1,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4381]) ).
cnf(c_0_4381_1,axiom,
( hBOOL(hAPP(hAPP(X1,X5),X4))
| hBOOL(hAPP(hAPP(X1,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4381]) ).
cnf(c_0_4381_2,axiom,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| hBOOL(hAPP(hAPP(X1,X5),X4))
| hBOOL(hAPP(hAPP(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_4381]) ).
cnf(c_0_4382_0,axiom,
( hBOOL(hAPP(hAPP(X1,X4),X5))
| hBOOL(hAPP(hAPP(X2,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4382]) ).
cnf(c_0_4382_1,axiom,
( hBOOL(hAPP(hAPP(X2,X5),X4))
| hBOOL(hAPP(hAPP(X1,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4382]) ).
cnf(c_0_4382_2,axiom,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| hBOOL(hAPP(hAPP(X2,X5),X4))
| hBOOL(hAPP(hAPP(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_4382]) ).
cnf(c_0_4383_0,axiom,
( hBOOL(hAPP(hAPP(X1,X4),X5))
| hBOOL(hAPP(hAPP(X2,X5),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4383]) ).
cnf(c_0_4383_1,axiom,
( hBOOL(hAPP(hAPP(X2,X5),X4))
| hBOOL(hAPP(hAPP(X1,X4),X5))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4383]) ).
cnf(c_0_4383_2,axiom,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| hBOOL(hAPP(hAPP(X2,X5),X4))
| hBOOL(hAPP(hAPP(X1,X4),X5)) ),
inference(literals_permutation,[status(thm)],[c_0_4383]) ).
cnf(c_0_4384_0,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X2))
| hBOOL(hAPP(hAPP(X3,X2),X2))
| ~ c_Orderings_Olinorder(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4384]) ).
cnf(c_0_4384_1,axiom,
( hBOOL(hAPP(hAPP(X3,X2),X2))
| hBOOL(hAPP(hAPP(X1,X2),X2))
| ~ c_Orderings_Olinorder(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4384]) ).
cnf(c_0_4384_2,axiom,
( ~ c_Orderings_Olinorder(X1,X3,X4)
| hBOOL(hAPP(hAPP(X3,X2),X2))
| hBOOL(hAPP(hAPP(X1,X2),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4384]) ).
cnf(c_0_4385_0,axiom,
( hAPP(c_Finite__Set_Olinorder__class_OMin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4385]) ).
cnf(c_0_4385_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| hAPP(c_Finite__Set_Olinorder__class_OMin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4385]) ).
cnf(c_0_4386_0,axiom,
( hAPP(c_Finite__Set_Olinorder__class_OMax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4386]) ).
cnf(c_0_4386_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| hAPP(c_Finite__Set_Olinorder__class_OMax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4386]) ).
cnf(c_0_4387_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4387]) ).
cnf(c_0_4387_1,axiom,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) != 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_4387]) ).
cnf(c_0_4388_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4388]) ).
cnf(c_0_4388_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) = X3
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4388]) ).
cnf(c_0_4388_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_4388]) ).
cnf(c_0_4389_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4389]) ).
cnf(c_0_4389_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2) = X3
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4389]) ).
cnf(c_0_4389_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_4389]) ).
cnf(c_0_4390_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4390]) ).
cnf(c_0_4390_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4390]) ).
cnf(c_0_4390_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4390]) ).
cnf(c_0_4391_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X2) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4391]) ).
cnf(c_0_4391_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X2) = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4391]) ).
cnf(c_0_4391_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4391]) ).
cnf(c_0_4392_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4392]) ).
cnf(c_0_4392_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2) = X3
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4392]) ).
cnf(c_0_4392_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_4392]) ).
cnf(c_0_4393_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4393]) ).
cnf(c_0_4393_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X3
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4393]) ).
cnf(c_0_4393_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_4393]) ).
cnf(c_0_4394_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4394]) ).
cnf(c_0_4394_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = X2
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4394]) ).
cnf(c_0_4394_2,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4394]) ).
cnf(c_0_4395_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4395]) ).
cnf(c_0_4395_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2) = X2
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4395]) ).
cnf(c_0_4395_2,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4395]) ).
cnf(c_0_4396_0,axiom,
( c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4396]) ).
cnf(c_0_4396_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4396]) ).
cnf(c_0_4397_0,axiom,
( c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4397]) ).
cnf(c_0_4397_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4397]) ).
cnf(c_0_4398_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X4,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4398]) ).
cnf(c_0_4398_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| c_Hoare__Mirabelle_Ohoare__derivs(X4,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4398]) ).
cnf(c_0_4398_2,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,X1,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| c_Hoare__Mirabelle_Ohoare__derivs(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4398]) ).
cnf(c_0_4399_0,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X2),X1))
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4399]) ).
cnf(c_0_4399_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X1),X2))
| X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X2),X1))
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4399]) ).
cnf(c_0_4399_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X1),X2))
| X1 = X2
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4399]) ).
cnf(c_0_4399_3,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X1),X2))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4399]) ).
cnf(c_0_4400_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| X2 = X3
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4400]) ).
cnf(c_0_4400_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4400]) ).
cnf(c_0_4400_2,axiom,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4400]) ).
cnf(c_0_4400_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4400]) ).
cnf(c_0_4401_0,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X2),X1))
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4401]) ).
cnf(c_0_4401_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X1),X2))
| X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X2),X1))
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4401]) ).
cnf(c_0_4401_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X1),X2))
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4401]) ).
cnf(c_0_4401_3,axiom,
( ~ class_Orderings_Olinorder(X3)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X3),X1),X2))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4401]) ).
cnf(c_0_4402_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4402]) ).
cnf(c_0_4402_1,axiom,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4402]) ).
cnf(c_0_4402_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4402]) ).
cnf(c_0_4402_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4402]) ).
cnf(c_0_4403_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4403]) ).
cnf(c_0_4403_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4403]) ).
cnf(c_0_4403_2,axiom,
( X3 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4403]) ).
cnf(c_0_4403_3,axiom,
( ~ class_Orderings_Olinorder(X1)
| X3 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4403]) ).
cnf(c_0_4404_0,axiom,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4404]) ).
cnf(c_0_4404_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_4404]) ).
cnf(c_0_4405_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4405]) ).
cnf(c_0_4405_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4405]) ).
cnf(c_0_4405_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4405]) ).
cnf(c_0_4406_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4406]) ).
cnf(c_0_4406_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4406]) ).
cnf(c_0_4406_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4406]) ).
cnf(c_0_4407_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4407]) ).
cnf(c_0_4407_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4407]) ).
cnf(c_0_4407_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4407]) ).
cnf(c_0_4408_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4408]) ).
cnf(c_0_4408_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4408]) ).
cnf(c_0_4408_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4408]) ).
cnf(c_0_4409_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4409]) ).
cnf(c_0_4409_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4409]) ).
cnf(c_0_4409_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4409]) ).
cnf(c_0_4410_0,axiom,
( ~ c_Orderings_Olinorder(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(X2,X4),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_4410]) ).
cnf(c_0_4410_1,axiom,
( ~ hBOOL(hAPP(hAPP(X2,X4),X4))
| ~ c_Orderings_Olinorder(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4410]) ).
cnf(c_0_4411_0,axiom,
( ~ hBOOL(hAPP(hAPP(X1,X2),X2))
| ~ c_Orderings_Olinorder(X3,X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4411]) ).
cnf(c_0_4411_1,axiom,
( ~ c_Orderings_Olinorder(X3,X1,X4)
| ~ hBOOL(hAPP(hAPP(X1,X2),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4411]) ).
cnf(c_0_4412_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4412]) ).
cnf(c_0_4412_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4412]) ).
cnf(c_0_4413_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4413]) ).
cnf(c_0_4413_1,axiom,
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4413]) ).
cnf(c_0_4414_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4414]) ).
cnf(c_0_4414_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4414]) ).
cnf(c_0_4415_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4415]) ).
cnf(c_0_4415_1,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4415]) ).
cnf(c_0_4416_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4416]) ).
cnf(c_0_4416_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4416]) ).
cnf(c_0_4417_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4417]) ).
cnf(c_0_4417_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4417]) ).
cnf(c_0_4418_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4418]) ).
cnf(c_0_4418_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4418]) ).
cnf(c_0_4419_0,axiom,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4419]) ).
cnf(c_0_4419_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4419]) ).
cnf(c_0_4419_2,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4419]) ).
cnf(c_0_4420_0,axiom,
( c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Complete__Lattice_OSup__class_OSup(X3,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4420]) ).
cnf(c_0_4420_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Complete__Lattice_OSup__class_OSup(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4420]) ).
cnf(c_0_4421_0,axiom,
( c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Complete__Lattice_OInf__class_OInf(X3,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4421]) ).
cnf(c_0_4421_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Complete__Lattice_OInf__class_OInf(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4421]) ).
cnf(c_0_4422_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4422]) ).
cnf(c_0_4422_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_4422]) ).
cnf(c_0_4423_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),c_Suc(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_4423]) ).
cnf(c_0_4423_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),c_Suc(X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4423]) ).
cnf(c_0_4424_0,axiom,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4424]) ).
cnf(c_0_4424_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| hBOOL(hAPP(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4424]) ).
cnf(c_0_4425_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) != X3
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4425]) ).
cnf(c_0_4425_1,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) != X3
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4425]) ).
cnf(c_0_4425_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) != X3
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4425]) ).
cnf(c_0_4426_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) != X2
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4426]) ).
cnf(c_0_4426_1,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) != X2
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4426]) ).
cnf(c_0_4426_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) != X2
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4426]) ).
cnf(c_0_4427_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) != X3
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4427]) ).
cnf(c_0_4427_1,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) != X3
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4427]) ).
cnf(c_0_4427_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) != X3
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4427]) ).
cnf(c_0_4428_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) != X2
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4428]) ).
cnf(c_0_4428_1,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) != X2
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4428]) ).
cnf(c_0_4428_2,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) != X2
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4428]) ).
cnf(c_0_4429_0,axiom,
( c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4429]) ).
cnf(c_0_4429_1,axiom,
( ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X1)
| c_Finite__Set_Ofinite(X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_4429]) ).
cnf(c_0_4430_0,axiom,
( X1 = c_COMBK(c_Option_Ooption_ONone(X2),tc_Option_Ooption(X2),X3)
| c_Map_Odom(X1,X3,X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4430]) ).
cnf(c_0_4430_1,axiom,
( c_Map_Odom(X1,X3,X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X1 = c_COMBK(c_Option_Ooption_ONone(X2),tc_Option_Ooption(X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4430]) ).
cnf(c_0_4431_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4431]) ).
cnf(c_0_4431_1,axiom,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4431]) ).
cnf(c_0_4431_2,axiom,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4431]) ).
cnf(c_0_4432_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4432]) ).
cnf(c_0_4432_1,axiom,
( c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4432]) ).
cnf(c_0_4432_2,axiom,
( ~ class_Orderings_Oorder(X1)
| c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4432]) ).
cnf(c_0_4433_0,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4433]) ).
cnf(c_0_4433_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4433]) ).
cnf(c_0_4433_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4433]) ).
cnf(c_0_4434_0,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4434]) ).
cnf(c_0_4434_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4434]) ).
cnf(c_0_4434_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4434]) ).
cnf(c_0_4435_0,axiom,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4435]) ).
cnf(c_0_4435_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4435]) ).
cnf(c_0_4436_0,axiom,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4436]) ).
cnf(c_0_4436_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| X1 = X2
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4436]) ).
cnf(c_0_4436_2,axiom,
( ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| X1 = X2
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4436]) ).
cnf(c_0_4436_3,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4436]) ).
cnf(c_0_4437_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_4437]) ).
cnf(c_0_4437_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_4437]) ).
cnf(c_0_4437_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_4437]) ).
cnf(c_0_4438_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_4438]) ).
cnf(c_0_4438_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_4438]) ).
cnf(c_0_4438_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_4438]) ).
cnf(c_0_4439_0,axiom,
( hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X3),X4)) = hAPP(hAPP(X1,X3),X4)
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4439]) ).
cnf(c_0_4439_1,axiom,
( ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2)
| hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X3),X4)) = hAPP(hAPP(X1,X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_4439]) ).
cnf(c_0_4440_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4440]) ).
cnf(c_0_4440_1,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4440]) ).
cnf(c_0_4441_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4441]) ).
cnf(c_0_4441_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4441]) ).
cnf(c_0_4442_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4442]) ).
cnf(c_0_4442_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4442]) ).
cnf(c_0_4443_0,axiom,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4443]) ).
cnf(c_0_4443_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| X1 = X2
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4443]) ).
cnf(c_0_4443_2,axiom,
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4443]) ).
cnf(c_0_4444_0,axiom,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4444]) ).
cnf(c_0_4444_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| X1 = X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4444]) ).
cnf(c_0_4444_2,axiom,
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X4),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4444]) ).
cnf(c_0_4445_0,axiom,
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4445]) ).
cnf(c_0_4445_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4)
| X1 = X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4445]) ).
cnf(c_0_4445_2,axiom,
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X1),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X3),X2),X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4445]) ).
cnf(c_0_4446_0,axiom,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3)) ),
inference(literals_permutation,[status(thm)],[c_0_4446]) ).
cnf(c_0_4446_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_fequal(X1),X2),X3))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_4446]) ).
cnf(c_0_4447_0,axiom,
( c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,X2) = hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4447]) ).
cnf(c_0_4447_1,axiom,
( ~ class_Orderings_Oorder(X2)
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X1,X2) = hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) ),
inference(literals_permutation,[status(thm)],[c_0_4447]) ).
cnf(c_0_4448_0,axiom,
( c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X3,X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4448]) ).
cnf(c_0_4448_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3),X3,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4448]) ).
cnf(c_0_4449_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4449]) ).
cnf(c_0_4449_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4449]) ).
cnf(c_0_4450_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4450]) ).
cnf(c_0_4450_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4450]) ).
cnf(c_0_4451_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)) = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4451]) ).
cnf(c_0_4451_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4451]) ).
cnf(c_0_4452_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)) = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4452]) ).
cnf(c_0_4452_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4452]) ).
cnf(c_0_4453_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X3),X2),X1))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4453]) ).
cnf(c_0_4453_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_in(X3),X2),X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4453]) ).
cnf(c_0_4454_0,axiom,
( X2 = X1
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X1),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4454]) ).
cnf(c_0_4454_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X1),X2))
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_4454]) ).
cnf(c_0_4455_0,axiom,
( c_Hoare__Mirabelle_Ohoare__valids(X1,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4455]) ).
cnf(c_0_4455_1,axiom,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| c_Hoare__Mirabelle_Ohoare__valids(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_4455]) ).
cnf(c_0_4456_0,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4456]) ).
cnf(c_0_4456_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(X2),X3),X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4456]) ).
cnf(c_0_4457_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_Orderings_Obot__class_Obot(X1)),X2))
| ~ class_Orderings_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4457]) ).
cnf(c_0_4457_1,axiom,
( ~ class_Orderings_Obot(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),c_Orderings_Obot__class_Obot(X1)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4457]) ).
cnf(c_0_4458_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4458]) ).
cnf(c_0_4458_1,axiom,
( ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4458]) ).
cnf(c_0_4459_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4459]) ).
cnf(c_0_4459_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4459]) ).
cnf(c_0_4460_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4460]) ).
cnf(c_0_4460_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4460]) ).
cnf(c_0_4461_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4461]) ).
cnf(c_0_4461_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4461]) ).
cnf(c_0_4462_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4462]) ).
cnf(c_0_4462_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4462]) ).
cnf(c_0_4463_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4463]) ).
cnf(c_0_4463_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4463]) ).
cnf(c_0_4464_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4464]) ).
cnf(c_0_4464_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4464]) ).
cnf(c_0_4465_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4465]) ).
cnf(c_0_4465_1,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4465]) ).
cnf(c_0_4466_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4466]) ).
cnf(c_0_4466_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4466]) ).
cnf(c_0_4467_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4467]) ).
cnf(c_0_4467_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4467]) ).
cnf(c_0_4468_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4468]) ).
cnf(c_0_4468_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4468]) ).
cnf(c_0_4469_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4469]) ).
cnf(c_0_4469_1,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4469]) ).
cnf(c_0_4470_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4470]) ).
cnf(c_0_4470_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4470]) ).
cnf(c_0_4471_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4471]) ).
cnf(c_0_4471_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2
| ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4471]) ).
cnf(c_0_4471_2,axiom,
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2
| ~ class_Ring__and__Field_Oidom(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4471]) ).
cnf(c_0_4471_3,axiom,
( ~ class_Ring__and__Field_Oidom(X3)
| ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4471]) ).
cnf(c_0_4472_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4472]) ).
cnf(c_0_4472_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4472]) ).
cnf(c_0_4472_2,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4472]) ).
cnf(c_0_4472_3,axiom,
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4472]) ).
cnf(c_0_4473_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4473]) ).
cnf(c_0_4473_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4473]) ).
cnf(c_0_4473_2,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4473]) ).
cnf(c_0_4473_3,axiom,
( ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3) != c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4473]) ).
cnf(c_0_4474_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4474]) ).
cnf(c_0_4474_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4474]) ).
cnf(c_0_4474_2,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Ono__zero__divisors(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4474]) ).
cnf(c_0_4474_3,axiom,
( ~ class_Ring__and__Field_Ono__zero__divisors(X2)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X2),X3),X1) != c_HOL_Ozero__class_Ozero(X2)
| X3 = c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4474]) ).
cnf(c_0_4475_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != X3
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4475]) ).
cnf(c_0_4475_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != X3
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4475]) ).
cnf(c_0_4475_2,axiom,
( ~ class_Int_Onumber__ring(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != X3
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4475]) ).
cnf(c_0_4475_3,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X3),X1) != X3
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4475]) ).
cnf(c_0_4476_0,axiom,
( hAPP(hAPP(X1,X3),X4) = hAPP(hAPP(X1,X4),X3)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4476]) ).
cnf(c_0_4476_1,axiom,
( ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| hAPP(hAPP(X1,X3),X4) = hAPP(hAPP(X1,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_4476]) ).
cnf(c_0_4477_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4477]) ).
cnf(c_0_4477_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2
| ~ class_OrderedGroup_Ogroup__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4477]) ).
cnf(c_0_4477_2,axiom,
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4477]) ).
cnf(c_0_4478_0,axiom,
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4478]) ).
cnf(c_0_4478_1,axiom,
( c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2
| ~ class_OrderedGroup_Oab__group__add(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4478]) ).
cnf(c_0_4478_2,axiom,
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ozero__class_Ozero(X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4478]) ).
cnf(c_0_4479_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1) != c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4479]) ).
cnf(c_0_4479_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Olordered__ab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4479]) ).
cnf(c_0_4479_2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),X1) != c_HOL_Ozero__class_Ozero(X2)
| X1 = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4479]) ).
cnf(c_0_4480_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),X1) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4480]) ).
cnf(c_0_4480_1,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),X1) != 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_4480]) ).
cnf(c_0_4480_2,axiom,
( ~ class_Lattices_Obounded__lattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X3),X1) != c_Orderings_Obot__class_Obot(X2)
| X1 = c_Orderings_Obot__class_Obot(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4480]) ).
cnf(c_0_4481_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X1),X3) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4481]) ).
cnf(c_0_4481_1,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X1),X3) != 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_4481]) ).
cnf(c_0_4481_2,axiom,
( ~ class_Lattices_Obounded__lattice(X2)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2),X1),X3) != c_Orderings_Obot__class_Obot(X2)
| X1 = c_Orderings_Obot__class_Obot(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4481]) ).
cnf(c_0_4482_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hAPP(c_Finite__Set_Olattice__class_OInf__fin(X2),X1) = c_Complete__Lattice_OInf__class_OInf(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4482]) ).
cnf(c_0_4482_1,axiom,
( hAPP(c_Finite__Set_Olattice__class_OInf__fin(X2),X1) = c_Complete__Lattice_OInf__class_OInf(X1,X2)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4482]) ).
cnf(c_0_4482_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(c_Finite__Set_Olattice__class_OInf__fin(X2),X1) = c_Complete__Lattice_OInf__class_OInf(X1,X2)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4482]) ).
cnf(c_0_4482_3,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| hAPP(c_Finite__Set_Olattice__class_OInf__fin(X2),X1) = c_Complete__Lattice_OInf__class_OInf(X1,X2)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4482]) ).
cnf(c_0_4483_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4483]) ).
cnf(c_0_4483_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4483]) ).
cnf(c_0_4484_0,axiom,
( c_Finite__Set_Ofun__left__comm(X1,X2,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4484]) ).
cnf(c_0_4484_1,axiom,
( ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2)
| c_Finite__Set_Ofun__left__comm(X1,X2,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4484]) ).
cnf(c_0_4485_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_4485]) ).
cnf(c_0_4485_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_4485]) ).
cnf(c_0_4486_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4486]) ).
cnf(c_0_4486_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4486]) ).
cnf(c_0_4487_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4487]) ).
cnf(c_0_4487_1,axiom,
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4487]) ).
cnf(c_0_4488_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4488]) ).
cnf(c_0_4488_1,axiom,
( ~ class_Ring__and__Field_Omult__zero(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4488]) ).
cnf(c_0_4489_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4489]) ).
cnf(c_0_4489_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4489]) ).
cnf(c_0_4490_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X2) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4490]) ).
cnf(c_0_4490_1,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X2) = c_Orderings_Obot__class_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4490]) ).
cnf(c_0_4491_0,axiom,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4491]) ).
cnf(c_0_4491_1,axiom,
( ~ class_Orderings_Obot(X1)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4491]) ).
cnf(c_0_4492_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Ozero__class_Ozero(X2)) = X1
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4492]) ).
cnf(c_0_4492_1,axiom,
( ~ class_Int_Onumber__ring(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Ozero__class_Ozero(X2)) = X1
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4492]) ).
cnf(c_0_4492_2,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X2),X1),c_HOL_Ozero__class_Ozero(X2)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_4492]) ).
cnf(c_0_4493_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4493]) ).
cnf(c_0_4493_1,axiom,
( ~ class_Int_Onumber__ring(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4493]) ).
cnf(c_0_4493_2,axiom,
( ~ class_Ring__and__Field_Oidom(X2)
| ~ class_Int_Onumber__ring(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4493]) ).
cnf(c_0_4494_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4494]) ).
cnf(c_0_4494_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4494]) ).
cnf(c_0_4495_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4495]) ).
cnf(c_0_4495_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4495]) ).
cnf(c_0_4496_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4496]) ).
cnf(c_0_4496_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4496]) ).
cnf(c_0_4497_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4497]) ).
cnf(c_0_4497_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4497]) ).
cnf(c_0_4498_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4498]) ).
cnf(c_0_4498_1,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4498]) ).
cnf(c_0_4499_0,axiom,
( X1 = c_Option_Ooption_ONone(X2)
| c_Option_Oset(X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_4499]) ).
cnf(c_0_4499_1,axiom,
( c_Option_Oset(X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X1 = c_Option_Ooption_ONone(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4499]) ).
cnf(c_0_4500_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4500]) ).
cnf(c_0_4500_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4500]) ).
cnf(c_0_4501_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4501]) ).
cnf(c_0_4501_1,axiom,
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4501]) ).
cnf(c_0_4502_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4502]) ).
cnf(c_0_4502_1,axiom,
( ~ class_Ring__and__Field_Omult__zero(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4502]) ).
cnf(c_0_4503_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4503]) ).
cnf(c_0_4503_1,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Obot__class_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4503]) ).
cnf(c_0_4504_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4504]) ).
cnf(c_0_4504_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_4504]) ).
cnf(c_0_4505_0,axiom,
( c_Finite__Set_Ofun__left__comm(c_HOL_Otimes__class_Otimes(X1),X1,X1)
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4505]) ).
cnf(c_0_4505_1,axiom,
( ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| c_Finite__Set_Ofun__left__comm(c_HOL_Otimes__class_Otimes(X1),X1,X1) ),
inference(literals_permutation,[status(thm)],[c_0_4505]) ).
cnf(c_0_4506_0,axiom,
( c_Finite__Set_Ofun__left__comm(c_HOL_Oplus__class_Oplus(X1),X1,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4506]) ).
cnf(c_0_4506_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_Finite__Set_Ofun__left__comm(c_HOL_Oplus__class_Oplus(X1),X1,X1) ),
inference(literals_permutation,[status(thm)],[c_0_4506]) ).
cnf(c_0_4507_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4507]) ).
cnf(c_0_4507_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4507]) ).
cnf(c_0_4508_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4508]) ).
cnf(c_0_4508_1,axiom,
( ~ class_OrderedGroup_Omonoid__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4508]) ).
cnf(c_0_4509_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4509]) ).
cnf(c_0_4509_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4509]) ).
cnf(c_0_4510_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Orderings_Obot__class_Obot(X1)) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4510]) ).
cnf(c_0_4510_1,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Orderings_Obot__class_Obot(X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4510]) ).
cnf(c_0_4511_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4511]) ).
cnf(c_0_4511_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4511]) ).
cnf(c_0_4512_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4512]) ).
cnf(c_0_4512_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4512]) ).
cnf(c_0_4513_0,axiom,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4513]) ).
cnf(c_0_4513_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(X2)
| c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4513]) ).
cnf(c_0_4514_0,axiom,
( X1 = X2
| hAPP(c_Option_Ooption_OSome(X3),X1) != hAPP(c_Option_Ooption_OSome(X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_4514]) ).
cnf(c_0_4514_1,axiom,
( hAPP(c_Option_Ooption_OSome(X3),X1) != hAPP(c_Option_Ooption_OSome(X3),X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4514]) ).
cnf(c_0_4515_0,axiom,
( hAPP(hAPP(X1,X3),X3) = X3
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4515]) ).
cnf(c_0_4515_1,axiom,
( ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2)
| hAPP(hAPP(X1,X3),X3) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_4515]) ).
cnf(c_0_4516_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X2) = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4516]) ).
cnf(c_0_4516_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4516]) ).
cnf(c_0_4517_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X2) = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4517]) ).
cnf(c_0_4517_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4517]) ).
cnf(c_0_4518_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X2) = X2
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4518]) ).
cnf(c_0_4518_1,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4518]) ).
cnf(c_0_4519_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2) = X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4519]) ).
cnf(c_0_4519_1,axiom,
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4519]) ).
cnf(c_0_4520_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X2) = X2
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4520]) ).
cnf(c_0_4520_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X2) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4520]) ).
cnf(c_0_4521_0,axiom,
( X1 = X2
| c_SetInterval_Oord__class_OlessThan(X1,X3) != c_SetInterval_Oord__class_OlessThan(X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4521]) ).
cnf(c_0_4521_1,axiom,
( c_SetInterval_Oord__class_OlessThan(X1,X3) != c_SetInterval_Oord__class_OlessThan(X2,X3)
| X1 = X2
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_4521]) ).
cnf(c_0_4521_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_SetInterval_Oord__class_OlessThan(X1,X3) != c_SetInterval_Oord__class_OlessThan(X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4521]) ).
cnf(c_0_4522_0,axiom,
( X1 = X2
| c_Com_Ocom_OSemi(X3,X1) != c_Com_Ocom_OSemi(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4522]) ).
cnf(c_0_4522_1,axiom,
( c_Com_Ocom_OSemi(X3,X1) != c_Com_Ocom_OSemi(X4,X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4522]) ).
cnf(c_0_4523_0,axiom,
( X1 = X2
| c_Com_Ocom_OSemi(X1,X3) != c_Com_Ocom_OSemi(X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_4523]) ).
cnf(c_0_4523_1,axiom,
( c_Com_Ocom_OSemi(X1,X3) != c_Com_Ocom_OSemi(X2,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4523]) ).
cnf(c_0_4524_0,axiom,
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2))
| ~ class_Finite__Set_Ofinite_Ofinite(X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4524]) ).
cnf(c_0_4524_1,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(X1)
| class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2))
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4524]) ).
cnf(c_0_4524_2,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X1)
| class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_4524]) ).
cnf(c_0_4525_0,axiom,
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4525]) ).
cnf(c_0_4525_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4525]) ).
cnf(c_0_4526_0,axiom,
( class_Lattices_Oupper__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4526]) ).
cnf(c_0_4526_1,axiom,
( ~ class_Lattices_Olattice(X1)
| class_Lattices_Oupper__semilattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4526]) ).
cnf(c_0_4527_0,axiom,
( class_Lattices_Olower__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4527]) ).
cnf(c_0_4527_1,axiom,
( ~ class_Lattices_Olattice(X1)
| class_Lattices_Olower__semilattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4527]) ).
cnf(c_0_4528_0,axiom,
( class_Lattices_Odistrib__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4528]) ).
cnf(c_0_4528_1,axiom,
( ~ class_Lattices_Odistrib__lattice(X1)
| class_Lattices_Odistrib__lattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4528]) ).
cnf(c_0_4529_0,axiom,
( class_Lattices_Obounded__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4529]) ).
cnf(c_0_4529_1,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| class_Lattices_Obounded__lattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4529]) ).
cnf(c_0_4530_0,axiom,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4530]) ).
cnf(c_0_4530_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4530]) ).
cnf(c_0_4531_0,axiom,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4531]) ).
cnf(c_0_4531_1,axiom,
( ~ class_Lattices_Olattice(X1)
| class_Lattices_Olattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4531]) ).
cnf(c_0_4532_0,axiom,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4532]) ).
cnf(c_0_4532_1,axiom,
( ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4532]) ).
cnf(c_0_4533_0,axiom,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4533]) ).
cnf(c_0_4533_1,axiom,
( ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4533]) ).
cnf(c_0_4534_0,axiom,
( class_HOL_Ominus(tc_fun(X2,X1))
| ~ class_HOL_Ominus(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4534]) ).
cnf(c_0_4534_1,axiom,
( ~ class_HOL_Ominus(X1)
| class_HOL_Ominus(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4534]) ).
cnf(c_0_4535_0,axiom,
( class_HOL_Oord(tc_fun(X2,X1))
| ~ class_HOL_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4535]) ).
cnf(c_0_4535_1,axiom,
( ~ class_HOL_Oord(X1)
| class_HOL_Oord(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4535]) ).
cnf(c_0_4536_0,axiom,
( c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X1),X1) = c_Finite__Set_Olattice__class_OInf__fin(X1)
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4536]) ).
cnf(c_0_4536_1,axiom,
( ~ class_Lattices_Olattice(X1)
| c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X1),X1) = c_Finite__Set_Olattice__class_OInf__fin(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4536]) ).
cnf(c_0_4537_0,axiom,
( c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(X1),X1) = c_Finite__Set_Olinorder__class_OMax(X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4537]) ).
cnf(c_0_4537_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(X1),X1) = c_Finite__Set_Olinorder__class_OMax(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4537]) ).
cnf(c_0_4538_0,axiom,
( c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X1),X1) = c_Finite__Set_Olinorder__class_OMin(X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4538]) ).
cnf(c_0_4538_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X1),X1) = c_Finite__Set_Olinorder__class_OMin(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4538]) ).
cnf(c_0_4539_0,axiom,
( c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omin(X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4539]) ).
cnf(c_0_4539_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omin(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4539]) ).
cnf(c_0_4540_0,axiom,
( c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omax(X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4540]) ).
cnf(c_0_4540_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omax(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4540]) ).
cnf(c_0_4541_0,axiom,
( c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Oupper__semilattice__class_Osup(X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4541]) ).
cnf(c_0_4541_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Oupper__semilattice__class_Osup(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4541]) ).
cnf(c_0_4542_0,axiom,
( c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Olower__semilattice__class_Oinf(X1),X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4542]) ).
cnf(c_0_4542_1,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Olower__semilattice__class_Oinf(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_4542]) ).
cnf(c_0_4543_0,axiom,
( c_Orderings_Oord__class_Omax(X1) = c_Lattices_Oupper__semilattice__class_Osup(X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4543]) ).
cnf(c_0_4543_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| c_Orderings_Oord__class_Omax(X1) = c_Lattices_Oupper__semilattice__class_Osup(X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4543]) ).
cnf(c_0_4543_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| c_Orderings_Oord__class_Omax(X1) = c_Lattices_Oupper__semilattice__class_Osup(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4543]) ).
cnf(c_0_4544_0,axiom,
( c_Orderings_Oord__class_Omin(X1) = c_Lattices_Olower__semilattice__class_Oinf(X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4544]) ).
cnf(c_0_4544_1,axiom,
( ~ class_Lattices_Olower__semilattice(X1)
| c_Orderings_Oord__class_Omin(X1) = c_Lattices_Olower__semilattice__class_Oinf(X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4544]) ).
cnf(c_0_4544_2,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ class_Lattices_Olower__semilattice(X1)
| c_Orderings_Oord__class_Omin(X1) = c_Lattices_Olower__semilattice__class_Oinf(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4544]) ).
cnf(c_0_4545_0,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4545]) ).
cnf(c_0_4545_1,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(X2)
| c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_4545]) ).
cnf(c_0_4546_0,axiom,
( class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(X1))
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
inference(literals_permutation,[status(thm)],[c_0_4546]) ).
cnf(c_0_4546_1,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(X1)
| class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_4546]) ).
cnf(c_0_4547_0,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4547]) ).
cnf(c_0_4547_1,axiom,
( c_Suc(X1) != c_Suc(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4547]) ).
cnf(c_0_4548_0,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4548]) ).
cnf(c_0_4548_1,axiom,
( c_Suc(X1) != c_Suc(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4548]) ).
cnf(c_0_4549_0,axiom,
( X1 = X2
| c_Com_Ocom_OBODY(X1) != c_Com_Ocom_OBODY(X2) ),
inference(literals_permutation,[status(thm)],[c_0_4549]) ).
cnf(c_0_4549_1,axiom,
( c_Com_Ocom_OBODY(X1) != c_Com_Ocom_OBODY(X2)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_4549]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_981,negated_conjecture,
! [X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_Otriple_Otriple(c_fequal(tc_Com_Ostate),c_Com_Ocom_OBODY(X1),c_Natural_Oevalc(c_Com_Ocom_OBODY(X1)),tc_Com_Ostate)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))),tc_Com_Ostate)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),X1),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom))) ),
file('<stdin>',cls_conjecture_1) ).
fof(c_0_1_982,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),v_x),v_x)),
file('<stdin>',cls_conjecture_0) ).
fof(c_0_2_983,negated_conjecture,
! [X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_Otriple_Otriple(c_fequal(tc_Com_Ostate),c_Com_Ocom_OBODY(X1),c_Natural_Oevalc(c_Com_Ocom_OBODY(X1)),tc_Com_Ostate)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))),tc_Com_Ostate)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),X1),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom))) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_3_984,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),v_x),v_x)),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_4_985,negated_conjecture,
! [X2] :
( c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_Otriple_Otriple(c_fequal(tc_Com_Ostate),c_Com_Ocom_OBODY(X2),c_Natural_Oevalc(c_Com_Ocom_OBODY(X2)),tc_Com_Ostate)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))),tc_Com_Ostate)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),X2),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom))) ),
inference(variable_rename,[status(thm)],[c_0_2]) ).
fof(c_0_5_986,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),v_x),v_x)),
c_0_3 ).
cnf(c_0_6_987,negated_conjecture,
( c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_Otriple_Otriple(c_fequal(tc_Com_Ostate),c_Com_Ocom_OBODY(X1),c_Natural_Oevalc(c_Com_Ocom_OBODY(X1)),tc_Com_Ostate)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))),tc_Com_Ostate)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),X1),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom))) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7_988,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),v_x),v_x)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8_989,negated_conjecture,
( c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_Otriple_Otriple(c_fequal(tc_Com_Ostate),c_Com_Ocom_OBODY(X1),c_Natural_Oevalc(c_Com_Ocom_OBODY(X1)),tc_Com_Ostate)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))),tc_Com_Ostate)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),X1),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom))) ),
c_0_6,
[final] ).
cnf(c_0_9_990,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),v_x),v_x)),
c_0_7,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_2889,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),v_x),v_x)),
file('/export/starexec/sandbox/tmp/iprover_modulo_3e2e1d.p',c_0_9) ).
cnf(c_3600,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),v_x),v_x)),
inference(copy,[status(esa)],[c_2889]) ).
cnf(c_3607,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),v_x),v_x)),
inference(copy,[status(esa)],[c_3600]) ).
cnf(c_3608,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),v_x),v_x)),
inference(copy,[status(esa)],[c_3607]) ).
cnf(c_3610,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),v_x),v_x)),
inference(copy,[status(esa)],[c_3608]) ).
cnf(c_12191,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),v_x),v_x)),
inference(copy,[status(esa)],[c_3610]) ).
cnf(c_2753,plain,
hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X0),X0)),
file('/export/starexec/sandbox/tmp/iprover_modulo_3e2e1d.p',c_0_918_0) ).
cnf(c_12003,plain,
hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X0),X0)),
inference(copy,[status(esa)],[c_2753]) ).
cnf(c_12196,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_12191,c_12003]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWV875-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.12 % Command : iprover_modulo %s %d
% 0.12/0.32 % Computer : n032.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Thu Jun 16 04:05:59 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.32 % Running in mono-core mode
% 0.17/0.55 % Orienting using strategy Equiv(ClausalAll)
% 0.17/0.55 % Orientation found
% 0.17/0.55 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_e6ce56.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_3e2e1d.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_492a58 | grep -v "SZS"
% 0.17/0.57
% 0.17/0.57 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.17/0.57
% 0.17/0.57 %
% 0.17/0.57 % ------ iProver source info
% 0.17/0.57
% 0.17/0.57 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.17/0.57 % git: non_committed_changes: true
% 0.17/0.57 % git: last_make_outside_of_git: true
% 0.17/0.57
% 0.17/0.57 %
% 0.17/0.57 % ------ Input Options
% 0.17/0.57
% 0.17/0.57 % --out_options all
% 0.17/0.57 % --tptp_safe_out true
% 0.17/0.57 % --problem_path ""
% 0.17/0.57 % --include_path ""
% 0.17/0.57 % --clausifier .//eprover
% 0.17/0.57 % --clausifier_options --tstp-format
% 0.17/0.57 % --stdin false
% 0.17/0.57 % --dbg_backtrace false
% 0.17/0.57 % --dbg_dump_prop_clauses false
% 0.17/0.57 % --dbg_dump_prop_clauses_file -
% 0.17/0.57 % --dbg_out_stat false
% 0.17/0.57
% 0.17/0.57 % ------ General Options
% 0.17/0.57
% 0.17/0.57 % --fof false
% 0.17/0.57 % --time_out_real 150.
% 0.17/0.57 % --time_out_prep_mult 0.2
% 0.17/0.57 % --time_out_virtual -1.
% 0.17/0.57 % --schedule none
% 0.17/0.57 % --ground_splitting input
% 0.17/0.57 % --splitting_nvd 16
% 0.17/0.57 % --non_eq_to_eq false
% 0.17/0.57 % --prep_gs_sim true
% 0.17/0.57 % --prep_unflatten false
% 0.17/0.57 % --prep_res_sim true
% 0.17/0.57 % --prep_upred true
% 0.17/0.57 % --res_sim_input true
% 0.17/0.57 % --clause_weak_htbl true
% 0.17/0.57 % --gc_record_bc_elim false
% 0.17/0.57 % --symbol_type_check false
% 0.17/0.57 % --clausify_out false
% 0.17/0.57 % --large_theory_mode false
% 0.17/0.57 % --prep_sem_filter none
% 0.17/0.57 % --prep_sem_filter_out false
% 0.17/0.57 % --preprocessed_out false
% 0.17/0.57 % --sub_typing false
% 0.17/0.57 % --brand_transform false
% 0.17/0.57 % --pure_diseq_elim true
% 0.17/0.57 % --min_unsat_core false
% 0.17/0.57 % --pred_elim true
% 0.17/0.57 % --add_important_lit false
% 0.17/0.57 % --soft_assumptions false
% 0.17/0.57 % --reset_solvers false
% 0.17/0.57 % --bc_imp_inh []
% 0.17/0.57 % --conj_cone_tolerance 1.5
% 0.17/0.57 % --prolific_symb_bound 500
% 0.17/0.57 % --lt_threshold 2000
% 0.17/0.57
% 0.17/0.57 % ------ SAT Options
% 0.17/0.57
% 0.17/0.57 % --sat_mode false
% 0.17/0.57 % --sat_fm_restart_options ""
% 0.17/0.57 % --sat_gr_def false
% 0.17/0.57 % --sat_epr_types true
% 0.17/0.57 % --sat_non_cyclic_types false
% 0.17/0.57 % --sat_finite_models false
% 0.17/0.57 % --sat_fm_lemmas false
% 0.17/0.57 % --sat_fm_prep false
% 0.17/0.57 % --sat_fm_uc_incr true
% 0.17/0.57 % --sat_out_model small
% 0.17/0.57 % --sat_out_clauses false
% 0.17/0.57
% 0.17/0.57 % ------ QBF Options
% 0.17/0.57
% 0.17/0.57 % --qbf_mode false
% 0.17/0.57 % --qbf_elim_univ true
% 0.17/0.57 % --qbf_sk_in true
% 0.17/0.57 % --qbf_pred_elim true
% 0.17/0.57 % --qbf_split 32
% 0.17/0.57
% 0.17/0.57 % ------ BMC1 Options
% 0.17/0.57
% 0.17/0.57 % --bmc1_incremental false
% 0.17/0.57 % --bmc1_axioms reachable_all
% 0.17/0.57 % --bmc1_min_bound 0
% 0.17/0.57 % --bmc1_max_bound -1
% 0.17/0.57 % --bmc1_max_bound_default -1
% 0.17/0.57 % --bmc1_symbol_reachability true
% 0.17/0.57 % --bmc1_property_lemmas false
% 0.17/0.57 % --bmc1_k_induction false
% 0.17/0.57 % --bmc1_non_equiv_states false
% 0.17/0.57 % --bmc1_deadlock false
% 0.17/0.57 % --bmc1_ucm false
% 0.17/0.57 % --bmc1_add_unsat_core none
% 0.17/0.57 % --bmc1_unsat_core_children false
% 0.17/0.57 % --bmc1_unsat_core_extrapolate_axioms false
% 0.17/0.57 % --bmc1_out_stat full
% 0.17/0.57 % --bmc1_ground_init false
% 0.17/0.57 % --bmc1_pre_inst_next_state false
% 0.17/0.57 % --bmc1_pre_inst_state false
% 0.17/0.57 % --bmc1_pre_inst_reach_state false
% 0.17/0.57 % --bmc1_out_unsat_core false
% 0.17/0.57 % --bmc1_aig_witness_out false
% 0.17/0.57 % --bmc1_verbose false
% 0.17/0.57 % --bmc1_dump_clauses_tptp false
% 7.79/8.12 % --bmc1_dump_unsat_core_tptp false
% 7.79/8.12 % --bmc1_dump_file -
% 7.79/8.12 % --bmc1_ucm_expand_uc_limit 128
% 7.79/8.12 % --bmc1_ucm_n_expand_iterations 6
% 7.79/8.12 % --bmc1_ucm_extend_mode 1
% 7.79/8.12 % --bmc1_ucm_init_mode 2
% 7.79/8.12 % --bmc1_ucm_cone_mode none
% 7.79/8.12 % --bmc1_ucm_reduced_relation_type 0
% 7.79/8.12 % --bmc1_ucm_relax_model 4
% 7.79/8.12 % --bmc1_ucm_full_tr_after_sat true
% 7.79/8.12 % --bmc1_ucm_expand_neg_assumptions false
% 7.79/8.12 % --bmc1_ucm_layered_model none
% 7.79/8.12 % --bmc1_ucm_max_lemma_size 10
% 7.79/8.12
% 7.79/8.12 % ------ AIG Options
% 7.79/8.12
% 7.79/8.12 % --aig_mode false
% 7.79/8.12
% 7.79/8.12 % ------ Instantiation Options
% 7.79/8.12
% 7.79/8.12 % --instantiation_flag true
% 7.79/8.12 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 7.79/8.12 % --inst_solver_per_active 750
% 7.79/8.12 % --inst_solver_calls_frac 0.5
% 7.79/8.12 % --inst_passive_queue_type priority_queues
% 7.79/8.12 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 7.79/8.12 % --inst_passive_queues_freq [25;2]
% 7.79/8.12 % --inst_dismatching true
% 7.79/8.12 % --inst_eager_unprocessed_to_passive true
% 7.79/8.12 % --inst_prop_sim_given true
% 7.79/8.12 % --inst_prop_sim_new false
% 7.79/8.12 % --inst_orphan_elimination true
% 7.79/8.12 % --inst_learning_loop_flag true
% 7.79/8.12 % --inst_learning_start 3000
% 7.79/8.12 % --inst_learning_factor 2
% 7.79/8.12 % --inst_start_prop_sim_after_learn 3
% 7.79/8.12 % --inst_sel_renew solver
% 7.79/8.12 % --inst_lit_activity_flag true
% 7.79/8.12 % --inst_out_proof true
% 7.79/8.12
% 7.79/8.12 % ------ Resolution Options
% 7.79/8.12
% 7.79/8.12 % --resolution_flag true
% 7.79/8.12 % --res_lit_sel kbo_max
% 7.79/8.12 % --res_to_prop_solver none
% 7.79/8.12 % --res_prop_simpl_new false
% 7.79/8.12 % --res_prop_simpl_given false
% 7.79/8.12 % --res_passive_queue_type priority_queues
% 7.79/8.12 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 7.79/8.12 % --res_passive_queues_freq [15;5]
% 7.79/8.12 % --res_forward_subs full
% 7.79/8.12 % --res_backward_subs full
% 7.79/8.12 % --res_forward_subs_resolution true
% 7.79/8.12 % --res_backward_subs_resolution true
% 7.79/8.12 % --res_orphan_elimination false
% 7.79/8.12 % --res_time_limit 1000.
% 7.79/8.12 % --res_out_proof true
% 7.79/8.12 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_e6ce56.s
% 7.79/8.12 % --modulo true
% 7.79/8.12
% 7.79/8.12 % ------ Combination Options
% 7.79/8.12
% 7.79/8.12 % --comb_res_mult 1000
% 7.79/8.12 % --comb_inst_mult 300
% 7.79/8.12 % ------
% 7.79/8.12
% 7.79/8.12 % ------ Parsing...% successful
% 7.79/8.12
% 7.79/8.12 % ------ 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 %
% 7.79/8.12
% 7.79/8.12 % ------ Proving...
% 7.79/8.12 % ------ Problem Properties
% 7.79/8.12
% 7.79/8.12 %
% 7.79/8.12 % EPR false
% 7.79/8.12 % Horn false
% 7.79/8.12 % Has equality true
% 7.79/8.12
% 7.79/8.12 % % ------ Input Options Time Limit: Unbounded
% 7.79/8.12
% 7.79/8.12
% 7.79/8.12 Compiling...
% 7.79/8.12 Loading plugin: done.
% 7.79/8.12 Compiling...
% 7.79/8.12 Loading plugin: done.
% 7.79/8.12 Compiling...
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% 7.79/8.12 Compiling...
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% 7.79/8.12 Compiling...
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% 7.79/8.12 Compiling...
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% 7.79/8.12 Compiling...
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% 7.79/8.12 Compiling...
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% 7.79/8.12 Compiling...
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% 7.79/8.12 Compiling...
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% 7.79/8.12 Compiling...
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% 7.79/8.12 Compiling...
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% 7.79/8.12 Compiling...
% 7.79/8.12 Loading plugin: done.
% 7.79/8.12 Compiling...
% 7.79/8.12 Loading plugin: done.
% 7.79/8.12 Compiling...
% 7.79/8.12 Loading plugin: done.
% 7.79/8.12 Compiling...
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% 7.79/8.12 Compiling...
% 7.79/8.12 Loading plugin: done.
% 7.79/8.12 Compiling...
% 7.79/8.12 Loading plugin: done.
% 7.79/8.12 Compiling...
% 7.79/8.12 Loading plugin: done.
% 7.79/8.12 % % ------ Current options:
% 7.79/8.12
% 7.79/8.12 % ------ Input Options
% 7.79/8.12
% 7.79/8.12 % --out_options all
% 7.79/8.12 % --tptp_safe_out true
% 7.79/8.12 % --problem_path ""
% 7.79/8.12 % --include_path ""
% 7.79/8.12 % --clausifier .//eprover
% 7.79/8.12 % --clausifier_options --tstp-format
% 7.79/8.12 % --stdin false
% 7.79/8.12 % --dbg_backtrace false
% 7.79/8.12 % --dbg_dump_prop_clauses false
% 7.79/8.12 % --dbg_dump_prop_clauses_file -
% 7.79/8.12 % --dbg_out_stat false
% 7.79/8.12
% 7.79/8.12 % ------ General Options
% 7.79/8.12
% 7.79/8.12 % --fof false
% 7.79/8.12 % --time_out_real 150.
% 7.79/8.12 % --time_out_prep_mult 0.2
% 7.79/8.12 % --time_out_virtual -1.
% 7.79/8.12 % --schedule none
% 7.79/8.12 % --ground_splitting input
% 7.79/8.12 % --splitting_nvd 16
% 7.79/8.12 % --non_eq_to_eq false
% 7.79/8.12 % --prep_gs_sim true
% 7.79/8.12 % --prep_unflatten false
% 7.79/8.12 % --prep_res_sim true
% 7.79/8.12 % --prep_upred true
% 7.79/8.12 % --res_sim_input true
% 7.79/8.12 % --clause_weak_htbl true
% 7.79/8.12 % --gc_record_bc_elim false
% 7.79/8.12 % --symbol_type_check false
% 7.79/8.12 % --clausify_out false
% 7.79/8.12 % --large_theory_mode false
% 7.79/8.12 % --prep_sem_filter none
% 7.79/8.12 % --prep_sem_filter_out false
% 7.79/8.12 % --preprocessed_out false
% 7.79/8.12 % --sub_typing false
% 7.79/8.12 % --brand_transform false
% 7.79/8.12 % --pure_diseq_elim true
% 7.79/8.12 % --min_unsat_core false
% 7.79/8.12 % --pred_elim true
% 7.79/8.12 % --add_important_lit false
% 7.79/8.12 % --soft_assumptions false
% 7.79/8.12 % --reset_solvers false
% 7.79/8.12 % --bc_imp_inh []
% 7.79/8.12 % --conj_cone_tolerance 1.5
% 7.79/8.12 % --prolific_symb_bound 500
% 7.79/8.12 % --lt_threshold 2000
% 7.79/8.12
% 7.79/8.12 % ------ SAT Options
% 7.79/8.12
% 7.79/8.12 % --sat_mode false
% 7.79/8.12 % --sat_fm_restart_options ""
% 7.79/8.12 % --sat_gr_def false
% 7.79/8.12 % --sat_epr_types true
% 7.79/8.12 % --sat_non_cyclic_types false
% 7.79/8.12 % --sat_finite_models false
% 7.79/8.12 % --sat_fm_lemmas false
% 7.79/8.12 % --sat_fm_prep false
% 7.79/8.12 % --sat_fm_uc_incr true
% 7.79/8.12 % --sat_out_model small
% 7.79/8.12 % --sat_out_clauses false
% 7.79/8.12
% 7.79/8.12 % ------ QBF Options
% 7.79/8.12
% 7.79/8.12 % --qbf_mode false
% 7.79/8.12 % --qbf_elim_univ true
% 7.79/8.12 % --qbf_sk_in true
% 7.79/8.12 % --qbf_pred_elim true
% 7.79/8.12 % --qbf_split 32
% 7.79/8.12
% 7.79/8.12 % ------ BMC1 Options
% 7.79/8.12
% 7.79/8.12 % --bmc1_incremental false
% 7.79/8.12 % --bmc1_axioms reachable_all
% 7.79/8.12 % --bmc1_min_bound 0
% 7.79/8.12 % --bmc1_max_bound -1
% 7.79/8.12 % --bmc1_max_bound_default -1
% 7.79/8.12 % --bmc1_symbol_reachability true
% 7.79/8.12 % --bmc1_property_lemmas false
% 7.79/8.12 % --bmc1_k_induction false
% 7.79/8.12 % --bmc1_non_equiv_states false
% 7.79/8.12 % --bmc1_deadlock false
% 7.79/8.12 % --bmc1_ucm false
% 7.79/8.12 % --bmc1_add_unsat_core none
% 7.79/8.12 % --bmc1_unsat_core_children false
% 7.79/8.12 % --bmc1_unsat_core_extrapolate_axioms false
% 7.79/8.12 % --bmc1_out_stat full
% 7.79/8.12 % --bmc1_ground_init false
% 7.79/8.12 % --bmc1_pre_inst_next_state false
% 7.79/8.12 % --bmc1_pre_inst_state false
% 7.79/8.12 % --bmc1_pre_inst_reach_state false
% 7.79/8.12 % --bmc1_out_unsat_core false
% 7.79/8.12 % --bmc1_aig_witness_out false
% 7.79/8.12 % --bmc1_verbose false
% 7.79/8.12 % --bmc1_dump_clauses_tptp false
% 7.79/8.12 % --bmc1_dump_unsat_core_tptp false
% 7.79/8.12 % --bmc1_dump_file -
% 7.79/8.12 % --bmc1_ucm_expand_uc_limit 128
% 7.79/8.12 % --bmc1_ucm_n_expand_iterations 6
% 7.79/8.12 % --bmc1_ucm_extend_mode 1
% 7.79/8.12 % --bmc1_ucm_init_mode 2
% 7.79/8.12 % --bmc1_ucm_cone_mode none
% 7.79/8.12 % --bmc1_ucm_reduced_relation_type 0
% 7.79/8.12 % --bmc1_ucm_relax_model 4
% 7.79/8.12 % --bmc1_ucm_full_tr_after_sat true
% 7.79/8.12 % --bmc1_ucm_expand_neg_assumptions false
% 7.79/8.12 % --bmc1_ucm_layered_model none
% 7.79/8.12 % --bmc1_ucm_max_lemma_size 10
% 7.79/8.12
% 7.79/8.12 % ------ AIG Options
% 7.79/8.12
% 7.79/8.12 % --aig_mode false
% 7.79/8.12
% 7.79/8.12 % ------ Instantiation Options
% 7.79/8.12
% 7.79/8.12 % --instantiation_flag true
% 7.79/8.12 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 7.79/8.12 % --inst_solver_per_active 750
% 7.79/8.12 % --inst_solver_calls_frac 0.5
% 7.79/8.12 % --inst_passive_queue_type priority_queues
% 7.79/8.12 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 7.79/8.12 % --inst_passive_queues_freq [25;2]
% 7.79/8.12 % --inst_dismatching true
% 7.79/8.12 % --inst_eager_unprocessed_to_passive true
% 7.79/8.12 % --inst_prop_sim_given true
% 7.79/8.12 % --inst_prop_sim_new false
% 7.79/8.12 % --inst_orphan_elimination true
% 7.79/8.12 % --inst_learning_loop_flag true
% 7.79/8.12 % --inst_learning_start 3000
% 7.79/8.12 % --inst_learning_factor 2
% 7.79/8.12 % --inst_start_prop_sim_after_learn 3
% 7.79/8.12 % --inst_sel_renew solver
% 7.79/8.12 % --inst_lit_activity_flag true
% 7.79/8.12 % --inst_out_proof true
% 7.79/8.12
% 7.79/8.12 % ------ Resolution Options
% 7.79/8.12
% 7.79/8.12 % --resolution_flag true
% 7.79/8.12 % --res_lit_sel kbo_max
% 7.79/8.12 % --res_to_prop_solver none
% 7.79/8.12 % --res_prop_simpl_new false
% 7.79/8.12 % --res_prop_simpl_given false
% 7.79/8.12 % --res_passive_queue_type priority_queues
% 7.79/8.12 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 7.79/8.12 % --res_passive_queues_freq [15;5]
% 7.79/8.12 % --res_forward_subs full
% 7.79/8.12 % --res_backward_subs full
% 7.79/8.12 % --res_forward_subs_resolution true
% 7.79/8.12 % --res_backward_subs_resolution true
% 7.79/8.12 % --res_orphan_elimination false
% 7.79/8.12 % --res_time_limit 1000.
% 7.79/8.12 % --res_out_proof true
% 7.79/8.12 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_e6ce56.s
% 7.79/8.12 % --modulo true
% 7.79/8.12
% 7.79/8.12 % ------ Combination Options
% 7.79/8.12
% 7.79/8.12 % --comb_res_mult 1000
% 7.79/8.12 % --comb_inst_mult 300
% 7.79/8.12 % ------
% 7.79/8.12
% 7.79/8.12
% 7.79/8.12
% 7.79/8.12 % ------ Proving...
% 7.79/8.12 %
% 7.79/8.12
% 7.79/8.12
% 7.79/8.12 % Resolution empty clause
% 7.79/8.12
% 7.79/8.12 % ------ Statistics
% 7.79/8.12
% 7.79/8.12 % ------ General
% 7.79/8.12
% 7.79/8.12 % num_of_input_clauses: 2890
% 7.79/8.12 % num_of_input_neg_conjectures: 2
% 7.79/8.12 % num_of_splits: 0
% 7.79/8.12 % num_of_split_atoms: 0
% 7.79/8.12 % num_of_sem_filtered_clauses: 0
% 7.79/8.12 % num_of_subtypes: 0
% 7.79/8.12 % monotx_restored_types: 0
% 7.79/8.12 % sat_num_of_epr_types: 0
% 7.79/8.12 % sat_num_of_non_cyclic_types: 0
% 7.79/8.12 % sat_guarded_non_collapsed_types: 0
% 7.79/8.12 % is_epr: 0
% 7.79/8.12 % is_horn: 0
% 7.79/8.12 % has_eq: 1
% 7.79/8.12 % num_pure_diseq_elim: 0
% 7.79/8.12 % simp_replaced_by: 0
% 7.79/8.12 % res_preprocessed: 4
% 7.79/8.12 % prep_upred: 0
% 7.79/8.12 % prep_unflattend: 0
% 7.79/8.12 % pred_elim_cands: 0
% 7.79/8.12 % pred_elim: 0
% 7.79/8.12 % pred_elim_cl: 0
% 7.79/8.12 % pred_elim_cycles: 0
% 7.79/8.12 % forced_gc_time: 0
% 7.79/8.12 % gc_basic_clause_elim: 0
% 7.79/8.12 % parsing_time: 0.118
% 7.79/8.12 % sem_filter_time: 0.
% 7.79/8.12 % pred_elim_time: 0.
% 7.79/8.12 % out_proof_time: 0.
% 7.79/8.12 % monotx_time: 0.
% 7.79/8.12 % subtype_inf_time: 0.
% 7.79/8.12 % unif_index_cands_time: 0.
% 7.79/8.12 % unif_index_add_time: 0.001
% 7.79/8.12 % total_time: 7.56
% 7.79/8.12 % num_of_symbols: 179
% 7.79/8.12 % num_of_terms: 9334
% 7.79/8.12
% 7.79/8.12 % ------ Propositional Solver
% 7.79/8.12
% 7.79/8.12 % prop_solver_calls: 1
% 7.79/8.12 % prop_fast_solver_calls: 9
% 7.79/8.12 % prop_num_of_clauses: 2341
% 7.79/8.12 % prop_preprocess_simplified: 9143
% 7.79/8.12 % prop_fo_subsumed: 0
% 7.79/8.12 % prop_solver_time: 0.
% 7.79/8.12 % prop_fast_solver_time: 0.
% 7.79/8.12 % prop_unsat_core_time: 0.
% 7.79/8.12
% 7.79/8.12 % ------ QBF
% 7.79/8.12
% 7.79/8.12 % qbf_q_res: 0
% 7.79/8.12 % qbf_num_tautologies: 0
% 7.79/8.12 % qbf_prep_cycles: 0
% 7.79/8.12
% 7.79/8.12 % ------ BMC1
% 7.79/8.12
% 7.79/8.12 % bmc1_current_bound: -1
% 7.79/8.12 % bmc1_last_solved_bound: -1
% 7.79/8.12 % bmc1_unsat_core_size: -1
% 7.79/8.12 % bmc1_unsat_core_parents_size: -1
% 7.79/8.12 % bmc1_merge_next_fun: 0
% 7.79/8.12 % bmc1_unsat_core_clauses_time: 0.
% 7.79/8.12
% 7.79/8.12 % ------ Instantiation
% 7.79/8.12
% 7.79/8.12 % inst_num_of_clauses: 2609
% 7.79/8.12 % inst_num_in_passive: 0
% 7.79/8.12 % inst_num_in_active: 0
% 7.79/8.12 % inst_num_in_unprocessed: 2890
% 7.79/8.12 % inst_num_of_loops: 0
% 7.79/8.12 % inst_num_of_learning_restarts: 0
% 7.79/8.12 % inst_num_moves_active_passive: 0
% 7.79/8.12 % inst_lit_activity: 0
% 7.79/8.12 % inst_lit_activity_moves: 0
% 7.79/8.12 % inst_num_tautologies: 0
% 7.79/8.12 % inst_num_prop_implied: 0
% 7.79/8.12 % inst_num_existing_simplified: 0
% 7.79/8.12 % inst_num_eq_res_simplified: 0
% 7.79/8.12 % inst_num_child_elim: 0
% 7.79/8.12 % inst_num_of_dismatching_blockings: 0
% 7.79/8.12 % inst_num_of_non_proper_insts: 0
% 7.79/8.12 % inst_num_of_duplicates: 0
% 7.79/8.12 % inst_inst_num_from_inst_to_res: 0
% 7.79/8.12 % inst_dismatching_checking_time: 0.
% 7.79/8.12
% 7.79/8.12 % ------ Resolution
% 7.79/8.12
% 7.79/8.12 % res_num_of_clauses: 3013
% 7.79/8.12 % res_num_in_passive: 1
% 7.79/8.12 % res_num_in_active: 1073
% 7.79/8.12 % res_num_of_loops: 1
% 7.79/8.12 % res_forward_subset_subsumed: 1723
% 7.79/8.12 % res_backward_subset_subsumed: 5
% 7.79/8.12 % res_forward_subsumed: 0
% 7.79/8.12 % res_backward_subsumed: 0
% 7.79/8.12 % res_forward_subsumption_resolution: 1
% 7.79/8.12 % res_backward_subsumption_resolution: 0
% 7.79/8.12 % res_clause_to_clause_subsumption: 1
% 7.79/8.12 % res_orphan_elimination: 0
% 7.79/8.12 % res_tautology_del: 0
% 7.79/8.12 % res_num_eq_res_simplified: 0
% 7.79/8.12 % res_num_sel_changes: 0
% 7.79/8.12 % res_moves_from_active_to_pass: 0
% 7.79/8.12
% 7.79/8.12 % Status Unsatisfiable
% 7.79/8.12 % SZS status Unsatisfiable
% 7.79/8.12 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------