TSTP Solution File: SCT073-1 by iProverMo---2.5-0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SCT073-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 21:37:17 EDT 2022
% Result : Unsatisfiable 3.40s 3.63s
% Output : CNFRefutation 3.40s
% 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,
c_fequal(V_x,V_x,T_a),
input ).
fof(cls_ATP__Linkup_Oequal__imp__fequal_0_0,plain,
! [T_a,V_x] :
( c_fequal(V_x,V_x,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_ATP__Linkup_Oequal__imp__fequal_0]) ).
cnf(clsarity_bool__HOL_Oord,axiom,
class_HOL_Oord(tc_bool),
input ).
fof(clsarity_bool__HOL_Oord_0,plain,
( class_HOL_Oord(tc_bool)
| $false ),
inference(orientation,[status(thm)],[clsarity_bool__HOL_Oord]) ).
cnf(clsarity_bool__Orderings_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_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(cls_CHAINED_0,axiom,
v_a____ != v_b____,
input ).
fof(cls_CHAINED_0_0,plain,
( v_a____ != v_b____
| $false ),
inference(orientation,[status(thm)],[cls_CHAINED_0]) ).
cnf(cls_linear__alt_0,axiom,
c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
input ).
fof(cls_linear__alt_0_0,plain,
( c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_linear__alt_0]) ).
cnf(cls_in__mkbot_0,axiom,
~ c_in(c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
input ).
fof(cls_in__mkbot_0_0,plain,
! [V_L,V_x,V_xa] :
( ~ c_in(c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| $false ),
inference(orientation,[status(thm)],[cls_in__mkbot_0]) ).
cnf(cls_in__mkbot_1,axiom,
~ c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
input ).
fof(cls_in__mkbot_1_0,plain,
! [V_L,V_x] :
( ~ c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| $false ),
inference(orientation,[status(thm)],[cls_in__mkbot_1]) ).
cnf(cls_in__mktop_0,axiom,
~ c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
input ).
fof(cls_in__mktop_0_0,plain,
! [V_L,V_x,V_y] :
( ~ c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| $false ),
inference(orientation,[status(thm)],[cls_in__mktop_0]) ).
cnf(cls_in__mktop_1,axiom,
~ c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
input ).
fof(cls_in__mktop_1_0,plain,
! [V_L,V_x] :
( ~ c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| $false ),
inference(orientation,[status(thm)],[cls_in__mktop_1]) ).
cnf(cls_IdI_0,axiom,
c_in(c_Pair(V_a,V_a,T_a,T_a),c_Relation_OId(T_a),tc_prod(T_a,T_a)),
input ).
fof(cls_IdI_0_0,plain,
! [T_a,V_a] :
( c_in(c_Pair(V_a,V_a,T_a,T_a),c_Relation_OId(T_a),tc_prod(T_a,T_a))
| $false ),
inference(orientation,[status(thm)],[cls_IdI_0]) ).
cnf(cls_pair__in__Id__conv_1,axiom,
c_in(c_Pair(V_x,V_x,T_a,T_a),c_Relation_OId(T_a),tc_prod(T_a,T_a)),
input ).
fof(cls_pair__in__Id__conv_1_0,plain,
! [T_a,V_x] :
( c_in(c_Pair(V_x,V_x,T_a,T_a),c_Relation_OId(T_a),tc_prod(T_a,T_a))
| $false ),
inference(orientation,[status(thm)],[cls_pair__in__Id__conv_1]) ).
cnf(cls_Range__def_0,axiom,
c_Relation_ORange(V_r,T_b,T_a) = c_Relation_ODomain(c_Relation_Oconverse(V_r,T_b,T_a),T_a,T_b),
input ).
fof(cls_Range__def_0_0,plain,
! [T_a,T_b,V_r] :
( c_Relation_ORange(V_r,T_b,T_a) = c_Relation_ODomain(c_Relation_Oconverse(V_r,T_b,T_a),T_a,T_b)
| $false ),
inference(orientation,[status(thm)],[cls_Range__def_0]) ).
cnf(cls_Domain__converse_0,axiom,
c_Relation_ODomain(c_Relation_Oconverse(V_r,T_b,T_a),T_a,T_b) = c_Relation_ORange(V_r,T_b,T_a),
input ).
fof(cls_Domain__converse_0_0,plain,
! [T_a,T_b,V_r] :
( c_Relation_ODomain(c_Relation_Oconverse(V_r,T_b,T_a),T_a,T_b) = c_Relation_ORange(V_r,T_b,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_Domain__converse_0]) ).
cnf(cls_converse__converse_0,axiom,
c_Relation_Oconverse(c_Relation_Oconverse(V_r,T_a,T_b),T_b,T_a) = V_r,
input ).
fof(cls_converse__converse_0_0,plain,
! [T_a,T_b,V_r] :
( c_Relation_Oconverse(c_Relation_Oconverse(V_r,T_a,T_b),T_b,T_a) = V_r
| $false ),
inference(orientation,[status(thm)],[cls_converse__converse_0]) ).
cnf(cls_Range__Id__on_0,axiom,
c_Relation_ORange(c_Relation_OId__on(V_A,T_a),T_a,T_a) = V_A,
input ).
fof(cls_Range__Id__on_0_0,plain,
! [T_a,V_A] :
( c_Relation_ORange(c_Relation_OId__on(V_A,T_a),T_a,T_a) = V_A
| $false ),
inference(orientation,[status(thm)],[cls_Range__Id__on_0]) ).
cnf(cls_Range__converse_0,axiom,
c_Relation_ORange(c_Relation_Oconverse(V_r,T_a,T_b),T_b,T_a) = c_Relation_ODomain(V_r,T_a,T_b),
input ).
fof(cls_Range__converse_0_0,plain,
! [T_a,T_b,V_r] :
( c_Relation_ORange(c_Relation_Oconverse(V_r,T_a,T_b),T_b,T_a) = c_Relation_ODomain(V_r,T_a,T_b)
| $false ),
inference(orientation,[status(thm)],[cls_Range__converse_0]) ).
cnf(cls_converse__Id__on_0,axiom,
c_Relation_Oconverse(c_Relation_OId__on(V_A,T_a),T_a,T_a) = c_Relation_OId__on(V_A,T_a),
input ).
fof(cls_converse__Id__on_0_0,plain,
! [T_a,V_A] :
( c_Relation_Oconverse(c_Relation_OId__on(V_A,T_a),T_a,T_a) = c_Relation_OId__on(V_A,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_converse__Id__on_0]) ).
cnf(cls_trancl__converse_0,axiom,
c_Transitive__Closure_Otrancl(c_Relation_Oconverse(V_r,T_a,T_a),T_a) = c_Relation_Oconverse(c_Transitive__Closure_Otrancl(V_r,T_a),T_a,T_a),
input ).
fof(cls_trancl__converse_0_0,plain,
! [T_a,V_r] :
( c_Transitive__Closure_Otrancl(c_Relation_Oconverse(V_r,T_a,T_a),T_a) = c_Relation_Oconverse(c_Transitive__Closure_Otrancl(V_r,T_a),T_a,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_trancl__converse_0]) ).
cnf(cls_converse__inv__image_0,axiom,
c_Relation_Oconverse(c_Relation_Oinv__image(V_R,V_f,T_b,T_a),T_a,T_a) = c_Relation_Oinv__image(c_Relation_Oconverse(V_R,T_b,T_b),V_f,T_b,T_a),
input ).
fof(cls_converse__inv__image_0_0,plain,
! [T_a,T_b,V_R,V_f] :
( c_Relation_Oconverse(c_Relation_Oinv__image(V_R,V_f,T_b,T_a),T_a,T_a) = c_Relation_Oinv__image(c_Relation_Oconverse(V_R,T_b,T_b),V_f,T_b,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_converse__inv__image_0]) ).
cnf(cls_O__assoc_0,axiom,
c_Relation_Orel__comp(c_Relation_Orel__comp(V_R,V_S,T_a,T_d,T_c),V_T,T_a,T_c,T_b) = c_Relation_Orel__comp(V_R,c_Relation_Orel__comp(V_S,V_T,T_d,T_c,T_b),T_a,T_d,T_b),
input ).
fof(cls_O__assoc_0_0,plain,
! [T_a,T_b,T_c,T_d,V_R,V_S,V_T] :
( c_Relation_Orel__comp(c_Relation_Orel__comp(V_R,V_S,T_a,T_d,T_c),V_T,T_a,T_c,T_b) = c_Relation_Orel__comp(V_R,c_Relation_Orel__comp(V_S,V_T,T_d,T_c,T_b),T_a,T_d,T_b)
| $false ),
inference(orientation,[status(thm)],[cls_O__assoc_0]) ).
cnf(cls_converse__Id_0,axiom,
c_Relation_Oconverse(c_Relation_OId(T_a),T_a,T_a) = c_Relation_OId(T_a),
input ).
fof(cls_converse__Id_0_0,plain,
! [T_a] :
( c_Relation_Oconverse(c_Relation_OId(T_a),T_a,T_a) = c_Relation_OId(T_a)
| $false ),
inference(orientation,[status(thm)],[cls_converse__Id_0]) ).
cnf(cls_refl__on__Id__on_0,axiom,
c_Relation_Orefl__on(V_A,c_Relation_OId__on(V_A,T_a),T_a),
input ).
fof(cls_refl__on__Id__on_0_0,plain,
! [T_a,V_A] :
( c_Relation_Orefl__on(V_A,c_Relation_OId__on(V_A,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_refl__on__Id__on_0]) ).
cnf(cls_sym__Id__on_0,axiom,
c_Relation_Osym(c_Relation_OId__on(V_A,T_a),T_a),
input ).
fof(cls_sym__Id__on_0_0,plain,
! [T_a,V_A] :
( c_Relation_Osym(c_Relation_OId__on(V_A,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_sym__Id__on_0]) ).
cnf(cls_converse__rel__comp_0,axiom,
c_Relation_Oconverse(c_Relation_Orel__comp(V_r,V_s,T_b,T_c,T_a),T_b,T_a) = c_Relation_Orel__comp(c_Relation_Oconverse(V_s,T_c,T_a),c_Relation_Oconverse(V_r,T_b,T_c),T_a,T_c,T_b),
input ).
fof(cls_converse__rel__comp_0_0,plain,
! [T_a,T_b,T_c,V_r,V_s] :
( c_Relation_Oconverse(c_Relation_Orel__comp(V_r,V_s,T_b,T_c,T_a),T_b,T_a) = c_Relation_Orel__comp(c_Relation_Oconverse(V_s,T_c,T_a),c_Relation_Oconverse(V_r,T_b,T_c),T_a,T_c,T_b)
| $false ),
inference(orientation,[status(thm)],[cls_converse__rel__comp_0]) ).
cnf(cls_trancl__range_0,axiom,
c_Relation_ORange(c_Transitive__Closure_Otrancl(V_r,T_a),T_a,T_a) = c_Relation_ORange(V_r,T_a,T_a),
input ).
fof(cls_trancl__range_0_0,plain,
! [T_a,V_r] :
( c_Relation_ORange(c_Transitive__Closure_Otrancl(V_r,T_a),T_a,T_a) = c_Relation_ORange(V_r,T_a,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_trancl__range_0]) ).
cnf(cls_Domain__Id__on_0,axiom,
c_Relation_ODomain(c_Relation_OId__on(V_A,T_a),T_a,T_a) = V_A,
input ).
fof(cls_Domain__Id__on_0_0,plain,
! [T_a,V_A] :
( c_Relation_ODomain(c_Relation_OId__on(V_A,T_a),T_a,T_a) = V_A
| $false ),
inference(orientation,[status(thm)],[cls_Domain__Id__on_0]) ).
cnf(cls_Image__Id_0,axiom,
c_Relation_OImage(c_Relation_OId(T_a),V_A,T_a,T_a) = V_A,
input ).
fof(cls_Image__Id_0_0,plain,
! [T_a,V_A] :
( c_Relation_OImage(c_Relation_OId(T_a),V_A,T_a,T_a) = V_A
| $false ),
inference(orientation,[status(thm)],[cls_Image__Id_0]) ).
cnf(cls_R__O__Id_0,axiom,
c_Relation_Orel__comp(V_R,c_Relation_OId(T_b),T_a,T_b,T_b) = V_R,
input ).
fof(cls_R__O__Id_0_0,plain,
! [T_a,T_b,V_R] :
( c_Relation_Orel__comp(V_R,c_Relation_OId(T_b),T_a,T_b,T_b) = V_R
| $false ),
inference(orientation,[status(thm)],[cls_R__O__Id_0]) ).
cnf(cls_Id__O__R_0,axiom,
c_Relation_Orel__comp(c_Relation_OId(T_a),V_R,T_a,T_a,T_b) = V_R,
input ).
fof(cls_Id__O__R_0_0,plain,
! [T_a,T_b,V_R] :
( c_Relation_Orel__comp(c_Relation_OId(T_a),V_R,T_a,T_a,T_b) = V_R
| $false ),
inference(orientation,[status(thm)],[cls_Id__O__R_0]) ).
cnf(cls_sym__Id_0,axiom,
c_Relation_Osym(c_Relation_OId(T_a),T_a),
input ).
fof(cls_sym__Id_0_0,plain,
! [T_a] :
( c_Relation_Osym(c_Relation_OId(T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_sym__Id_0]) ).
cnf(cls_trancl__domain_0,axiom,
c_Relation_ODomain(c_Transitive__Closure_Otrancl(V_r,T_a),T_a,T_a) = c_Relation_ODomain(V_r,T_a,T_a),
input ).
fof(cls_trancl__domain_0_0,plain,
! [T_a,V_r] :
( c_Relation_ODomain(c_Transitive__Closure_Otrancl(V_r,T_a),T_a,T_a) = c_Relation_ODomain(V_r,T_a,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_trancl__domain_0]) ).
cnf(cls_Range__def__raw_0,axiom,
c_Relation_ORange(v_r,t_a,t_b) = c_Relation_ODomain(c_Relation_Oconverse(v_r,t_a,t_b),t_b,t_a),
input ).
fof(cls_Range__def__raw_0_0,plain,
( c_Relation_ORange(v_r,t_a,t_b) = c_Relation_ODomain(c_Relation_Oconverse(v_r,t_a,t_b),t_b,t_a)
| $false ),
inference(orientation,[status(thm)],[cls_Range__def__raw_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_Id__on__subset__Times_0,axiom,
c_lessequals(c_Relation_OId__on(V_A,T_a),c_Product__Type_OSigma(V_A,c_COMBK(V_A,tc_fun(T_a,tc_bool),T_a),T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),
input ).
fof(cls_Id__on__subset__Times_0_0,plain,
! [T_a,V_A] :
( c_lessequals(c_Relation_OId__on(V_A,T_a),c_Product__Type_OSigma(V_A,c_COMBK(V_A,tc_fun(T_a,tc_bool),T_a),T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Id__on__subset__Times_0]) ).
cnf(cls_r__comp__rtrancl__eq_0,axiom,
c_Relation_Orel__comp(V_r,c_Transitive__Closure_Ortrancl(V_r,T_a),T_a,T_a,T_a) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(V_r,T_a),V_r,T_a,T_a,T_a),
input ).
fof(cls_r__comp__rtrancl__eq_0_0,plain,
! [T_a,V_r] :
( c_Relation_Orel__comp(V_r,c_Transitive__Closure_Ortrancl(V_r,T_a),T_a,T_a,T_a) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(V_r,T_a),V_r,T_a,T_a,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_r__comp__rtrancl__eq_0]) ).
cnf(cls_rtrancl__trancl__absorb_0,axiom,
c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(V_R,T_a),T_a) = c_Transitive__Closure_Ortrancl(V_R,T_a),
input ).
fof(cls_rtrancl__trancl__absorb_0_0,plain,
! [T_a,V_R] :
( c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(V_R,T_a),T_a) = c_Transitive__Closure_Ortrancl(V_R,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_rtrancl__trancl__absorb_0]) ).
cnf(cls_rtrancl__idemp__self__comp_0,axiom,
c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(V_R,T_a),c_Transitive__Closure_Ortrancl(V_R,T_a),T_a,T_a,T_a) = c_Transitive__Closure_Ortrancl(V_R,T_a),
input ).
fof(cls_rtrancl__idemp__self__comp_0_0,plain,
! [T_a,V_R] :
( c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(V_R,T_a),c_Transitive__Closure_Ortrancl(V_R,T_a),T_a,T_a,T_a) = c_Transitive__Closure_Ortrancl(V_R,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_rtrancl__idemp__self__comp_0]) ).
cnf(cls_rtrancl__converse_0,axiom,
c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(V_r,T_a,T_a),T_a) = c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(V_r,T_a),T_a,T_a),
input ).
fof(cls_rtrancl__converse_0_0,plain,
! [T_a,V_r] :
( c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(V_r,T_a,T_a),T_a) = c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(V_r,T_a),T_a,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_rtrancl__converse_0]) ).
cnf(cls_equalityE_0,axiom,
c_lessequals(V_x,V_x,tc_fun(T_a,tc_bool)),
input ).
fof(cls_equalityE_0_0,plain,
! [T_a,V_x] :
( c_lessequals(V_x,V_x,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_equalityE_0]) ).
cnf(cls_subset__refl_0,axiom,
c_lessequals(V_A,V_A,tc_fun(T_a,tc_bool)),
input ).
fof(cls_subset__refl_0_0,plain,
! [T_a,V_A] :
( c_lessequals(V_A,V_A,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_subset__refl_0]) ).
cnf(cls_trancl__rtrancl__absorb_0,axiom,
c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(V_R,T_a),T_a) = c_Transitive__Closure_Ortrancl(V_R,T_a),
input ).
fof(cls_trancl__rtrancl__absorb_0_0,plain,
! [T_a,V_R] :
( c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(V_R,T_a),T_a) = c_Transitive__Closure_Ortrancl(V_R,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_trancl__rtrancl__absorb_0]) ).
cnf(cls_rtrancl__idemp_0,axiom,
c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(V_r,T_a),T_a) = c_Transitive__Closure_Ortrancl(V_r,T_a),
input ).
fof(cls_rtrancl__idemp_0_0,plain,
! [T_a,V_r] :
( c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(V_r,T_a),T_a) = c_Transitive__Closure_Ortrancl(V_r,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_rtrancl__idemp_0]) ).
cnf(cls_rtrancl__eq__or__trancl_1,axiom,
c_in(c_Pair(V_x,V_x,T_a,T_a),c_Transitive__Closure_Ortrancl(V_R,T_a),tc_prod(T_a,T_a)),
input ).
fof(cls_rtrancl__eq__or__trancl_1_0,plain,
! [T_a,V_R,V_x] :
( c_in(c_Pair(V_x,V_x,T_a,T_a),c_Transitive__Closure_Ortrancl(V_R,T_a),tc_prod(T_a,T_a))
| $false ),
inference(orientation,[status(thm)],[cls_rtrancl__eq__or__trancl_1]) ).
cnf(cls_rtrancl_Ortrancl__refl_0,axiom,
c_in(c_Pair(V_a,V_a,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)),
input ).
fof(cls_rtrancl_Ortrancl__refl_0_0,plain,
! [T_a,V_a,V_r] :
( c_in(c_Pair(V_a,V_a,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| $false ),
inference(orientation,[status(thm)],[cls_rtrancl_Ortrancl__refl_0]) ).
cnf(cls_trancl__unfold__right_0,axiom,
c_Transitive__Closure_Otrancl(V_r,T_a) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(V_r,T_a),V_r,T_a,T_a,T_a),
input ).
fof(cls_trancl__unfold__right_0_0,plain,
! [T_a,V_r] :
( c_Transitive__Closure_Otrancl(V_r,T_a) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(V_r,T_a),V_r,T_a,T_a,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_trancl__unfold__right_0]) ).
cnf(cls_trancl__unfold__left_0,axiom,
c_Transitive__Closure_Otrancl(V_r,T_a) = c_Relation_Orel__comp(V_r,c_Transitive__Closure_Ortrancl(V_r,T_a),T_a,T_a,T_a),
input ).
fof(cls_trancl__unfold__left_0_0,plain,
! [T_a,V_r] :
( c_Transitive__Closure_Otrancl(V_r,T_a) = c_Relation_Orel__comp(V_r,c_Transitive__Closure_Ortrancl(V_r,T_a),T_a,T_a,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_trancl__unfold__left_0]) ).
cnf(cls_trancl__subset__Field2_0,axiom,
c_lessequals(c_Transitive__Closure_Otrancl(V_r,T_a),c_Product__Type_OSigma(c_Relation_OField(V_r,T_a),c_COMBK(c_Relation_OField(V_r,T_a),tc_fun(T_a,tc_bool),T_a),T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),
input ).
fof(cls_trancl__subset__Field2_0_0,plain,
! [T_a,V_r] :
( c_lessequals(c_Transitive__Closure_Otrancl(V_r,T_a),c_Product__Type_OSigma(c_Relation_OField(V_r,T_a),c_COMBK(c_Relation_OField(V_r,T_a),tc_fun(T_a,tc_bool),T_a),T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_trancl__subset__Field2_0]) ).
cnf(cls_rtrancl__unfold_0,axiom,
c_Transitive__Closure_Ortrancl(V_r,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(T_a),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(V_r,T_a),V_r,T_a,T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),
input ).
fof(cls_rtrancl__unfold_0_0,plain,
! [T_a,V_r] :
( c_Transitive__Closure_Ortrancl(V_r,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(T_a),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(V_r,T_a),V_r,T_a,T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_rtrancl__unfold_0]) ).
cnf(cls_Nitpick_Ortrancl__def_0,axiom,
c_Transitive__Closure_Ortrancl(V_r,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(V_r,T_a),c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),
input ).
fof(cls_Nitpick_Ortrancl__def_0_0,plain,
! [T_a,V_r] :
( c_Transitive__Closure_Ortrancl(V_r,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(V_r,T_a),c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Nitpick_Ortrancl__def_0]) ).
cnf(cls_Image__Id__on_0,axiom,
c_Relation_OImage(c_Relation_OId__on(V_A,T_a),V_B,T_a,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),
input ).
fof(cls_Image__Id__on_0_0,plain,
! [T_a,V_A,V_B] :
( c_Relation_OImage(c_Relation_OId__on(V_A,T_a),V_B,T_a,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Image__Id__on_0]) ).
cnf(cls_sym__Int__converse_0,axiom,
c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(V_r,c_Relation_Oconverse(V_r,T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a),
input ).
fof(cls_sym__Int__converse_0_0,plain,
! [T_a,V_r] :
( c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(V_r,c_Relation_Oconverse(V_r,T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_sym__Int__converse_0]) ).
cnf(cls_sym__Un__converse_0,axiom,
c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(V_r,c_Relation_Oconverse(V_r,T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a),
input ).
fof(cls_sym__Un__converse_0_0,plain,
! [T_a,V_r] :
( c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(V_r,c_Relation_Oconverse(V_r,T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_sym__Un__converse_0]) ).
cnf(cls_trancl__unfold_0,axiom,
c_Transitive__Closure_Otrancl(V_r,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_r,c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(V_r,T_a),V_r,T_a,T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),
input ).
fof(cls_trancl__unfold_0_0,plain,
! [T_a,V_r] :
( c_Transitive__Closure_Otrancl(V_r,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_r,c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(V_r,T_a),V_r,T_a,T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_trancl__unfold_0]) ).
cnf(cls_image__Un_0,axiom,
c_Set_Oimage(V_f,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(V_f,V_A,T_b,T_a),c_Set_Oimage(V_f,V_B,T_b,T_a),tc_fun(T_a,tc_bool)),
input ).
fof(cls_image__Un_0_0,plain,
! [T_a,T_b,V_A,V_B,V_f] :
( c_Set_Oimage(V_f,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(V_f,V_A,T_b,T_a),c_Set_Oimage(V_f,V_B,T_b,T_a),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_image__Un_0]) ).
cnf(cls_Field__def_0,axiom,
c_Relation_OField(V_r,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(V_r,T_a,T_a),c_Relation_ORange(V_r,T_a,T_a),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Field__def_0_0,plain,
! [T_a,V_r] :
( c_Relation_OField(V_r,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(V_r,T_a,T_a),c_Relation_ORange(V_r,T_a,T_a),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Field__def_0]) ).
cnf(cls_Int__absorb_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,V_A,tc_fun(T_a,tc_bool)) = V_A,
input ).
fof(cls_Int__absorb_0_0,plain,
! [T_a,V_A] :
( c_Lattices_Olower__semilattice__class_Oinf(V_A,V_A,tc_fun(T_a,tc_bool)) = V_A
| $false ),
inference(orientation,[status(thm)],[cls_Int__absorb_0]) ).
cnf(cls_Range__Un__eq_0,axiom,
c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(tc_prod(T_b,T_a),tc_bool)),T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(V_A,T_b,T_a),c_Relation_ORange(V_B,T_b,T_a),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Range__Un__eq_0_0,plain,
! [T_a,T_b,V_A,V_B] :
( c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(tc_prod(T_b,T_a),tc_bool)),T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(V_A,T_b,T_a),c_Relation_ORange(V_B,T_b,T_a),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Range__Un__eq_0]) ).
cnf(cls_Int__left__absorb_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),
input ).
fof(cls_Int__left__absorb_0_0,plain,
! [T_a,V_A,V_B] :
( c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Int__left__absorb_0]) ).
cnf(cls_insert__code_1,axiom,
hBOOL(hAPP(c_Set_Oinsert(V_x,V_A,T_a),V_x)),
input ).
fof(cls_insert__code_1_0,plain,
! [T_a,V_A,V_x] :
( hBOOL(hAPP(c_Set_Oinsert(V_x,V_A,T_a),V_x))
| $false ),
inference(orientation,[status(thm)],[cls_insert__code_1]) ).
cnf(cls_Un__Int__distrib2_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Un__Int__distrib2_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__Int__distrib2_0]) ).
cnf(cls_Un__Int__distrib_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Un__Int__distrib_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__Int__distrib_0]) ).
cnf(cls_Times__Un__distrib1_0,axiom,
c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),c_COMBK(V_C,tc_fun(T_b,tc_bool),T_a),T_a,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(V_A,c_COMBK(V_C,tc_fun(T_b,tc_bool),T_a),T_a,T_b),c_Product__Type_OSigma(V_B,c_COMBK(V_C,tc_fun(T_b,tc_bool),T_a),T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool)),
input ).
fof(cls_Times__Un__distrib1_0_0,plain,
! [T_a,T_b,V_A,V_B,V_C] :
( c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),c_COMBK(V_C,tc_fun(T_b,tc_bool),T_a),T_a,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(V_A,c_COMBK(V_C,tc_fun(T_b,tc_bool),T_a),T_a,T_b),c_Product__Type_OSigma(V_B,c_COMBK(V_C,tc_fun(T_b,tc_bool),T_a),T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Times__Un__distrib1_0]) ).
cnf(cls_Int__lower2_0,axiom,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)),
input ).
fof(cls_Int__lower2_0_0,plain,
! [T_a,V_A,V_B] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Int__lower2_0]) ).
cnf(cls_Int__lower1_0,axiom,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)),
input ).
fof(cls_Int__lower1_0_0,plain,
! [T_a,V_A,V_B] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Int__lower1_0]) ).
cnf(cls_converse__Un_0,axiom,
c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(V_r,V_s,tc_fun(tc_prod(T_b,T_a),tc_bool)),T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Oconverse(V_r,T_b,T_a),c_Relation_Oconverse(V_s,T_b,T_a),tc_fun(tc_prod(T_a,T_b),tc_bool)),
input ).
fof(cls_converse__Un_0_0,plain,
! [T_a,T_b,V_r,V_s] :
( c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(V_r,V_s,tc_fun(tc_prod(T_b,T_a),tc_bool)),T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Oconverse(V_r,T_b,T_a),c_Relation_Oconverse(V_s,T_b,T_a),tc_fun(tc_prod(T_a,T_b),tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_converse__Un_0]) ).
cnf(cls_image__insert_0,axiom,
c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a),
input ).
fof(cls_image__insert_0_0,plain,
! [T_a,T_b,V_B,V_a,V_f] :
( c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_image__insert_0]) ).
cnf(cls_insert__times__insert_0,axiom,
c_Product__Type_OSigma(c_Set_Oinsert(V_a,V_A,T_a),c_COMBK(c_Set_Oinsert(V_b,V_B,T_b),tc_fun(T_b,tc_bool),T_a),T_a,T_b) = c_Set_Oinsert(c_Pair(V_a,V_b,T_a,T_b),c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(V_A,c_COMBK(c_Set_Oinsert(V_b,V_B,T_b),tc_fun(T_b,tc_bool),T_a),T_a,T_b),c_Product__Type_OSigma(c_Set_Oinsert(V_a,V_A,T_a),c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool)),tc_prod(T_a,T_b)),
input ).
fof(cls_insert__times__insert_0_0,plain,
! [T_a,T_b,V_A,V_B,V_a,V_b] :
( c_Product__Type_OSigma(c_Set_Oinsert(V_a,V_A,T_a),c_COMBK(c_Set_Oinsert(V_b,V_B,T_b),tc_fun(T_b,tc_bool),T_a),T_a,T_b) = c_Set_Oinsert(c_Pair(V_a,V_b,T_a,T_b),c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(V_A,c_COMBK(c_Set_Oinsert(V_b,V_B,T_b),tc_fun(T_b,tc_bool),T_a),T_a,T_b),c_Product__Type_OSigma(c_Set_Oinsert(V_a,V_A,T_a),c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool)),tc_prod(T_a,T_b))
| $false ),
inference(orientation,[status(thm)],[cls_insert__times__insert_0]) ).
cnf(cls_trans__Id_0,axiom,
c_Relation_Otrans(c_Relation_OId(T_a),T_a),
input ).
fof(cls_trans__Id_0_0,plain,
! [T_a] :
( c_Relation_Otrans(c_Relation_OId(T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_trans__Id_0]) ).
cnf(cls_Int__left__commute_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_B,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Int__left__commute_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_B,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Int__left__commute_0]) ).
cnf(cls_Int__assoc_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Int__assoc_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Int__assoc_0]) ).
cnf(cls_Times__Int__distrib1_0,axiom,
c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),c_COMBK(V_C,tc_fun(T_b,tc_bool),T_a),T_a,T_b) = c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(V_A,c_COMBK(V_C,tc_fun(T_b,tc_bool),T_a),T_a,T_b),c_Product__Type_OSigma(V_B,c_COMBK(V_C,tc_fun(T_b,tc_bool),T_a),T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool)),
input ).
fof(cls_Times__Int__distrib1_0_0,plain,
! [T_a,T_b,V_A,V_B,V_C] :
( c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),c_COMBK(V_C,tc_fun(T_b,tc_bool),T_a),T_a,T_b) = c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(V_A,c_COMBK(V_C,tc_fun(T_b,tc_bool),T_a),T_a,T_b),c_Product__Type_OSigma(V_B,c_COMBK(V_C,tc_fun(T_b,tc_bool),T_a),T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Times__Int__distrib1_0]) ).
cnf(cls_Image__Int__subset_0,axiom,
c_lessequals(c_Relation_OImage(V_R,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(V_R,V_A,T_b,T_a),c_Relation_OImage(V_R,V_B,T_b,T_a),tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Image__Int__subset_0_0,plain,
! [T_a,T_b,V_A,V_B,V_R] :
( c_lessequals(c_Relation_OImage(V_R,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(V_R,V_A,T_b,T_a),c_Relation_OImage(V_R,V_B,T_b,T_a),tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Image__Int__subset_0]) ).
cnf(cls_image__Int__subset_0,axiom,
c_lessequals(c_Set_Oimage(V_f,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(V_f,V_A,T_b,T_a),c_Set_Oimage(V_f,V_B,T_b,T_a),tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_image__Int__subset_0_0,plain,
! [T_a,T_b,V_A,V_B,V_f] :
( c_lessequals(c_Set_Oimage(V_f,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(V_f,V_A,T_b,T_a),c_Set_Oimage(V_f,V_B,T_b,T_a),tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_image__Int__subset_0]) ).
cnf(cls_subset__insertI_0,axiom,
c_lessequals(V_B,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)),
input ).
fof(cls_subset__insertI_0_0,plain,
! [T_a,V_B,V_a] :
( c_lessequals(V_B,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_subset__insertI_0]) ).
cnf(cls_Domain__Int__subset_0,axiom,
c_lessequals(c_Relation_ODomain(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(tc_prod(T_a,T_b),tc_bool)),T_a,T_b),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(V_A,T_a,T_b),c_Relation_ODomain(V_B,T_a,T_b),tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Domain__Int__subset_0_0,plain,
! [T_a,T_b,V_A,V_B] :
( c_lessequals(c_Relation_ODomain(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(tc_prod(T_a,T_b),tc_bool)),T_a,T_b),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(V_A,T_a,T_b),c_Relation_ODomain(V_B,T_a,T_b),tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Domain__Int__subset_0]) ).
cnf(cls_trancl__reflcl_0,axiom,
c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) = c_Transitive__Closure_Ortrancl(V_r,T_a),
input ).
fof(cls_trancl__reflcl_0_0,plain,
! [T_a,V_r] :
( c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) = c_Transitive__Closure_Ortrancl(V_r,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_trancl__reflcl_0]) ).
cnf(cls_reflcl__trancl_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(V_r,T_a),c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) = c_Transitive__Closure_Ortrancl(V_r,T_a),
input ).
fof(cls_reflcl__trancl_0_0,plain,
! [T_a,V_r] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(V_r,T_a),c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) = c_Transitive__Closure_Ortrancl(V_r,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_reflcl__trancl_0]) ).
cnf(cls_insertCI_1,axiom,
c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a),
input ).
fof(cls_insertCI_1_0,plain,
! [T_a,V_B,V_x] :
( c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_insertCI_1]) ).
cnf(cls_insertI1_0,axiom,
c_in(V_a,c_Set_Oinsert(V_a,V_B,T_a),T_a),
input ).
fof(cls_insertI1_0_0,plain,
! [T_a,V_B,V_a] :
( c_in(V_a,c_Set_Oinsert(V_a,V_B,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_insertI1_0]) ).
cnf(cls_insert__iff_1,axiom,
c_in(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a),
input ).
fof(cls_insert__iff_1_0,plain,
! [T_a,V_A,V_x] :
( c_in(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_insert__iff_1]) ).
cnf(cls_Range__insert_0,axiom,
c_Relation_ORange(c_Set_Oinsert(c_Pair(V_a,V_b,T_b,T_a),V_r,tc_prod(T_b,T_a)),T_b,T_a) = c_Set_Oinsert(V_b,c_Relation_ORange(V_r,T_b,T_a),T_a),
input ).
fof(cls_Range__insert_0_0,plain,
! [T_a,T_b,V_a,V_b,V_r] :
( c_Relation_ORange(c_Set_Oinsert(c_Pair(V_a,V_b,T_b,T_a),V_r,tc_prod(T_b,T_a)),T_b,T_a) = c_Set_Oinsert(V_b,c_Relation_ORange(V_r,T_b,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_Range__insert_0]) ).
cnf(cls_rtrancl__Un__rtrancl_0,axiom,
c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(V_R,T_a),c_Transitive__Closure_Ortrancl(V_S,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(V_R,V_S,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a),
input ).
fof(cls_rtrancl__Un__rtrancl_0_0,plain,
! [T_a,V_R,V_S] :
( c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(V_R,T_a),c_Transitive__Closure_Ortrancl(V_S,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(V_R,V_S,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_rtrancl__Un__rtrancl_0]) ).
cnf(cls_Range__Int__subset_0,axiom,
c_lessequals(c_Relation_ORange(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(tc_prod(T_b,T_a),tc_bool)),T_b,T_a),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(V_A,T_b,T_a),c_Relation_ORange(V_B,T_b,T_a),tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Range__Int__subset_0_0,plain,
! [T_a,T_b,V_A,V_B] :
( c_lessequals(c_Relation_ORange(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(tc_prod(T_b,T_a),tc_bool)),T_b,T_a),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(V_A,T_b,T_a),c_Relation_ORange(V_B,T_b,T_a),tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Range__Int__subset_0]) ).
cnf(cls_Un__left__absorb_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),
input ).
fof(cls_Un__left__absorb_0_0,plain,
! [T_a,V_A,V_B] :
( c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__left__absorb_0]) ).
cnf(cls_Domain__Un__eq_0,axiom,
c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(tc_prod(T_a,T_b),tc_bool)),T_a,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(V_A,T_a,T_b),c_Relation_ODomain(V_B,T_a,T_b),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Domain__Un__eq_0_0,plain,
! [T_a,T_b,V_A,V_B] :
( c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(tc_prod(T_a,T_b),tc_bool)),T_a,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(V_A,T_a,T_b),c_Relation_ODomain(V_B,T_a,T_b),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Domain__Un__eq_0]) ).
cnf(cls_Un__commute_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool)),
input ).
fof(cls_Un__commute_0_0,plain,
! [T_a,V_A,V_B] :
( c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__commute_0]) ).
cnf(cls_Field__def__raw_0,axiom,
c_Relation_OField(v_r,t_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(v_r,t_a,t_a),c_Relation_ORange(v_r,t_a,t_a),tc_fun(t_a,tc_bool)),
input ).
fof(cls_Field__def__raw_0_0,plain,
( c_Relation_OField(v_r,t_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(v_r,t_a,t_a),c_Relation_ORange(v_r,t_a,t_a),tc_fun(t_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Field__def__raw_0]) ).
cnf(cls_Field__Un_0,axiom,
c_Relation_OField(c_Lattices_Oupper__semilattice__class_Osup(V_r,V_s,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OField(V_r,T_a),c_Relation_OField(V_s,T_a),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Field__Un_0_0,plain,
! [T_a,V_r,V_s] :
( c_Relation_OField(c_Lattices_Oupper__semilattice__class_Osup(V_r,V_s,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OField(V_r,T_a),c_Relation_OField(V_s,T_a),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Field__Un_0]) ).
cnf(cls_trans__Id__on_0,axiom,
c_Relation_Otrans(c_Relation_OId__on(V_A,T_a),T_a),
input ).
fof(cls_trans__Id__on_0_0,plain,
! [T_a,V_A] :
( c_Relation_Otrans(c_Relation_OId__on(V_A,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_trans__Id__on_0]) ).
cnf(cls_rel__comp__distrib_0,axiom,
c_Relation_Orel__comp(V_R,c_Lattices_Oupper__semilattice__class_Osup(V_S,V_T,tc_fun(tc_prod(T_c,T_b),tc_bool)),T_a,T_c,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(V_R,V_S,T_a,T_c,T_b),c_Relation_Orel__comp(V_R,V_T,T_a,T_c,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool)),
input ).
fof(cls_rel__comp__distrib_0_0,plain,
! [T_a,T_b,T_c,V_R,V_S,V_T] :
( c_Relation_Orel__comp(V_R,c_Lattices_Oupper__semilattice__class_Osup(V_S,V_T,tc_fun(tc_prod(T_c,T_b),tc_bool)),T_a,T_c,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(V_R,V_S,T_a,T_c,T_b),c_Relation_Orel__comp(V_R,V_T,T_a,T_c,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_rel__comp__distrib_0]) ).
cnf(cls_rel__comp__distrib2_0,axiom,
c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(V_S,V_T,tc_fun(tc_prod(T_a,T_c),tc_bool)),V_R,T_a,T_c,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(V_S,V_R,T_a,T_c,T_b),c_Relation_Orel__comp(V_T,V_R,T_a,T_c,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool)),
input ).
fof(cls_rel__comp__distrib2_0_0,plain,
! [T_a,T_b,T_c,V_R,V_S,V_T] :
( c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(V_S,V_T,tc_fun(tc_prod(T_a,T_c),tc_bool)),V_R,T_a,T_c,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(V_S,V_R,T_a,T_c,T_b),c_Relation_Orel__comp(V_T,V_R,T_a,T_c,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_rel__comp__distrib2_0]) ).
cnf(cls_converse__Int_0,axiom,
c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(V_r,V_s,tc_fun(tc_prod(T_b,T_a),tc_bool)),T_b,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(V_r,T_b,T_a),c_Relation_Oconverse(V_s,T_b,T_a),tc_fun(tc_prod(T_a,T_b),tc_bool)),
input ).
fof(cls_converse__Int_0_0,plain,
! [T_a,T_b,V_r,V_s] :
( c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(V_r,V_s,tc_fun(tc_prod(T_b,T_a),tc_bool)),T_b,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(V_r,T_b,T_a),c_Relation_Oconverse(V_s,T_b,T_a),tc_fun(tc_prod(T_a,T_b),tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_converse__Int_0]) ).
cnf(cls_Sigma__Un__distrib1_0,axiom,
c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(V_I,V_J,tc_fun(T_a,tc_bool)),V_C,T_a,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(V_I,V_C,T_a,T_b),c_Product__Type_OSigma(V_J,V_C,T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool)),
input ).
fof(cls_Sigma__Un__distrib1_0_0,plain,
! [T_a,T_b,V_C,V_I,V_J] :
( c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(V_I,V_J,tc_fun(T_a,tc_bool)),V_C,T_a,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(V_I,V_C,T_a,T_b),c_Product__Type_OSigma(V_J,V_C,T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Sigma__Un__distrib1_0]) ).
cnf(cls_Field__converse_0,axiom,
c_Relation_OField(c_Relation_Oconverse(V_r,T_a,T_a),T_a) = c_Relation_OField(V_r,T_a),
input ).
fof(cls_Field__converse_0_0,plain,
! [T_a,V_r] :
( c_Relation_OField(c_Relation_Oconverse(V_r,T_a,T_a),T_a) = c_Relation_OField(V_r,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_Field__converse_0]) ).
cnf(cls_Un__Int__crazy_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Un__Int__crazy_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__Int__crazy_0]) ).
cnf(cls_Int__commute_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_B,V_A,tc_fun(T_a,tc_bool)),
input ).
fof(cls_Int__commute_0_0,plain,
! [T_a,V_A,V_B] :
( c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_B,V_A,tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Int__commute_0]) ).
cnf(cls_Un__upper1_0,axiom,
c_lessequals(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Un__upper1_0_0,plain,
! [T_a,V_A,V_B] :
( c_lessequals(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__upper1_0]) ).
cnf(cls_Un__upper2_0,axiom,
c_lessequals(V_B,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Un__upper2_0_0,plain,
! [T_a,V_A,V_B] :
( c_lessequals(V_B,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__upper2_0]) ).
cnf(cls_rtrancl__reflcl__absorb_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(V_R,T_a),c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) = c_Transitive__Closure_Ortrancl(V_R,T_a),
input ).
fof(cls_rtrancl__reflcl__absorb_0_0,plain,
! [T_a,V_R] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(V_R,T_a),c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) = c_Transitive__Closure_Ortrancl(V_R,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_rtrancl__reflcl__absorb_0]) ).
cnf(cls_Un__assoc_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Un__assoc_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__assoc_0]) ).
cnf(cls_Un__left__commute_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Un__left__commute_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__left__commute_0]) ).
cnf(cls_insert__commute_0,axiom,
c_Set_Oinsert(V_x,c_Set_Oinsert(V_y,V_A,T_a),T_a) = c_Set_Oinsert(V_y,c_Set_Oinsert(V_x,V_A,T_a),T_a),
input ).
fof(cls_insert__commute_0_0,plain,
! [T_a,V_A,V_x,V_y] :
( c_Set_Oinsert(V_x,c_Set_Oinsert(V_y,V_A,T_a),T_a) = c_Set_Oinsert(V_y,c_Set_Oinsert(V_x,V_A,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_insert__commute_0]) ).
cnf(cls_Image__Un_0,axiom,
c_Relation_OImage(V_R,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(V_R,V_A,T_b,T_a),c_Relation_OImage(V_R,V_B,T_b,T_a),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Image__Un_0_0,plain,
! [T_a,T_b,V_A,V_B,V_R] :
( c_Relation_OImage(V_R,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(V_R,V_A,T_b,T_a),c_Relation_OImage(V_R,V_B,T_b,T_a),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Image__Un_0]) ).
cnf(cls_Un__Image_0,axiom,
c_Relation_OImage(c_Lattices_Oupper__semilattice__class_Osup(V_R,V_S,tc_fun(tc_prod(T_b,T_a),tc_bool)),V_A,T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(V_R,V_A,T_b,T_a),c_Relation_OImage(V_S,V_A,T_b,T_a),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Un__Image_0_0,plain,
! [T_a,T_b,V_A,V_R,V_S] :
( c_Relation_OImage(c_Lattices_Oupper__semilattice__class_Osup(V_R,V_S,tc_fun(tc_prod(T_b,T_a),tc_bool)),V_A,T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(V_R,V_A,T_b,T_a),c_Relation_OImage(V_S,V_A,T_b,T_a),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Un__Image_0]) ).
cnf(cls_Domain__insert_0,axiom,
c_Relation_ODomain(c_Set_Oinsert(c_Pair(V_a,V_b,T_a,T_b),V_r,tc_prod(T_a,T_b)),T_a,T_b) = c_Set_Oinsert(V_a,c_Relation_ODomain(V_r,T_a,T_b),T_a),
input ).
fof(cls_Domain__insert_0_0,plain,
! [T_a,T_b,V_a,V_b,V_r] :
( c_Relation_ODomain(c_Set_Oinsert(c_Pair(V_a,V_b,T_a,T_b),V_r,tc_prod(T_a,T_b)),T_a,T_b) = c_Set_Oinsert(V_a,c_Relation_ODomain(V_r,T_a,T_b),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_Domain__insert_0]) ).
cnf(cls_insert__absorb2_0,axiom,
c_Set_Oinsert(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Set_Oinsert(V_x,V_A,T_a),
input ).
fof(cls_insert__absorb2_0_0,plain,
! [T_a,V_A,V_x] :
( c_Set_Oinsert(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Set_Oinsert(V_x,V_A,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_insert__absorb2_0]) ).
cnf(cls_insert__inter__insert_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(V_a,V_A,T_a),c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),T_a),
input ).
fof(cls_insert__inter__insert_0_0,plain,
! [T_a,V_A,V_B,V_a] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(V_a,V_A,T_a),c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_insert__inter__insert_0]) ).
cnf(cls_trans__rtrancl_0,axiom,
c_Relation_Otrans(c_Transitive__Closure_Ortrancl(V_r,T_a),T_a),
input ).
fof(cls_trans__rtrancl_0_0,plain,
! [T_a,V_r] :
( c_Relation_Otrans(c_Transitive__Closure_Ortrancl(V_r,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_trans__rtrancl_0]) ).
cnf(cls_Un__insert__right_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a),
input ).
fof(cls_Un__insert__right_0_0,plain,
! [T_a,V_A,V_B,V_a] :
( c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_Un__insert__right_0]) ).
cnf(cls_Un__insert__left_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,V_B,T_a),V_C,tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),T_a),
input ).
fof(cls_Un__insert__left_0_0,plain,
! [T_a,V_B,V_C,V_a] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,V_B,T_a),V_C,tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_Un__insert__left_0]) ).
cnf(cls_rtrancl__Un__subset_0,axiom,
c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(V_R,T_a),c_Transitive__Closure_Ortrancl(V_S,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(V_R,V_S,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),
input ).
fof(cls_rtrancl__Un__subset_0_0,plain,
! [T_a,V_R,V_S] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(V_R,T_a),c_Transitive__Closure_Ortrancl(V_S,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(V_R,V_S,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a),tc_fun(tc_prod(T_a,T_a),tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_rtrancl__Un__subset_0]) ).
cnf(cls_rtrancl__reflcl_0,axiom,
c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(V_R,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) = c_Transitive__Closure_Ortrancl(V_R,T_a),
input ).
fof(cls_rtrancl__reflcl_0_0,plain,
! [T_a,V_R] :
( c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(V_R,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) = c_Transitive__Closure_Ortrancl(V_R,T_a)
| $false ),
inference(orientation,[status(thm)],[cls_rtrancl__reflcl_0]) ).
cnf(cls_Sigma__Int__distrib1_0,axiom,
c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(V_I,V_J,tc_fun(T_a,tc_bool)),V_C,T_a,T_b) = c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(V_I,V_C,T_a,T_b),c_Product__Type_OSigma(V_J,V_C,T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool)),
input ).
fof(cls_Sigma__Int__distrib1_0_0,plain,
! [T_a,T_b,V_C,V_I,V_J] :
( c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(V_I,V_J,tc_fun(T_a,tc_bool)),V_C,T_a,T_b) = c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(V_I,V_C,T_a,T_b),c_Product__Type_OSigma(V_J,V_C,T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Sigma__Int__distrib1_0]) ).
cnf(cls_Int__Un__distrib2_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_B,V_A,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Int__Un__distrib2_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_B,V_A,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Int__Un__distrib2_0]) ).
cnf(cls_Int__Un__distrib_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),
input ).
fof(cls_Int__Un__distrib_0_0,plain,
! [T_a,V_A,V_B,V_C] :
( c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| $false ),
inference(orientation,[status(thm)],[cls_Int__Un__distrib_0]) ).
cnf(cls_Un__absorb_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,V_A,tc_fun(T_a,tc_bool)) = V_A,
input ).
fof(cls_Un__absorb_0_0,plain,
! [T_a,V_A] :
( c_Lattices_Oupper__semilattice__class_Osup(V_A,V_A,tc_fun(T_a,tc_bool)) = V_A
| $false ),
inference(orientation,[status(thm)],[cls_Un__absorb_0]) ).
cnf(cls_trans__trancl_0,axiom,
c_Relation_Otrans(c_Transitive__Closure_Otrancl(V_r,T_a),T_a),
input ).
fof(cls_trans__trancl_0_0,plain,
! [T_a,V_r] :
( c_Relation_Otrans(c_Transitive__Closure_Otrancl(V_r,T_a),T_a)
| $false ),
inference(orientation,[status(thm)],[cls_trans__trancl_0]) ).
fof(def_lhs_atom1,axiom,
! [V_r,T_a] :
( lhs_atom1(V_r,T_a)
<=> c_Relation_Otrans(c_Transitive__Closure_Otrancl(V_r,T_a),T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_0,plain,
! [T_a,V_r] :
( lhs_atom1(V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_trans__trancl_0_0,def_lhs_atom1]) ).
fof(def_lhs_atom2,axiom,
! [V_A,T_a] :
( lhs_atom2(V_A,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(V_A,V_A,tc_fun(T_a,tc_bool)) = V_A ),
inference(definition,[],]) ).
fof(to_be_clausified_1,plain,
! [T_a,V_A] :
( lhs_atom2(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__absorb_0_0,def_lhs_atom2]) ).
fof(def_lhs_atom3,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom3(V_C,V_B,V_A,T_a)
<=> c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_2,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom3(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__Un__distrib_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)
<=> c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_B,V_A,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_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__Un__distrib2_0_0,def_lhs_atom4]) ).
fof(def_lhs_atom5,axiom,
! [V_J,V_I,V_C,T_b,T_a] :
( lhs_atom5(V_J,V_I,V_C,T_b,T_a)
<=> c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(V_I,V_J,tc_fun(T_a,tc_bool)),V_C,T_a,T_b) = c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(V_I,V_C,T_a,T_b),c_Product__Type_OSigma(V_J,V_C,T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_4,plain,
! [T_a,T_b,V_C,V_I,V_J] :
( lhs_atom5(V_J,V_I,V_C,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Sigma__Int__distrib1_0_0,def_lhs_atom5]) ).
fof(def_lhs_atom6,axiom,
! [V_R,T_a] :
( lhs_atom6(V_R,T_a)
<=> c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(V_R,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) = c_Transitive__Closure_Ortrancl(V_R,T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_5,plain,
! [T_a,V_R] :
( lhs_atom6(V_R,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rtrancl__reflcl_0_0,def_lhs_atom6]) ).
fof(def_lhs_atom7,axiom,
! [V_S,V_R,T_a] :
( lhs_atom7(V_S,V_R,T_a)
<=> c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(V_R,T_a),c_Transitive__Closure_Ortrancl(V_S,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(V_R,V_S,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_6,plain,
! [T_a,V_R,V_S] :
( lhs_atom7(V_S,V_R,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rtrancl__Un__subset_0_0,def_lhs_atom7]) ).
fof(def_lhs_atom8,axiom,
! [V_a,V_C,V_B,T_a] :
( lhs_atom8(V_a,V_C,V_B,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,V_B,T_a),V_C,tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_7,plain,
! [T_a,V_B,V_C,V_a] :
( lhs_atom8(V_a,V_C,V_B,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__insert__left_0_0,def_lhs_atom8]) ).
fof(def_lhs_atom9,axiom,
! [V_a,V_B,V_A,T_a] :
( lhs_atom9(V_a,V_B,V_A,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_8,plain,
! [T_a,V_A,V_B,V_a] :
( lhs_atom9(V_a,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__insert__right_0_0,def_lhs_atom9]) ).
fof(def_lhs_atom10,axiom,
! [V_r,T_a] :
( lhs_atom10(V_r,T_a)
<=> c_Relation_Otrans(c_Transitive__Closure_Ortrancl(V_r,T_a),T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_9,plain,
! [T_a,V_r] :
( lhs_atom10(V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_trans__rtrancl_0_0,def_lhs_atom10]) ).
fof(def_lhs_atom11,axiom,
! [V_a,V_B,V_A,T_a] :
( lhs_atom11(V_a,V_B,V_A,T_a)
<=> c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(V_a,V_A,T_a),c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_10,plain,
! [T_a,V_A,V_B,V_a] :
( lhs_atom11(V_a,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__inter__insert_0_0,def_lhs_atom11]) ).
fof(def_lhs_atom12,axiom,
! [V_x,V_A,T_a] :
( lhs_atom12(V_x,V_A,T_a)
<=> c_Set_Oinsert(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Set_Oinsert(V_x,V_A,T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_11,plain,
! [T_a,V_A,V_x] :
( lhs_atom12(V_x,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__absorb2_0_0,def_lhs_atom12]) ).
fof(def_lhs_atom13,axiom,
! [V_r,V_b,V_a,T_b,T_a] :
( lhs_atom13(V_r,V_b,V_a,T_b,T_a)
<=> c_Relation_ODomain(c_Set_Oinsert(c_Pair(V_a,V_b,T_a,T_b),V_r,tc_prod(T_a,T_b)),T_a,T_b) = c_Set_Oinsert(V_a,c_Relation_ODomain(V_r,T_a,T_b),T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_12,plain,
! [T_a,T_b,V_a,V_b,V_r] :
( lhs_atom13(V_r,V_b,V_a,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Domain__insert_0_0,def_lhs_atom13]) ).
fof(def_lhs_atom14,axiom,
! [V_S,V_R,V_A,T_b,T_a] :
( lhs_atom14(V_S,V_R,V_A,T_b,T_a)
<=> c_Relation_OImage(c_Lattices_Oupper__semilattice__class_Osup(V_R,V_S,tc_fun(tc_prod(T_b,T_a),tc_bool)),V_A,T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(V_R,V_A,T_b,T_a),c_Relation_OImage(V_S,V_A,T_b,T_a),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_13,plain,
! [T_a,T_b,V_A,V_R,V_S] :
( lhs_atom14(V_S,V_R,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__Image_0_0,def_lhs_atom14]) ).
fof(def_lhs_atom15,axiom,
! [V_R,V_B,V_A,T_b,T_a] :
( lhs_atom15(V_R,V_B,V_A,T_b,T_a)
<=> c_Relation_OImage(V_R,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(V_R,V_A,T_b,T_a),c_Relation_OImage(V_R,V_B,T_b,T_a),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_14,plain,
! [T_a,T_b,V_A,V_B,V_R] :
( lhs_atom15(V_R,V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Image__Un_0_0,def_lhs_atom15]) ).
fof(def_lhs_atom16,axiom,
! [V_y,V_x,V_A,T_a] :
( lhs_atom16(V_y,V_x,V_A,T_a)
<=> c_Set_Oinsert(V_x,c_Set_Oinsert(V_y,V_A,T_a),T_a) = c_Set_Oinsert(V_y,c_Set_Oinsert(V_x,V_A,T_a),T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_15,plain,
! [T_a,V_A,V_x,V_y] :
( lhs_atom16(V_y,V_x,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__commute_0_0,def_lhs_atom16]) ).
fof(def_lhs_atom17,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom17(V_C,V_B,V_A,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_16,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom17(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__left__commute_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)
<=> c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_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_Un__assoc_0_0,def_lhs_atom18]) ).
fof(def_lhs_atom19,axiom,
! [V_R,T_a] :
( lhs_atom19(V_R,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(V_R,T_a),c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) = c_Transitive__Closure_Ortrancl(V_R,T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_18,plain,
! [T_a,V_R] :
( lhs_atom19(V_R,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rtrancl__reflcl__absorb_0_0,def_lhs_atom19]) ).
fof(def_lhs_atom20,axiom,
! [V_B,V_A,T_a] :
( lhs_atom20(V_B,V_A,T_a)
<=> c_lessequals(V_B,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_19,plain,
! [T_a,V_A,V_B] :
( lhs_atom20(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__upper2_0_0,def_lhs_atom20]) ).
fof(def_lhs_atom21,axiom,
! [V_B,V_A,T_a] :
( lhs_atom21(V_B,V_A,T_a)
<=> c_lessequals(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_20,plain,
! [T_a,V_A,V_B] :
( lhs_atom21(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__upper1_0_0,def_lhs_atom21]) ).
fof(def_lhs_atom22,axiom,
! [V_B,V_A,T_a] :
( lhs_atom22(V_B,V_A,T_a)
<=> c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_B,V_A,tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_21,plain,
! [T_a,V_A,V_B] :
( lhs_atom22(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__commute_0_0,def_lhs_atom22]) ).
fof(def_lhs_atom23,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom23(V_C,V_B,V_A,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_22,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom23(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__Int__crazy_0_0,def_lhs_atom23]) ).
fof(def_lhs_atom24,axiom,
! [V_r,T_a] :
( lhs_atom24(V_r,T_a)
<=> c_Relation_OField(c_Relation_Oconverse(V_r,T_a,T_a),T_a) = c_Relation_OField(V_r,T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_23,plain,
! [T_a,V_r] :
( lhs_atom24(V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Field__converse_0_0,def_lhs_atom24]) ).
fof(def_lhs_atom25,axiom,
! [V_J,V_I,V_C,T_b,T_a] :
( lhs_atom25(V_J,V_I,V_C,T_b,T_a)
<=> c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(V_I,V_J,tc_fun(T_a,tc_bool)),V_C,T_a,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(V_I,V_C,T_a,T_b),c_Product__Type_OSigma(V_J,V_C,T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_24,plain,
! [T_a,T_b,V_C,V_I,V_J] :
( lhs_atom25(V_J,V_I,V_C,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Sigma__Un__distrib1_0_0,def_lhs_atom25]) ).
fof(def_lhs_atom26,axiom,
! [V_s,V_r,T_b,T_a] :
( lhs_atom26(V_s,V_r,T_b,T_a)
<=> c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(V_r,V_s,tc_fun(tc_prod(T_b,T_a),tc_bool)),T_b,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(V_r,T_b,T_a),c_Relation_Oconverse(V_s,T_b,T_a),tc_fun(tc_prod(T_a,T_b),tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_25,plain,
! [T_a,T_b,V_r,V_s] :
( lhs_atom26(V_s,V_r,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_converse__Int_0_0,def_lhs_atom26]) ).
fof(def_lhs_atom27,axiom,
! [V_T,V_S,V_R,T_c,T_b,T_a] :
( lhs_atom27(V_T,V_S,V_R,T_c,T_b,T_a)
<=> c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(V_S,V_T,tc_fun(tc_prod(T_a,T_c),tc_bool)),V_R,T_a,T_c,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(V_S,V_R,T_a,T_c,T_b),c_Relation_Orel__comp(V_T,V_R,T_a,T_c,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_26,plain,
! [T_a,T_b,T_c,V_R,V_S,V_T] :
( lhs_atom27(V_T,V_S,V_R,T_c,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rel__comp__distrib2_0_0,def_lhs_atom27]) ).
fof(def_lhs_atom28,axiom,
! [V_T,V_S,V_R,T_c,T_b,T_a] :
( lhs_atom28(V_T,V_S,V_R,T_c,T_b,T_a)
<=> c_Relation_Orel__comp(V_R,c_Lattices_Oupper__semilattice__class_Osup(V_S,V_T,tc_fun(tc_prod(T_c,T_b),tc_bool)),T_a,T_c,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(V_R,V_S,T_a,T_c,T_b),c_Relation_Orel__comp(V_R,V_T,T_a,T_c,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_27,plain,
! [T_a,T_b,T_c,V_R,V_S,V_T] :
( lhs_atom28(V_T,V_S,V_R,T_c,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rel__comp__distrib_0_0,def_lhs_atom28]) ).
fof(def_lhs_atom29,axiom,
! [V_A,T_a] :
( lhs_atom29(V_A,T_a)
<=> c_Relation_Otrans(c_Relation_OId__on(V_A,T_a),T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_28,plain,
! [T_a,V_A] :
( lhs_atom29(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_trans__Id__on_0_0,def_lhs_atom29]) ).
fof(def_lhs_atom30,axiom,
! [V_s,V_r,T_a] :
( lhs_atom30(V_s,V_r,T_a)
<=> c_Relation_OField(c_Lattices_Oupper__semilattice__class_Osup(V_r,V_s,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OField(V_r,T_a),c_Relation_OField(V_s,T_a),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_29,plain,
! [T_a,V_r,V_s] :
( lhs_atom30(V_s,V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Field__Un_0_0,def_lhs_atom30]) ).
fof(def_lhs_atom31,axiom,
( lhs_atom31
<=> c_Relation_OField(v_r,t_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(v_r,t_a,t_a),c_Relation_ORange(v_r,t_a,t_a),tc_fun(t_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_30,plain,
( lhs_atom31
| $false ),
inference(fold_definition,[status(thm)],[cls_Field__def__raw_0_0,def_lhs_atom31]) ).
fof(def_lhs_atom32,axiom,
! [V_B,V_A,T_a] :
( lhs_atom32(V_B,V_A,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_31,plain,
! [T_a,V_A,V_B] :
( lhs_atom32(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__commute_0_0,def_lhs_atom32]) ).
fof(def_lhs_atom33,axiom,
! [V_B,V_A,T_b,T_a] :
( lhs_atom33(V_B,V_A,T_b,T_a)
<=> c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(tc_prod(T_a,T_b),tc_bool)),T_a,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(V_A,T_a,T_b),c_Relation_ODomain(V_B,T_a,T_b),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_32,plain,
! [T_a,T_b,V_A,V_B] :
( lhs_atom33(V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Domain__Un__eq_0_0,def_lhs_atom33]) ).
fof(def_lhs_atom34,axiom,
! [V_B,V_A,T_a] :
( lhs_atom34(V_B,V_A,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_33,plain,
! [T_a,V_A,V_B] :
( lhs_atom34(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__left__absorb_0_0,def_lhs_atom34]) ).
fof(def_lhs_atom35,axiom,
! [V_B,V_A,T_b,T_a] :
( lhs_atom35(V_B,V_A,T_b,T_a)
<=> c_lessequals(c_Relation_ORange(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(tc_prod(T_b,T_a),tc_bool)),T_b,T_a),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(V_A,T_b,T_a),c_Relation_ORange(V_B,T_b,T_a),tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_34,plain,
! [T_a,T_b,V_A,V_B] :
( lhs_atom35(V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Range__Int__subset_0_0,def_lhs_atom35]) ).
fof(def_lhs_atom36,axiom,
! [V_S,V_R,T_a] :
( lhs_atom36(V_S,V_R,T_a)
<=> c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(V_R,T_a),c_Transitive__Closure_Ortrancl(V_S,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(V_R,V_S,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_35,plain,
! [T_a,V_R,V_S] :
( lhs_atom36(V_S,V_R,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rtrancl__Un__rtrancl_0_0,def_lhs_atom36]) ).
fof(def_lhs_atom37,axiom,
! [V_r,V_b,V_a,T_b,T_a] :
( lhs_atom37(V_r,V_b,V_a,T_b,T_a)
<=> c_Relation_ORange(c_Set_Oinsert(c_Pair(V_a,V_b,T_b,T_a),V_r,tc_prod(T_b,T_a)),T_b,T_a) = c_Set_Oinsert(V_b,c_Relation_ORange(V_r,T_b,T_a),T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_36,plain,
! [T_a,T_b,V_a,V_b,V_r] :
( lhs_atom37(V_r,V_b,V_a,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Range__insert_0_0,def_lhs_atom37]) ).
fof(def_lhs_atom38,axiom,
! [V_x,V_A,T_a] :
( lhs_atom38(V_x,V_A,T_a)
<=> c_in(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_37,plain,
! [T_a,V_A,V_x] :
( lhs_atom38(V_x,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__iff_1_0,def_lhs_atom38]) ).
fof(def_lhs_atom39,axiom,
! [V_a,V_B,T_a] :
( lhs_atom39(V_a,V_B,T_a)
<=> c_in(V_a,c_Set_Oinsert(V_a,V_B,T_a),T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_38,plain,
! [T_a,V_B,V_a] :
( lhs_atom39(V_a,V_B,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insertI1_0_0,def_lhs_atom39]) ).
fof(def_lhs_atom40,axiom,
! [V_x,V_B,T_a] :
( lhs_atom40(V_x,V_B,T_a)
<=> c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_39,plain,
! [T_a,V_B,V_x] :
( lhs_atom40(V_x,V_B,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insertCI_1_0,def_lhs_atom40]) ).
fof(def_lhs_atom41,axiom,
! [V_r,T_a] :
( lhs_atom41(V_r,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(V_r,T_a),c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) = c_Transitive__Closure_Ortrancl(V_r,T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_40,plain,
! [T_a,V_r] :
( lhs_atom41(V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_reflcl__trancl_0_0,def_lhs_atom41]) ).
fof(def_lhs_atom42,axiom,
! [V_r,T_a] :
( lhs_atom42(V_r,T_a)
<=> c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) = c_Transitive__Closure_Ortrancl(V_r,T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_41,plain,
! [T_a,V_r] :
( lhs_atom42(V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_trancl__reflcl_0_0,def_lhs_atom42]) ).
fof(def_lhs_atom43,axiom,
! [V_B,V_A,T_b,T_a] :
( lhs_atom43(V_B,V_A,T_b,T_a)
<=> c_lessequals(c_Relation_ODomain(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(tc_prod(T_a,T_b),tc_bool)),T_a,T_b),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(V_A,T_a,T_b),c_Relation_ODomain(V_B,T_a,T_b),tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_42,plain,
! [T_a,T_b,V_A,V_B] :
( lhs_atom43(V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Domain__Int__subset_0_0,def_lhs_atom43]) ).
fof(def_lhs_atom44,axiom,
! [V_a,V_B,T_a] :
( lhs_atom44(V_a,V_B,T_a)
<=> c_lessequals(V_B,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_43,plain,
! [T_a,V_B,V_a] :
( lhs_atom44(V_a,V_B,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_subset__insertI_0_0,def_lhs_atom44]) ).
fof(def_lhs_atom45,axiom,
! [V_f,V_B,V_A,T_b,T_a] :
( lhs_atom45(V_f,V_B,V_A,T_b,T_a)
<=> c_lessequals(c_Set_Oimage(V_f,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(V_f,V_A,T_b,T_a),c_Set_Oimage(V_f,V_B,T_b,T_a),tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_44,plain,
! [T_a,T_b,V_A,V_B,V_f] :
( lhs_atom45(V_f,V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_image__Int__subset_0_0,def_lhs_atom45]) ).
fof(def_lhs_atom46,axiom,
! [V_R,V_B,V_A,T_b,T_a] :
( lhs_atom46(V_R,V_B,V_A,T_b,T_a)
<=> c_lessequals(c_Relation_OImage(V_R,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(V_R,V_A,T_b,T_a),c_Relation_OImage(V_R,V_B,T_b,T_a),tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_45,plain,
! [T_a,T_b,V_A,V_B,V_R] :
( lhs_atom46(V_R,V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Image__Int__subset_0_0,def_lhs_atom46]) ).
fof(def_lhs_atom47,axiom,
! [V_C,V_B,V_A,T_b,T_a] :
( lhs_atom47(V_C,V_B,V_A,T_b,T_a)
<=> c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),c_COMBK(V_C,tc_fun(T_b,tc_bool),T_a),T_a,T_b) = c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(V_A,c_COMBK(V_C,tc_fun(T_b,tc_bool),T_a),T_a,T_b),c_Product__Type_OSigma(V_B,c_COMBK(V_C,tc_fun(T_b,tc_bool),T_a),T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_46,plain,
! [T_a,T_b,V_A,V_B,V_C] :
( lhs_atom47(V_C,V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Times__Int__distrib1_0_0,def_lhs_atom47]) ).
fof(def_lhs_atom48,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom48(V_C,V_B,V_A,T_a)
<=> c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_47,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom48(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__assoc_0_0,def_lhs_atom48]) ).
fof(def_lhs_atom49,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom49(V_C,V_B,V_A,T_a)
<=> c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_B,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_48,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom49(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__left__commute_0_0,def_lhs_atom49]) ).
fof(def_lhs_atom50,axiom,
! [T_a] :
( lhs_atom50(T_a)
<=> c_Relation_Otrans(c_Relation_OId(T_a),T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_49,plain,
! [T_a] :
( lhs_atom50(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_trans__Id_0_0,def_lhs_atom50]) ).
fof(def_lhs_atom51,axiom,
! [V_b,V_a,V_B,V_A,T_b,T_a] :
( lhs_atom51(V_b,V_a,V_B,V_A,T_b,T_a)
<=> c_Product__Type_OSigma(c_Set_Oinsert(V_a,V_A,T_a),c_COMBK(c_Set_Oinsert(V_b,V_B,T_b),tc_fun(T_b,tc_bool),T_a),T_a,T_b) = c_Set_Oinsert(c_Pair(V_a,V_b,T_a,T_b),c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(V_A,c_COMBK(c_Set_Oinsert(V_b,V_B,T_b),tc_fun(T_b,tc_bool),T_a),T_a,T_b),c_Product__Type_OSigma(c_Set_Oinsert(V_a,V_A,T_a),c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool)),tc_prod(T_a,T_b)) ),
inference(definition,[],]) ).
fof(to_be_clausified_50,plain,
! [T_a,T_b,V_A,V_B,V_a,V_b] :
( lhs_atom51(V_b,V_a,V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__times__insert_0_0,def_lhs_atom51]) ).
fof(def_lhs_atom52,axiom,
! [V_f,V_a,V_B,T_b,T_a] :
( lhs_atom52(V_f,V_a,V_B,T_b,T_a)
<=> c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_51,plain,
! [T_a,T_b,V_B,V_a,V_f] :
( lhs_atom52(V_f,V_a,V_B,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_image__insert_0_0,def_lhs_atom52]) ).
fof(def_lhs_atom53,axiom,
! [V_s,V_r,T_b,T_a] :
( lhs_atom53(V_s,V_r,T_b,T_a)
<=> c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(V_r,V_s,tc_fun(tc_prod(T_b,T_a),tc_bool)),T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Oconverse(V_r,T_b,T_a),c_Relation_Oconverse(V_s,T_b,T_a),tc_fun(tc_prod(T_a,T_b),tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_52,plain,
! [T_a,T_b,V_r,V_s] :
( lhs_atom53(V_s,V_r,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_converse__Un_0_0,def_lhs_atom53]) ).
fof(def_lhs_atom54,axiom,
! [V_B,V_A,T_a] :
( lhs_atom54(V_B,V_A,T_a)
<=> c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_53,plain,
! [T_a,V_A,V_B] :
( lhs_atom54(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__lower1_0_0,def_lhs_atom54]) ).
fof(def_lhs_atom55,axiom,
! [V_B,V_A,T_a] :
( lhs_atom55(V_B,V_A,T_a)
<=> c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_54,plain,
! [T_a,V_A,V_B] :
( lhs_atom55(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__lower2_0_0,def_lhs_atom55]) ).
fof(def_lhs_atom56,axiom,
! [V_C,V_B,V_A,T_b,T_a] :
( lhs_atom56(V_C,V_B,V_A,T_b,T_a)
<=> c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),c_COMBK(V_C,tc_fun(T_b,tc_bool),T_a),T_a,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(V_A,c_COMBK(V_C,tc_fun(T_b,tc_bool),T_a),T_a,T_b),c_Product__Type_OSigma(V_B,c_COMBK(V_C,tc_fun(T_b,tc_bool),T_a),T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_55,plain,
! [T_a,T_b,V_A,V_B,V_C] :
( lhs_atom56(V_C,V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Times__Un__distrib1_0_0,def_lhs_atom56]) ).
fof(def_lhs_atom57,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom57(V_C,V_B,V_A,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_56,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom57(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__Int__distrib_0_0,def_lhs_atom57]) ).
fof(def_lhs_atom58,axiom,
! [V_C,V_B,V_A,T_a] :
( lhs_atom58(V_C,V_B,V_A,T_a)
<=> c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_57,plain,
! [T_a,V_A,V_B,V_C] :
( lhs_atom58(V_C,V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Un__Int__distrib2_0_0,def_lhs_atom58]) ).
fof(def_lhs_atom59,axiom,
! [V_x,V_A,T_a] :
( lhs_atom59(V_x,V_A,T_a)
<=> hBOOL(hAPP(c_Set_Oinsert(V_x,V_A,T_a),V_x)) ),
inference(definition,[],]) ).
fof(to_be_clausified_58,plain,
! [T_a,V_A,V_x] :
( lhs_atom59(V_x,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_insert__code_1_0,def_lhs_atom59]) ).
fof(def_lhs_atom60,axiom,
! [V_B,V_A,T_a] :
( lhs_atom60(V_B,V_A,T_a)
<=> c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_59,plain,
! [T_a,V_A,V_B] :
( lhs_atom60(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__left__absorb_0_0,def_lhs_atom60]) ).
fof(def_lhs_atom61,axiom,
! [V_B,V_A,T_b,T_a] :
( lhs_atom61(V_B,V_A,T_b,T_a)
<=> c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(tc_prod(T_b,T_a),tc_bool)),T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(V_A,T_b,T_a),c_Relation_ORange(V_B,T_b,T_a),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_60,plain,
! [T_a,T_b,V_A,V_B] :
( lhs_atom61(V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Range__Un__eq_0_0,def_lhs_atom61]) ).
fof(def_lhs_atom62,axiom,
! [V_A,T_a] :
( lhs_atom62(V_A,T_a)
<=> c_Lattices_Olower__semilattice__class_Oinf(V_A,V_A,tc_fun(T_a,tc_bool)) = V_A ),
inference(definition,[],]) ).
fof(to_be_clausified_61,plain,
! [T_a,V_A] :
( lhs_atom62(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Int__absorb_0_0,def_lhs_atom62]) ).
fof(def_lhs_atom63,axiom,
! [V_r,T_a] :
( lhs_atom63(V_r,T_a)
<=> c_Relation_OField(V_r,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(V_r,T_a,T_a),c_Relation_ORange(V_r,T_a,T_a),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_62,plain,
! [T_a,V_r] :
( lhs_atom63(V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Field__def_0_0,def_lhs_atom63]) ).
fof(def_lhs_atom64,axiom,
! [V_f,V_B,V_A,T_b,T_a] :
( lhs_atom64(V_f,V_B,V_A,T_b,T_a)
<=> c_Set_Oimage(V_f,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(V_f,V_A,T_b,T_a),c_Set_Oimage(V_f,V_B,T_b,T_a),tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_63,plain,
! [T_a,T_b,V_A,V_B,V_f] :
( lhs_atom64(V_f,V_B,V_A,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_image__Un_0_0,def_lhs_atom64]) ).
fof(def_lhs_atom65,axiom,
! [V_r,T_a] :
( lhs_atom65(V_r,T_a)
<=> c_Transitive__Closure_Otrancl(V_r,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_r,c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(V_r,T_a),V_r,T_a,T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_64,plain,
! [T_a,V_r] :
( lhs_atom65(V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_trancl__unfold_0_0,def_lhs_atom65]) ).
fof(def_lhs_atom66,axiom,
! [V_r,T_a] :
( lhs_atom66(V_r,T_a)
<=> c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(V_r,c_Relation_Oconverse(V_r,T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_65,plain,
! [T_a,V_r] :
( lhs_atom66(V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_sym__Un__converse_0_0,def_lhs_atom66]) ).
fof(def_lhs_atom67,axiom,
! [V_r,T_a] :
( lhs_atom67(V_r,T_a)
<=> c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(V_r,c_Relation_Oconverse(V_r,T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_66,plain,
! [T_a,V_r] :
( lhs_atom67(V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_sym__Int__converse_0_0,def_lhs_atom67]) ).
fof(def_lhs_atom68,axiom,
! [V_B,V_A,T_a] :
( lhs_atom68(V_B,V_A,T_a)
<=> c_Relation_OImage(c_Relation_OId__on(V_A,T_a),V_B,T_a,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_67,plain,
! [T_a,V_A,V_B] :
( lhs_atom68(V_B,V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Image__Id__on_0_0,def_lhs_atom68]) ).
fof(def_lhs_atom69,axiom,
! [V_r,T_a] :
( lhs_atom69(V_r,T_a)
<=> c_Transitive__Closure_Ortrancl(V_r,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(V_r,T_a),c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_68,plain,
! [T_a,V_r] :
( lhs_atom69(V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Nitpick_Ortrancl__def_0_0,def_lhs_atom69]) ).
fof(def_lhs_atom70,axiom,
! [V_r,T_a] :
( lhs_atom70(V_r,T_a)
<=> c_Transitive__Closure_Ortrancl(V_r,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(T_a),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(V_r,T_a),V_r,T_a,T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_69,plain,
! [T_a,V_r] :
( lhs_atom70(V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rtrancl__unfold_0_0,def_lhs_atom70]) ).
fof(def_lhs_atom71,axiom,
! [V_r,T_a] :
( lhs_atom71(V_r,T_a)
<=> c_lessequals(c_Transitive__Closure_Otrancl(V_r,T_a),c_Product__Type_OSigma(c_Relation_OField(V_r,T_a),c_COMBK(c_Relation_OField(V_r,T_a),tc_fun(T_a,tc_bool),T_a),T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_70,plain,
! [T_a,V_r] :
( lhs_atom71(V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_trancl__subset__Field2_0_0,def_lhs_atom71]) ).
fof(def_lhs_atom72,axiom,
! [V_r,T_a] :
( lhs_atom72(V_r,T_a)
<=> c_Transitive__Closure_Otrancl(V_r,T_a) = c_Relation_Orel__comp(V_r,c_Transitive__Closure_Ortrancl(V_r,T_a),T_a,T_a,T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_71,plain,
! [T_a,V_r] :
( lhs_atom72(V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_trancl__unfold__left_0_0,def_lhs_atom72]) ).
fof(def_lhs_atom73,axiom,
! [V_r,T_a] :
( lhs_atom73(V_r,T_a)
<=> c_Transitive__Closure_Otrancl(V_r,T_a) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(V_r,T_a),V_r,T_a,T_a,T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_72,plain,
! [T_a,V_r] :
( lhs_atom73(V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_trancl__unfold__right_0_0,def_lhs_atom73]) ).
fof(def_lhs_atom74,axiom,
! [V_r,V_a,T_a] :
( lhs_atom74(V_r,V_a,T_a)
<=> c_in(c_Pair(V_a,V_a,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ),
inference(definition,[],]) ).
fof(to_be_clausified_73,plain,
! [T_a,V_a,V_r] :
( lhs_atom74(V_r,V_a,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rtrancl_Ortrancl__refl_0_0,def_lhs_atom74]) ).
fof(def_lhs_atom75,axiom,
! [V_x,V_R,T_a] :
( lhs_atom75(V_x,V_R,T_a)
<=> c_in(c_Pair(V_x,V_x,T_a,T_a),c_Transitive__Closure_Ortrancl(V_R,T_a),tc_prod(T_a,T_a)) ),
inference(definition,[],]) ).
fof(to_be_clausified_74,plain,
! [T_a,V_R,V_x] :
( lhs_atom75(V_x,V_R,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rtrancl__eq__or__trancl_1_0,def_lhs_atom75]) ).
fof(def_lhs_atom76,axiom,
! [V_r,T_a] :
( lhs_atom76(V_r,T_a)
<=> c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(V_r,T_a),T_a) = c_Transitive__Closure_Ortrancl(V_r,T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_75,plain,
! [T_a,V_r] :
( lhs_atom76(V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rtrancl__idemp_0_0,def_lhs_atom76]) ).
fof(def_lhs_atom77,axiom,
! [V_R,T_a] :
( lhs_atom77(V_R,T_a)
<=> c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(V_R,T_a),T_a) = c_Transitive__Closure_Ortrancl(V_R,T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_76,plain,
! [T_a,V_R] :
( lhs_atom77(V_R,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_trancl__rtrancl__absorb_0_0,def_lhs_atom77]) ).
fof(def_lhs_atom78,axiom,
! [V_A,T_a] :
( lhs_atom78(V_A,T_a)
<=> c_lessequals(V_A,V_A,tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_77,plain,
! [T_a,V_A] :
( lhs_atom78(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_subset__refl_0_0,def_lhs_atom78]) ).
fof(def_lhs_atom79,axiom,
! [V_x,T_a] :
( lhs_atom79(V_x,T_a)
<=> c_lessequals(V_x,V_x,tc_fun(T_a,tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_78,plain,
! [T_a,V_x] :
( lhs_atom79(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_equalityE_0_0,def_lhs_atom79]) ).
fof(def_lhs_atom80,axiom,
! [V_r,T_a] :
( lhs_atom80(V_r,T_a)
<=> c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(V_r,T_a,T_a),T_a) = c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(V_r,T_a),T_a,T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_79,plain,
! [T_a,V_r] :
( lhs_atom80(V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rtrancl__converse_0_0,def_lhs_atom80]) ).
fof(def_lhs_atom81,axiom,
! [V_R,T_a] :
( lhs_atom81(V_R,T_a)
<=> c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(V_R,T_a),c_Transitive__Closure_Ortrancl(V_R,T_a),T_a,T_a,T_a) = c_Transitive__Closure_Ortrancl(V_R,T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_80,plain,
! [T_a,V_R] :
( lhs_atom81(V_R,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rtrancl__idemp__self__comp_0_0,def_lhs_atom81]) ).
fof(def_lhs_atom82,axiom,
! [V_R,T_a] :
( lhs_atom82(V_R,T_a)
<=> c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(V_R,T_a),T_a) = c_Transitive__Closure_Ortrancl(V_R,T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_81,plain,
! [T_a,V_R] :
( lhs_atom82(V_R,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_rtrancl__trancl__absorb_0_0,def_lhs_atom82]) ).
fof(def_lhs_atom83,axiom,
! [V_r,T_a] :
( lhs_atom83(V_r,T_a)
<=> c_Relation_Orel__comp(V_r,c_Transitive__Closure_Ortrancl(V_r,T_a),T_a,T_a,T_a) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(V_r,T_a),V_r,T_a,T_a,T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_82,plain,
! [T_a,V_r] :
( lhs_atom83(V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_r__comp__rtrancl__eq_0_0,def_lhs_atom83]) ).
fof(def_lhs_atom84,axiom,
! [V_A,T_a] :
( lhs_atom84(V_A,T_a)
<=> c_lessequals(c_Relation_OId__on(V_A,T_a),c_Product__Type_OSigma(V_A,c_COMBK(V_A,tc_fun(T_a,tc_bool),T_a),T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_83,plain,
! [T_a,V_A] :
( lhs_atom84(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Id__on__subset__Times_0_0,def_lhs_atom84]) ).
fof(def_lhs_atom85,axiom,
! [V_Q,V_P,T_b,T_a] :
( lhs_atom85(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_84,plain,
! [T_a,T_b,V_P,V_Q] :
( lhs_atom85(V_Q,V_P,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_COMBK__def_0_0,def_lhs_atom85]) ).
fof(def_lhs_atom86,axiom,
( lhs_atom86
<=> c_Relation_ORange(v_r,t_a,t_b) = c_Relation_ODomain(c_Relation_Oconverse(v_r,t_a,t_b),t_b,t_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_85,plain,
( lhs_atom86
| $false ),
inference(fold_definition,[status(thm)],[cls_Range__def__raw_0_0,def_lhs_atom86]) ).
fof(def_lhs_atom87,axiom,
! [V_r,T_a] :
( lhs_atom87(V_r,T_a)
<=> c_Relation_ODomain(c_Transitive__Closure_Otrancl(V_r,T_a),T_a,T_a) = c_Relation_ODomain(V_r,T_a,T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_86,plain,
! [T_a,V_r] :
( lhs_atom87(V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_trancl__domain_0_0,def_lhs_atom87]) ).
fof(def_lhs_atom88,axiom,
! [T_a] :
( lhs_atom88(T_a)
<=> c_Relation_Osym(c_Relation_OId(T_a),T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_87,plain,
! [T_a] :
( lhs_atom88(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_sym__Id_0_0,def_lhs_atom88]) ).
fof(def_lhs_atom89,axiom,
! [V_R,T_b,T_a] :
( lhs_atom89(V_R,T_b,T_a)
<=> c_Relation_Orel__comp(c_Relation_OId(T_a),V_R,T_a,T_a,T_b) = V_R ),
inference(definition,[],]) ).
fof(to_be_clausified_88,plain,
! [T_a,T_b,V_R] :
( lhs_atom89(V_R,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Id__O__R_0_0,def_lhs_atom89]) ).
fof(def_lhs_atom90,axiom,
! [V_R,T_b,T_a] :
( lhs_atom90(V_R,T_b,T_a)
<=> c_Relation_Orel__comp(V_R,c_Relation_OId(T_b),T_a,T_b,T_b) = V_R ),
inference(definition,[],]) ).
fof(to_be_clausified_89,plain,
! [T_a,T_b,V_R] :
( lhs_atom90(V_R,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_R__O__Id_0_0,def_lhs_atom90]) ).
fof(def_lhs_atom91,axiom,
! [V_A,T_a] :
( lhs_atom91(V_A,T_a)
<=> c_Relation_OImage(c_Relation_OId(T_a),V_A,T_a,T_a) = V_A ),
inference(definition,[],]) ).
fof(to_be_clausified_90,plain,
! [T_a,V_A] :
( lhs_atom91(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Image__Id_0_0,def_lhs_atom91]) ).
fof(def_lhs_atom92,axiom,
! [V_A,T_a] :
( lhs_atom92(V_A,T_a)
<=> c_Relation_ODomain(c_Relation_OId__on(V_A,T_a),T_a,T_a) = 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_Domain__Id__on_0_0,def_lhs_atom92]) ).
fof(def_lhs_atom93,axiom,
! [V_r,T_a] :
( lhs_atom93(V_r,T_a)
<=> c_Relation_ORange(c_Transitive__Closure_Otrancl(V_r,T_a),T_a,T_a) = c_Relation_ORange(V_r,T_a,T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_92,plain,
! [T_a,V_r] :
( lhs_atom93(V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_trancl__range_0_0,def_lhs_atom93]) ).
fof(def_lhs_atom94,axiom,
! [V_s,V_r,T_c,T_b,T_a] :
( lhs_atom94(V_s,V_r,T_c,T_b,T_a)
<=> c_Relation_Oconverse(c_Relation_Orel__comp(V_r,V_s,T_b,T_c,T_a),T_b,T_a) = c_Relation_Orel__comp(c_Relation_Oconverse(V_s,T_c,T_a),c_Relation_Oconverse(V_r,T_b,T_c),T_a,T_c,T_b) ),
inference(definition,[],]) ).
fof(to_be_clausified_93,plain,
! [T_a,T_b,T_c,V_r,V_s] :
( lhs_atom94(V_s,V_r,T_c,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_converse__rel__comp_0_0,def_lhs_atom94]) ).
fof(def_lhs_atom95,axiom,
! [V_A,T_a] :
( lhs_atom95(V_A,T_a)
<=> c_Relation_Osym(c_Relation_OId__on(V_A,T_a),T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_94,plain,
! [T_a,V_A] :
( lhs_atom95(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_sym__Id__on_0_0,def_lhs_atom95]) ).
fof(def_lhs_atom96,axiom,
! [V_A,T_a] :
( lhs_atom96(V_A,T_a)
<=> c_Relation_Orefl__on(V_A,c_Relation_OId__on(V_A,T_a),T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_95,plain,
! [T_a,V_A] :
( lhs_atom96(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_refl__on__Id__on_0_0,def_lhs_atom96]) ).
fof(def_lhs_atom97,axiom,
! [T_a] :
( lhs_atom97(T_a)
<=> c_Relation_Oconverse(c_Relation_OId(T_a),T_a,T_a) = c_Relation_OId(T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_96,plain,
! [T_a] :
( lhs_atom97(T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_converse__Id_0_0,def_lhs_atom97]) ).
fof(def_lhs_atom98,axiom,
! [V_T,V_S,V_R,T_d,T_c,T_b,T_a] :
( lhs_atom98(V_T,V_S,V_R,T_d,T_c,T_b,T_a)
<=> c_Relation_Orel__comp(c_Relation_Orel__comp(V_R,V_S,T_a,T_d,T_c),V_T,T_a,T_c,T_b) = c_Relation_Orel__comp(V_R,c_Relation_Orel__comp(V_S,V_T,T_d,T_c,T_b),T_a,T_d,T_b) ),
inference(definition,[],]) ).
fof(to_be_clausified_97,plain,
! [T_a,T_b,T_c,T_d,V_R,V_S,V_T] :
( lhs_atom98(V_T,V_S,V_R,T_d,T_c,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_O__assoc_0_0,def_lhs_atom98]) ).
fof(def_lhs_atom99,axiom,
! [V_f,V_R,T_b,T_a] :
( lhs_atom99(V_f,V_R,T_b,T_a)
<=> c_Relation_Oconverse(c_Relation_Oinv__image(V_R,V_f,T_b,T_a),T_a,T_a) = c_Relation_Oinv__image(c_Relation_Oconverse(V_R,T_b,T_b),V_f,T_b,T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_98,plain,
! [T_a,T_b,V_R,V_f] :
( lhs_atom99(V_f,V_R,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_converse__inv__image_0_0,def_lhs_atom99]) ).
fof(def_lhs_atom100,axiom,
! [V_r,T_a] :
( lhs_atom100(V_r,T_a)
<=> c_Transitive__Closure_Otrancl(c_Relation_Oconverse(V_r,T_a,T_a),T_a) = c_Relation_Oconverse(c_Transitive__Closure_Otrancl(V_r,T_a),T_a,T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_99,plain,
! [T_a,V_r] :
( lhs_atom100(V_r,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_trancl__converse_0_0,def_lhs_atom100]) ).
fof(def_lhs_atom101,axiom,
! [V_A,T_a] :
( lhs_atom101(V_A,T_a)
<=> c_Relation_Oconverse(c_Relation_OId__on(V_A,T_a),T_a,T_a) = c_Relation_OId__on(V_A,T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_100,plain,
! [T_a,V_A] :
( lhs_atom101(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_converse__Id__on_0_0,def_lhs_atom101]) ).
fof(def_lhs_atom102,axiom,
! [V_r,T_b,T_a] :
( lhs_atom102(V_r,T_b,T_a)
<=> c_Relation_ORange(c_Relation_Oconverse(V_r,T_a,T_b),T_b,T_a) = c_Relation_ODomain(V_r,T_a,T_b) ),
inference(definition,[],]) ).
fof(to_be_clausified_101,plain,
! [T_a,T_b,V_r] :
( lhs_atom102(V_r,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Range__converse_0_0,def_lhs_atom102]) ).
fof(def_lhs_atom103,axiom,
! [V_A,T_a] :
( lhs_atom103(V_A,T_a)
<=> c_Relation_ORange(c_Relation_OId__on(V_A,T_a),T_a,T_a) = V_A ),
inference(definition,[],]) ).
fof(to_be_clausified_102,plain,
! [T_a,V_A] :
( lhs_atom103(V_A,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Range__Id__on_0_0,def_lhs_atom103]) ).
fof(def_lhs_atom104,axiom,
! [V_r,T_b,T_a] :
( lhs_atom104(V_r,T_b,T_a)
<=> c_Relation_Oconverse(c_Relation_Oconverse(V_r,T_a,T_b),T_b,T_a) = V_r ),
inference(definition,[],]) ).
fof(to_be_clausified_103,plain,
! [T_a,T_b,V_r] :
( lhs_atom104(V_r,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_converse__converse_0_0,def_lhs_atom104]) ).
fof(def_lhs_atom105,axiom,
! [V_r,T_b,T_a] :
( lhs_atom105(V_r,T_b,T_a)
<=> c_Relation_ODomain(c_Relation_Oconverse(V_r,T_b,T_a),T_a,T_b) = c_Relation_ORange(V_r,T_b,T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_104,plain,
! [T_a,T_b,V_r] :
( lhs_atom105(V_r,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Domain__converse_0_0,def_lhs_atom105]) ).
fof(def_lhs_atom106,axiom,
! [V_r,T_b,T_a] :
( lhs_atom106(V_r,T_b,T_a)
<=> c_Relation_ORange(V_r,T_b,T_a) = c_Relation_ODomain(c_Relation_Oconverse(V_r,T_b,T_a),T_a,T_b) ),
inference(definition,[],]) ).
fof(to_be_clausified_105,plain,
! [T_a,T_b,V_r] :
( lhs_atom106(V_r,T_b,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_Range__def_0_0,def_lhs_atom106]) ).
fof(def_lhs_atom107,axiom,
! [V_x,T_a] :
( lhs_atom107(V_x,T_a)
<=> c_in(c_Pair(V_x,V_x,T_a,T_a),c_Relation_OId(T_a),tc_prod(T_a,T_a)) ),
inference(definition,[],]) ).
fof(to_be_clausified_106,plain,
! [T_a,V_x] :
( lhs_atom107(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_pair__in__Id__conv_1_0,def_lhs_atom107]) ).
fof(def_lhs_atom108,axiom,
! [V_a,T_a] :
( lhs_atom108(V_a,T_a)
<=> c_in(c_Pair(V_a,V_a,T_a,T_a),c_Relation_OId(T_a),tc_prod(T_a,T_a)) ),
inference(definition,[],]) ).
fof(to_be_clausified_107,plain,
! [T_a,V_a] :
( lhs_atom108(V_a,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_IdI_0_0,def_lhs_atom108]) ).
fof(def_lhs_atom109,axiom,
! [V_x,V_L] :
( lhs_atom109(V_x,V_L)
<=> ~ c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(definition,[],]) ).
fof(to_be_clausified_108,plain,
! [V_L,V_x] :
( lhs_atom109(V_x,V_L)
| $false ),
inference(fold_definition,[status(thm)],[cls_in__mktop_1_0,def_lhs_atom109]) ).
fof(def_lhs_atom110,axiom,
! [V_y,V_x,V_L] :
( lhs_atom110(V_y,V_x,V_L)
<=> ~ c_in(c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(definition,[],]) ).
fof(to_be_clausified_109,plain,
! [V_L,V_x,V_y] :
( lhs_atom110(V_y,V_x,V_L)
| $false ),
inference(fold_definition,[status(thm)],[cls_in__mktop_0_0,def_lhs_atom110]) ).
fof(def_lhs_atom111,axiom,
! [V_x,V_L] :
( lhs_atom111(V_x,V_L)
<=> ~ c_in(c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(definition,[],]) ).
fof(to_be_clausified_110,plain,
! [V_L,V_x] :
( lhs_atom111(V_x,V_L)
| $false ),
inference(fold_definition,[status(thm)],[cls_in__mkbot_1_0,def_lhs_atom111]) ).
fof(def_lhs_atom112,axiom,
! [V_xa,V_x,V_L] :
( lhs_atom112(V_xa,V_x,V_L)
<=> ~ c_in(c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_x),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(definition,[],]) ).
fof(to_be_clausified_111,plain,
! [V_L,V_x,V_xa] :
( lhs_atom112(V_xa,V_x,V_L)
| $false ),
inference(fold_definition,[status(thm)],[cls_in__mkbot_0_0,def_lhs_atom112]) ).
fof(def_lhs_atom113,axiom,
( lhs_atom113
<=> c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_112,plain,
( lhs_atom113
| $false ),
inference(fold_definition,[status(thm)],[cls_linear__alt_0_0,def_lhs_atom113]) ).
fof(def_lhs_atom114,axiom,
( lhs_atom114
<=> v_a____ != v_b____ ),
inference(definition,[],]) ).
fof(to_be_clausified_113,plain,
( lhs_atom114
| $false ),
inference(fold_definition,[status(thm)],[cls_CHAINED_0_0,def_lhs_atom114]) ).
fof(def_lhs_atom115,axiom,
( lhs_atom115
<=> class_Complete__Lattice_Ocomplete__lattice(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_114,plain,
( lhs_atom115
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Complete__Lattice_Ocomplete__lattice_0,def_lhs_atom115]) ).
fof(def_lhs_atom116,axiom,
( lhs_atom116
<=> class_Lattices_Oupper__semilattice(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_115,plain,
( lhs_atom116
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Lattices_Oupper__semilattice_0,def_lhs_atom116]) ).
fof(def_lhs_atom117,axiom,
( lhs_atom117
<=> class_Lattices_Olower__semilattice(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_116,plain,
( lhs_atom117
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Lattices_Olower__semilattice_0,def_lhs_atom117]) ).
fof(def_lhs_atom118,axiom,
( lhs_atom118
<=> class_Lattices_Odistrib__lattice(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_117,plain,
( lhs_atom118
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Lattices_Odistrib__lattice_0,def_lhs_atom118]) ).
fof(def_lhs_atom119,axiom,
( lhs_atom119
<=> class_Finite__Set_Ofinite_Ofinite(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_118,plain,
( lhs_atom119
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Finite__Set_Ofinite_Ofinite_0,def_lhs_atom119]) ).
fof(def_lhs_atom120,axiom,
( lhs_atom120
<=> class_Orderings_Opreorder(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_119,plain,
( lhs_atom120
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Orderings_Opreorder_0,def_lhs_atom120]) ).
fof(def_lhs_atom121,axiom,
( lhs_atom121
<=> class_Lattices_Olattice(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_120,plain,
( lhs_atom121
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Lattices_Olattice_0,def_lhs_atom121]) ).
fof(def_lhs_atom122,axiom,
( lhs_atom122
<=> class_Orderings_Oorder(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_121,plain,
( lhs_atom122
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__Orderings_Oorder_0,def_lhs_atom122]) ).
fof(def_lhs_atom123,axiom,
( lhs_atom123
<=> class_HOL_Oord(tc_bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_122,plain,
( lhs_atom123
| $false ),
inference(fold_definition,[status(thm)],[clsarity_bool__HOL_Oord_0,def_lhs_atom123]) ).
fof(def_lhs_atom124,axiom,
! [V_x,T_a] :
( lhs_atom124(V_x,T_a)
<=> c_fequal(V_x,V_x,T_a) ),
inference(definition,[],]) ).
fof(to_be_clausified_123,plain,
! [T_a,V_x] :
( lhs_atom124(V_x,T_a)
| $false ),
inference(fold_definition,[status(thm)],[cls_ATP__Linkup_Oequal__imp__fequal_0_0,def_lhs_atom124]) ).
% Start CNF derivation
fof(c_0_0,axiom,
! [X16,X10,X9,X21,X17,X8,X2] :
( lhs_atom98(X16,X10,X9,X21,X17,X8,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_97) ).
fof(c_0_1,axiom,
! [X13,X11,X5,X3,X8,X2] :
( lhs_atom51(X13,X11,X5,X3,X8,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_50) ).
fof(c_0_2,axiom,
! [X16,X10,X9,X17,X8,X2] :
( lhs_atom28(X16,X10,X9,X17,X8,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_27) ).
fof(c_0_3,axiom,
! [X16,X10,X9,X17,X8,X2] :
( lhs_atom27(X16,X10,X9,X17,X8,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_26) ).
fof(c_0_4,axiom,
! [X15,X1,X17,X8,X2] :
( lhs_atom94(X15,X1,X17,X8,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_93) ).
fof(c_0_5,axiom,
! [X18,X5,X3,X8,X2] :
( lhs_atom64(X18,X5,X3,X8,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_63) ).
fof(c_0_6,axiom,
! [X4,X5,X3,X8,X2] :
( lhs_atom56(X4,X5,X3,X8,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_55) ).
fof(c_0_7,axiom,
! [X18,X11,X5,X8,X2] :
( lhs_atom52(X18,X11,X5,X8,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_51) ).
fof(c_0_8,axiom,
! [X4,X5,X3,X8,X2] :
( lhs_atom47(X4,X5,X3,X8,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_46) ).
fof(c_0_9,axiom,
! [X9,X5,X3,X8,X2] :
( lhs_atom46(X9,X5,X3,X8,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_45) ).
fof(c_0_10,axiom,
! [X18,X5,X3,X8,X2] :
( lhs_atom45(X18,X5,X3,X8,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_44) ).
fof(c_0_11,axiom,
! [X1,X13,X11,X8,X2] :
( lhs_atom37(X1,X13,X11,X8,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_36) ).
fof(c_0_12,axiom,
! [X6,X7,X4,X8,X2] :
( lhs_atom25(X6,X7,X4,X8,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_24) ).
fof(c_0_13,axiom,
! [X9,X5,X3,X8,X2] :
( lhs_atom15(X9,X5,X3,X8,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_14) ).
fof(c_0_14,axiom,
! [X10,X9,X3,X8,X2] :
( lhs_atom14(X10,X9,X3,X8,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_13) ).
fof(c_0_15,axiom,
! [X1,X13,X11,X8,X2] :
( lhs_atom13(X1,X13,X11,X8,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_12) ).
fof(c_0_16,axiom,
! [X6,X7,X4,X8,X2] :
( lhs_atom5(X6,X7,X4,X8,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_4) ).
fof(c_0_17,axiom,
! [X18,X9,X8,X2] :
( lhs_atom99(X18,X9,X8,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_98) ).
fof(c_0_18,axiom,
! [X19,X20,X8,X2] :
( lhs_atom85(X19,X20,X8,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_84) ).
fof(c_0_19,axiom,
! [X5,X3,X8,X2] :
( lhs_atom61(X5,X3,X8,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_60) ).
fof(c_0_20,axiom,
! [X4,X5,X3,X2] :
( lhs_atom58(X4,X5,X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_57) ).
fof(c_0_21,axiom,
! [X4,X5,X3,X2] :
( lhs_atom57(X4,X5,X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_56) ).
fof(c_0_22,axiom,
! [X15,X1,X8,X2] :
( lhs_atom53(X15,X1,X8,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_52) ).
fof(c_0_23,axiom,
! [X4,X5,X3,X2] :
( lhs_atom49(X4,X5,X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_48) ).
fof(c_0_24,axiom,
! [X4,X5,X3,X2] :
( lhs_atom48(X4,X5,X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_47) ).
fof(c_0_25,axiom,
! [X5,X3,X8,X2] :
( lhs_atom43(X5,X3,X8,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_42) ).
fof(c_0_26,axiom,
! [X5,X3,X8,X2] :
( lhs_atom35(X5,X3,X8,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_34) ).
fof(c_0_27,axiom,
! [X5,X3,X8,X2] :
( lhs_atom33(X5,X3,X8,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_32) ).
fof(c_0_28,axiom,
! [X15,X1,X8,X2] :
( lhs_atom26(X15,X1,X8,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_25) ).
fof(c_0_29,axiom,
! [X4,X5,X3,X2] :
( lhs_atom23(X4,X5,X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_22) ).
fof(c_0_30,axiom,
! [X4,X5,X3,X2] :
( lhs_atom18(X4,X5,X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_17) ).
fof(c_0_31,axiom,
! [X4,X5,X3,X2] :
( lhs_atom17(X4,X5,X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_16) ).
fof(c_0_32,axiom,
! [X14,X12,X3,X2] :
( lhs_atom16(X14,X12,X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_15) ).
fof(c_0_33,axiom,
! [X11,X5,X3,X2] :
( lhs_atom11(X11,X5,X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_10) ).
fof(c_0_34,axiom,
! [X11,X5,X3,X2] :
( lhs_atom9(X11,X5,X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_8) ).
fof(c_0_35,axiom,
! [X11,X4,X5,X2] :
( lhs_atom8(X11,X4,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_7) ).
fof(c_0_36,axiom,
! [X4,X5,X3,X2] :
( lhs_atom4(X4,X5,X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_3) ).
fof(c_0_37,axiom,
! [X4,X5,X3,X2] :
( lhs_atom3(X4,X5,X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_2) ).
fof(c_0_38,axiom,
! [X23,X12,X22] :
( lhs_atom112(X23,X12,X22)
| ~ $true ),
file('<stdin>',to_be_clausified_111) ).
fof(c_0_39,axiom,
! [X14,X12,X22] :
( lhs_atom110(X14,X12,X22)
| ~ $true ),
file('<stdin>',to_be_clausified_109) ).
fof(c_0_40,axiom,
! [X1,X8,X2] :
( lhs_atom106(X1,X8,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_105) ).
fof(c_0_41,axiom,
! [X1,X8,X2] :
( lhs_atom105(X1,X8,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_104) ).
fof(c_0_42,axiom,
! [X1,X8,X2] :
( lhs_atom104(X1,X8,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_103) ).
fof(c_0_43,axiom,
! [X1,X8,X2] :
( lhs_atom102(X1,X8,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_101) ).
fof(c_0_44,axiom,
! [X9,X8,X2] :
( lhs_atom90(X9,X8,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_89) ).
fof(c_0_45,axiom,
! [X9,X8,X2] :
( lhs_atom89(X9,X8,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_88) ).
fof(c_0_46,axiom,
! [X12,X9,X2] :
( lhs_atom75(X12,X9,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_74) ).
fof(c_0_47,axiom,
! [X1,X11,X2] :
( lhs_atom74(X1,X11,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_73) ).
fof(c_0_48,axiom,
! [X5,X3,X2] :
( lhs_atom68(X5,X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_67) ).
fof(c_0_49,axiom,
! [X5,X3,X2] :
( lhs_atom60(X5,X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_59) ).
fof(c_0_50,axiom,
! [X12,X3,X2] :
( lhs_atom59(X12,X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_58) ).
fof(c_0_51,axiom,
! [X5,X3,X2] :
( lhs_atom55(X5,X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_54) ).
fof(c_0_52,axiom,
! [X5,X3,X2] :
( lhs_atom54(X5,X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_53) ).
fof(c_0_53,axiom,
! [X11,X5,X2] :
( lhs_atom44(X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_43) ).
fof(c_0_54,axiom,
! [X12,X5,X2] :
( lhs_atom40(X12,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_39) ).
fof(c_0_55,axiom,
! [X11,X5,X2] :
( lhs_atom39(X11,X5,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_38) ).
fof(c_0_56,axiom,
! [X12,X3,X2] :
( lhs_atom38(X12,X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_37) ).
fof(c_0_57,axiom,
! [X10,X9,X2] :
( lhs_atom36(X10,X9,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_35) ).
fof(c_0_58,axiom,
! [X5,X3,X2] :
( lhs_atom34(X5,X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_33) ).
fof(c_0_59,axiom,
! [X5,X3,X2] :
( lhs_atom32(X5,X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_31) ).
fof(c_0_60,axiom,
! [X15,X1,X2] :
( lhs_atom30(X15,X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_29) ).
fof(c_0_61,axiom,
! [X5,X3,X2] :
( lhs_atom22(X5,X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_21) ).
fof(c_0_62,axiom,
! [X5,X3,X2] :
( lhs_atom21(X5,X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_20) ).
fof(c_0_63,axiom,
! [X5,X3,X2] :
( lhs_atom20(X5,X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_19) ).
fof(c_0_64,axiom,
! [X12,X3,X2] :
( lhs_atom12(X12,X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_11) ).
fof(c_0_65,axiom,
! [X10,X9,X2] :
( lhs_atom7(X10,X9,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_6) ).
fof(c_0_66,axiom,
! [X12,X2] :
( lhs_atom124(X12,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_123) ).
fof(c_0_67,axiom,
! [X12,X22] :
( lhs_atom111(X12,X22)
| ~ $true ),
file('<stdin>',to_be_clausified_110) ).
fof(c_0_68,axiom,
! [X12,X22] :
( lhs_atom109(X12,X22)
| ~ $true ),
file('<stdin>',to_be_clausified_108) ).
fof(c_0_69,axiom,
! [X11,X2] :
( lhs_atom108(X11,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_107) ).
fof(c_0_70,axiom,
! [X12,X2] :
( lhs_atom107(X12,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_106) ).
fof(c_0_71,axiom,
! [X3,X2] :
( lhs_atom103(X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_102) ).
fof(c_0_72,axiom,
! [X3,X2] :
( lhs_atom101(X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_100) ).
fof(c_0_73,axiom,
! [X1,X2] :
( lhs_atom100(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_99) ).
fof(c_0_74,axiom,
! [X3,X2] :
( lhs_atom96(X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_95) ).
fof(c_0_75,axiom,
! [X3,X2] :
( lhs_atom95(X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_94) ).
fof(c_0_76,axiom,
! [X1,X2] :
( lhs_atom93(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_92) ).
fof(c_0_77,axiom,
! [X3,X2] :
( lhs_atom92(X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_91) ).
fof(c_0_78,axiom,
! [X3,X2] :
( lhs_atom91(X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_90) ).
fof(c_0_79,axiom,
! [X1,X2] :
( lhs_atom87(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_86) ).
fof(c_0_80,axiom,
! [X3,X2] :
( lhs_atom84(X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_83) ).
fof(c_0_81,axiom,
! [X1,X2] :
( lhs_atom83(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_82) ).
fof(c_0_82,axiom,
! [X9,X2] :
( lhs_atom82(X9,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_81) ).
fof(c_0_83,axiom,
! [X9,X2] :
( lhs_atom81(X9,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_80) ).
fof(c_0_84,axiom,
! [X1,X2] :
( lhs_atom80(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_79) ).
fof(c_0_85,axiom,
! [X12,X2] :
( lhs_atom79(X12,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_78) ).
fof(c_0_86,axiom,
! [X3,X2] :
( lhs_atom78(X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_77) ).
fof(c_0_87,axiom,
! [X9,X2] :
( lhs_atom77(X9,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_76) ).
fof(c_0_88,axiom,
! [X1,X2] :
( lhs_atom76(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_75) ).
fof(c_0_89,axiom,
! [X1,X2] :
( lhs_atom73(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_72) ).
fof(c_0_90,axiom,
! [X1,X2] :
( lhs_atom72(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_71) ).
fof(c_0_91,axiom,
! [X1,X2] :
( lhs_atom71(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_70) ).
fof(c_0_92,axiom,
! [X1,X2] :
( lhs_atom70(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_69) ).
fof(c_0_93,axiom,
! [X1,X2] :
( lhs_atom69(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_68) ).
fof(c_0_94,axiom,
! [X1,X2] :
( lhs_atom67(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_66) ).
fof(c_0_95,axiom,
! [X1,X2] :
( lhs_atom66(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_65) ).
fof(c_0_96,axiom,
! [X1,X2] :
( lhs_atom65(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_64) ).
fof(c_0_97,axiom,
! [X1,X2] :
( lhs_atom63(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_62) ).
fof(c_0_98,axiom,
! [X3,X2] :
( lhs_atom62(X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_61) ).
fof(c_0_99,axiom,
! [X1,X2] :
( lhs_atom42(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_41) ).
fof(c_0_100,axiom,
! [X1,X2] :
( lhs_atom41(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_40) ).
fof(c_0_101,axiom,
! [X3,X2] :
( lhs_atom29(X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_28) ).
fof(c_0_102,axiom,
! [X1,X2] :
( lhs_atom24(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_23) ).
fof(c_0_103,axiom,
! [X9,X2] :
( lhs_atom19(X9,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_18) ).
fof(c_0_104,axiom,
! [X1,X2] :
( lhs_atom10(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_9) ).
fof(c_0_105,axiom,
! [X9,X2] :
( lhs_atom6(X9,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_5) ).
fof(c_0_106,axiom,
! [X3,X2] :
( lhs_atom2(X3,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_1) ).
fof(c_0_107,axiom,
! [X1,X2] :
( lhs_atom1(X1,X2)
| ~ $true ),
file('<stdin>',to_be_clausified_0) ).
fof(c_0_108,axiom,
! [X2] :
( lhs_atom97(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_96) ).
fof(c_0_109,axiom,
! [X2] :
( lhs_atom88(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_87) ).
fof(c_0_110,axiom,
! [X2] :
( lhs_atom50(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_49) ).
fof(c_0_111,axiom,
( lhs_atom123
| ~ $true ),
file('<stdin>',to_be_clausified_122) ).
fof(c_0_112,axiom,
( lhs_atom122
| ~ $true ),
file('<stdin>',to_be_clausified_121) ).
fof(c_0_113,axiom,
( lhs_atom121
| ~ $true ),
file('<stdin>',to_be_clausified_120) ).
fof(c_0_114,axiom,
( lhs_atom120
| ~ $true ),
file('<stdin>',to_be_clausified_119) ).
fof(c_0_115,axiom,
( lhs_atom119
| ~ $true ),
file('<stdin>',to_be_clausified_118) ).
fof(c_0_116,axiom,
( lhs_atom118
| ~ $true ),
file('<stdin>',to_be_clausified_117) ).
fof(c_0_117,axiom,
( lhs_atom117
| ~ $true ),
file('<stdin>',to_be_clausified_116) ).
fof(c_0_118,axiom,
( lhs_atom116
| ~ $true ),
file('<stdin>',to_be_clausified_115) ).
fof(c_0_119,axiom,
( lhs_atom115
| ~ $true ),
file('<stdin>',to_be_clausified_114) ).
fof(c_0_120,axiom,
( lhs_atom114
| ~ $true ),
file('<stdin>',to_be_clausified_113) ).
fof(c_0_121,axiom,
( lhs_atom113
| ~ $true ),
file('<stdin>',to_be_clausified_112) ).
fof(c_0_122,axiom,
( lhs_atom86
| ~ $true ),
file('<stdin>',to_be_clausified_85) ).
fof(c_0_123,axiom,
( lhs_atom31
| ~ $true ),
file('<stdin>',to_be_clausified_30) ).
fof(c_0_124,plain,
! [X16,X10,X9,X21,X17,X8,X2] : lhs_atom98(X16,X10,X9,X21,X17,X8,X2),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_125,plain,
! [X13,X11,X5,X3,X8,X2] : lhs_atom51(X13,X11,X5,X3,X8,X2),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_126,plain,
! [X16,X10,X9,X17,X8,X2] : lhs_atom28(X16,X10,X9,X17,X8,X2),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_127,plain,
! [X16,X10,X9,X17,X8,X2] : lhs_atom27(X16,X10,X9,X17,X8,X2),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_128,plain,
! [X15,X1,X17,X8,X2] : lhs_atom94(X15,X1,X17,X8,X2),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_129,plain,
! [X18,X5,X3,X8,X2] : lhs_atom64(X18,X5,X3,X8,X2),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_130,plain,
! [X4,X5,X3,X8,X2] : lhs_atom56(X4,X5,X3,X8,X2),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_131,plain,
! [X18,X11,X5,X8,X2] : lhs_atom52(X18,X11,X5,X8,X2),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_132,plain,
! [X4,X5,X3,X8,X2] : lhs_atom47(X4,X5,X3,X8,X2),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_133,plain,
! [X9,X5,X3,X8,X2] : lhs_atom46(X9,X5,X3,X8,X2),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_134,plain,
! [X18,X5,X3,X8,X2] : lhs_atom45(X18,X5,X3,X8,X2),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_135,plain,
! [X1,X13,X11,X8,X2] : lhs_atom37(X1,X13,X11,X8,X2),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_136,plain,
! [X6,X7,X4,X8,X2] : lhs_atom25(X6,X7,X4,X8,X2),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_137,plain,
! [X9,X5,X3,X8,X2] : lhs_atom15(X9,X5,X3,X8,X2),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_138,plain,
! [X10,X9,X3,X8,X2] : lhs_atom14(X10,X9,X3,X8,X2),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_139,plain,
! [X1,X13,X11,X8,X2] : lhs_atom13(X1,X13,X11,X8,X2),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_140,plain,
! [X6,X7,X4,X8,X2] : lhs_atom5(X6,X7,X4,X8,X2),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_141,plain,
! [X18,X9,X8,X2] : lhs_atom99(X18,X9,X8,X2),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_142,plain,
! [X19,X20,X8,X2] : lhs_atom85(X19,X20,X8,X2),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_143,plain,
! [X5,X3,X8,X2] : lhs_atom61(X5,X3,X8,X2),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_144,plain,
! [X4,X5,X3,X2] : lhs_atom58(X4,X5,X3,X2),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_145,plain,
! [X4,X5,X3,X2] : lhs_atom57(X4,X5,X3,X2),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_146,plain,
! [X15,X1,X8,X2] : lhs_atom53(X15,X1,X8,X2),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_147,plain,
! [X4,X5,X3,X2] : lhs_atom49(X4,X5,X3,X2),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_148,plain,
! [X4,X5,X3,X2] : lhs_atom48(X4,X5,X3,X2),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_149,plain,
! [X5,X3,X8,X2] : lhs_atom43(X5,X3,X8,X2),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_150,plain,
! [X5,X3,X8,X2] : lhs_atom35(X5,X3,X8,X2),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_151,plain,
! [X5,X3,X8,X2] : lhs_atom33(X5,X3,X8,X2),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_152,plain,
! [X15,X1,X8,X2] : lhs_atom26(X15,X1,X8,X2),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_153,plain,
! [X4,X5,X3,X2] : lhs_atom23(X4,X5,X3,X2),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_154,plain,
! [X4,X5,X3,X2] : lhs_atom18(X4,X5,X3,X2),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_155,plain,
! [X4,X5,X3,X2] : lhs_atom17(X4,X5,X3,X2),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_156,plain,
! [X14,X12,X3,X2] : lhs_atom16(X14,X12,X3,X2),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_157,plain,
! [X11,X5,X3,X2] : lhs_atom11(X11,X5,X3,X2),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_158,plain,
! [X11,X5,X3,X2] : lhs_atom9(X11,X5,X3,X2),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_159,plain,
! [X11,X4,X5,X2] : lhs_atom8(X11,X4,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_160,plain,
! [X4,X5,X3,X2] : lhs_atom4(X4,X5,X3,X2),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_161,plain,
! [X4,X5,X3,X2] : lhs_atom3(X4,X5,X3,X2),
inference(fof_simplification,[status(thm)],[c_0_37]) ).
fof(c_0_162,plain,
! [X23,X12,X22] : lhs_atom112(X23,X12,X22),
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_163,plain,
! [X14,X12,X22] : lhs_atom110(X14,X12,X22),
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_164,plain,
! [X1,X8,X2] : lhs_atom106(X1,X8,X2),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_165,plain,
! [X1,X8,X2] : lhs_atom105(X1,X8,X2),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_166,plain,
! [X1,X8,X2] : lhs_atom104(X1,X8,X2),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_167,plain,
! [X1,X8,X2] : lhs_atom102(X1,X8,X2),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_168,plain,
! [X9,X8,X2] : lhs_atom90(X9,X8,X2),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_169,plain,
! [X9,X8,X2] : lhs_atom89(X9,X8,X2),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_170,plain,
! [X12,X9,X2] : lhs_atom75(X12,X9,X2),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_171,plain,
! [X1,X11,X2] : lhs_atom74(X1,X11,X2),
inference(fof_simplification,[status(thm)],[c_0_47]) ).
fof(c_0_172,plain,
! [X5,X3,X2] : lhs_atom68(X5,X3,X2),
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_173,plain,
! [X5,X3,X2] : lhs_atom60(X5,X3,X2),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_174,plain,
! [X12,X3,X2] : lhs_atom59(X12,X3,X2),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_175,plain,
! [X5,X3,X2] : lhs_atom55(X5,X3,X2),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_176,plain,
! [X5,X3,X2] : lhs_atom54(X5,X3,X2),
inference(fof_simplification,[status(thm)],[c_0_52]) ).
fof(c_0_177,plain,
! [X11,X5,X2] : lhs_atom44(X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_178,plain,
! [X12,X5,X2] : lhs_atom40(X12,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_179,plain,
! [X11,X5,X2] : lhs_atom39(X11,X5,X2),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_180,plain,
! [X12,X3,X2] : lhs_atom38(X12,X3,X2),
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_181,plain,
! [X10,X9,X2] : lhs_atom36(X10,X9,X2),
inference(fof_simplification,[status(thm)],[c_0_57]) ).
fof(c_0_182,plain,
! [X5,X3,X2] : lhs_atom34(X5,X3,X2),
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_183,plain,
! [X5,X3,X2] : lhs_atom32(X5,X3,X2),
inference(fof_simplification,[status(thm)],[c_0_59]) ).
fof(c_0_184,plain,
! [X15,X1,X2] : lhs_atom30(X15,X1,X2),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_185,plain,
! [X5,X3,X2] : lhs_atom22(X5,X3,X2),
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_186,plain,
! [X5,X3,X2] : lhs_atom21(X5,X3,X2),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_187,plain,
! [X5,X3,X2] : lhs_atom20(X5,X3,X2),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_188,plain,
! [X12,X3,X2] : lhs_atom12(X12,X3,X2),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_189,plain,
! [X10,X9,X2] : lhs_atom7(X10,X9,X2),
inference(fof_simplification,[status(thm)],[c_0_65]) ).
fof(c_0_190,plain,
! [X12,X2] : lhs_atom124(X12,X2),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_191,plain,
! [X12,X22] : lhs_atom111(X12,X22),
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_192,plain,
! [X12,X22] : lhs_atom109(X12,X22),
inference(fof_simplification,[status(thm)],[c_0_68]) ).
fof(c_0_193,plain,
! [X11,X2] : lhs_atom108(X11,X2),
inference(fof_simplification,[status(thm)],[c_0_69]) ).
fof(c_0_194,plain,
! [X12,X2] : lhs_atom107(X12,X2),
inference(fof_simplification,[status(thm)],[c_0_70]) ).
fof(c_0_195,plain,
! [X3,X2] : lhs_atom103(X3,X2),
inference(fof_simplification,[status(thm)],[c_0_71]) ).
fof(c_0_196,plain,
! [X3,X2] : lhs_atom101(X3,X2),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_197,plain,
! [X1,X2] : lhs_atom100(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_73]) ).
fof(c_0_198,plain,
! [X3,X2] : lhs_atom96(X3,X2),
inference(fof_simplification,[status(thm)],[c_0_74]) ).
fof(c_0_199,plain,
! [X3,X2] : lhs_atom95(X3,X2),
inference(fof_simplification,[status(thm)],[c_0_75]) ).
fof(c_0_200,plain,
! [X1,X2] : lhs_atom93(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_76]) ).
fof(c_0_201,plain,
! [X3,X2] : lhs_atom92(X3,X2),
inference(fof_simplification,[status(thm)],[c_0_77]) ).
fof(c_0_202,plain,
! [X3,X2] : lhs_atom91(X3,X2),
inference(fof_simplification,[status(thm)],[c_0_78]) ).
fof(c_0_203,plain,
! [X1,X2] : lhs_atom87(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_79]) ).
fof(c_0_204,plain,
! [X3,X2] : lhs_atom84(X3,X2),
inference(fof_simplification,[status(thm)],[c_0_80]) ).
fof(c_0_205,plain,
! [X1,X2] : lhs_atom83(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_206,plain,
! [X9,X2] : lhs_atom82(X9,X2),
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_207,plain,
! [X9,X2] : lhs_atom81(X9,X2),
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_208,plain,
! [X1,X2] : lhs_atom80(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_209,plain,
! [X12,X2] : lhs_atom79(X12,X2),
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_210,plain,
! [X3,X2] : lhs_atom78(X3,X2),
inference(fof_simplification,[status(thm)],[c_0_86]) ).
fof(c_0_211,plain,
! [X9,X2] : lhs_atom77(X9,X2),
inference(fof_simplification,[status(thm)],[c_0_87]) ).
fof(c_0_212,plain,
! [X1,X2] : lhs_atom76(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_88]) ).
fof(c_0_213,plain,
! [X1,X2] : lhs_atom73(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_214,plain,
! [X1,X2] : lhs_atom72(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_215,plain,
! [X1,X2] : lhs_atom71(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_216,plain,
! [X1,X2] : lhs_atom70(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_217,plain,
! [X1,X2] : lhs_atom69(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_218,plain,
! [X1,X2] : lhs_atom67(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_94]) ).
fof(c_0_219,plain,
! [X1,X2] : lhs_atom66(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_95]) ).
fof(c_0_220,plain,
! [X1,X2] : lhs_atom65(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_96]) ).
fof(c_0_221,plain,
! [X1,X2] : lhs_atom63(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_97]) ).
fof(c_0_222,plain,
! [X3,X2] : lhs_atom62(X3,X2),
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_223,plain,
! [X1,X2] : lhs_atom42(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_99]) ).
fof(c_0_224,plain,
! [X1,X2] : lhs_atom41(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_100]) ).
fof(c_0_225,plain,
! [X3,X2] : lhs_atom29(X3,X2),
inference(fof_simplification,[status(thm)],[c_0_101]) ).
fof(c_0_226,plain,
! [X1,X2] : lhs_atom24(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_102]) ).
fof(c_0_227,plain,
! [X9,X2] : lhs_atom19(X9,X2),
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_228,plain,
! [X1,X2] : lhs_atom10(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_229,plain,
! [X9,X2] : lhs_atom6(X9,X2),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_230,plain,
! [X3,X2] : lhs_atom2(X3,X2),
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_231,plain,
! [X1,X2] : lhs_atom1(X1,X2),
inference(fof_simplification,[status(thm)],[c_0_107]) ).
fof(c_0_232,plain,
! [X2] : lhs_atom97(X2),
inference(fof_simplification,[status(thm)],[c_0_108]) ).
fof(c_0_233,plain,
! [X2] : lhs_atom88(X2),
inference(fof_simplification,[status(thm)],[c_0_109]) ).
fof(c_0_234,plain,
! [X2] : lhs_atom50(X2),
inference(fof_simplification,[status(thm)],[c_0_110]) ).
fof(c_0_235,plain,
lhs_atom123,
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_236,plain,
lhs_atom122,
inference(fof_simplification,[status(thm)],[c_0_112]) ).
fof(c_0_237,plain,
lhs_atom121,
inference(fof_simplification,[status(thm)],[c_0_113]) ).
fof(c_0_238,plain,
lhs_atom120,
inference(fof_simplification,[status(thm)],[c_0_114]) ).
fof(c_0_239,plain,
lhs_atom119,
inference(fof_simplification,[status(thm)],[c_0_115]) ).
fof(c_0_240,plain,
lhs_atom118,
inference(fof_simplification,[status(thm)],[c_0_116]) ).
fof(c_0_241,plain,
lhs_atom117,
inference(fof_simplification,[status(thm)],[c_0_117]) ).
fof(c_0_242,plain,
lhs_atom116,
inference(fof_simplification,[status(thm)],[c_0_118]) ).
fof(c_0_243,plain,
lhs_atom115,
inference(fof_simplification,[status(thm)],[c_0_119]) ).
fof(c_0_244,plain,
lhs_atom114,
inference(fof_simplification,[status(thm)],[c_0_120]) ).
fof(c_0_245,plain,
lhs_atom113,
inference(fof_simplification,[status(thm)],[c_0_121]) ).
fof(c_0_246,plain,
lhs_atom86,
inference(fof_simplification,[status(thm)],[c_0_122]) ).
fof(c_0_247,plain,
lhs_atom31,
inference(fof_simplification,[status(thm)],[c_0_123]) ).
fof(c_0_248,plain,
! [X22,X23,X24,X25,X26,X27,X28] : lhs_atom98(X22,X23,X24,X25,X26,X27,X28),
inference(variable_rename,[status(thm)],[c_0_124]) ).
fof(c_0_249,plain,
! [X14,X15,X16,X17,X18,X19] : lhs_atom51(X14,X15,X16,X17,X18,X19),
inference(variable_rename,[status(thm)],[c_0_125]) ).
fof(c_0_250,plain,
! [X18,X19,X20,X21,X22,X23] : lhs_atom28(X18,X19,X20,X21,X22,X23),
inference(variable_rename,[status(thm)],[c_0_126]) ).
fof(c_0_251,plain,
! [X18,X19,X20,X21,X22,X23] : lhs_atom27(X18,X19,X20,X21,X22,X23),
inference(variable_rename,[status(thm)],[c_0_127]) ).
fof(c_0_252,plain,
! [X18,X19,X20,X21,X22] : lhs_atom94(X18,X19,X20,X21,X22),
inference(variable_rename,[status(thm)],[c_0_128]) ).
fof(c_0_253,plain,
! [X19,X20,X21,X22,X23] : lhs_atom64(X19,X20,X21,X22,X23),
inference(variable_rename,[status(thm)],[c_0_129]) ).
fof(c_0_254,plain,
! [X9,X10,X11,X12,X13] : lhs_atom56(X9,X10,X11,X12,X13),
inference(variable_rename,[status(thm)],[c_0_130]) ).
fof(c_0_255,plain,
! [X19,X20,X21,X22,X23] : lhs_atom52(X19,X20,X21,X22,X23),
inference(variable_rename,[status(thm)],[c_0_131]) ).
fof(c_0_256,plain,
! [X9,X10,X11,X12,X13] : lhs_atom47(X9,X10,X11,X12,X13),
inference(variable_rename,[status(thm)],[c_0_132]) ).
fof(c_0_257,plain,
! [X10,X11,X12,X13,X14] : lhs_atom46(X10,X11,X12,X13,X14),
inference(variable_rename,[status(thm)],[c_0_133]) ).
fof(c_0_258,plain,
! [X19,X20,X21,X22,X23] : lhs_atom45(X19,X20,X21,X22,X23),
inference(variable_rename,[status(thm)],[c_0_134]) ).
fof(c_0_259,plain,
! [X14,X15,X16,X17,X18] : lhs_atom37(X14,X15,X16,X17,X18),
inference(variable_rename,[status(thm)],[c_0_135]) ).
fof(c_0_260,plain,
! [X9,X10,X11,X12,X13] : lhs_atom25(X9,X10,X11,X12,X13),
inference(variable_rename,[status(thm)],[c_0_136]) ).
fof(c_0_261,plain,
! [X10,X11,X12,X13,X14] : lhs_atom15(X10,X11,X12,X13,X14),
inference(variable_rename,[status(thm)],[c_0_137]) ).
fof(c_0_262,plain,
! [X11,X12,X13,X14,X15] : lhs_atom14(X11,X12,X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_138]) ).
fof(c_0_263,plain,
! [X14,X15,X16,X17,X18] : lhs_atom13(X14,X15,X16,X17,X18),
inference(variable_rename,[status(thm)],[c_0_139]) ).
fof(c_0_264,plain,
! [X9,X10,X11,X12,X13] : lhs_atom5(X9,X10,X11,X12,X13),
inference(variable_rename,[status(thm)],[c_0_140]) ).
fof(c_0_265,plain,
! [X19,X20,X21,X22] : lhs_atom99(X19,X20,X21,X22),
inference(variable_rename,[status(thm)],[c_0_141]) ).
fof(c_0_266,plain,
! [X21,X22,X23,X24] : lhs_atom85(X21,X22,X23,X24),
inference(variable_rename,[status(thm)],[c_0_142]) ).
fof(c_0_267,plain,
! [X9,X10,X11,X12] : lhs_atom61(X9,X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_143]) ).
fof(c_0_268,plain,
! [X6,X7,X8,X9] : lhs_atom58(X6,X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_144]) ).
fof(c_0_269,plain,
! [X6,X7,X8,X9] : lhs_atom57(X6,X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_145]) ).
fof(c_0_270,plain,
! [X16,X17,X18,X19] : lhs_atom53(X16,X17,X18,X19),
inference(variable_rename,[status(thm)],[c_0_146]) ).
fof(c_0_271,plain,
! [X6,X7,X8,X9] : lhs_atom49(X6,X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_147]) ).
fof(c_0_272,plain,
! [X6,X7,X8,X9] : lhs_atom48(X6,X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_148]) ).
fof(c_0_273,plain,
! [X9,X10,X11,X12] : lhs_atom43(X9,X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_149]) ).
fof(c_0_274,plain,
! [X9,X10,X11,X12] : lhs_atom35(X9,X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_150]) ).
fof(c_0_275,plain,
! [X9,X10,X11,X12] : lhs_atom33(X9,X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_151]) ).
fof(c_0_276,plain,
! [X16,X17,X18,X19] : lhs_atom26(X16,X17,X18,X19),
inference(variable_rename,[status(thm)],[c_0_152]) ).
fof(c_0_277,plain,
! [X6,X7,X8,X9] : lhs_atom23(X6,X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_153]) ).
fof(c_0_278,plain,
! [X6,X7,X8,X9] : lhs_atom18(X6,X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_154]) ).
fof(c_0_279,plain,
! [X6,X7,X8,X9] : lhs_atom17(X6,X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_155]) ).
fof(c_0_280,plain,
! [X15,X16,X17,X18] : lhs_atom16(X15,X16,X17,X18),
inference(variable_rename,[status(thm)],[c_0_156]) ).
fof(c_0_281,plain,
! [X12,X13,X14,X15] : lhs_atom11(X12,X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_157]) ).
fof(c_0_282,plain,
! [X12,X13,X14,X15] : lhs_atom9(X12,X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_158]) ).
fof(c_0_283,plain,
! [X12,X13,X14,X15] : lhs_atom8(X12,X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_159]) ).
fof(c_0_284,plain,
! [X6,X7,X8,X9] : lhs_atom4(X6,X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_160]) ).
fof(c_0_285,plain,
! [X6,X7,X8,X9] : lhs_atom3(X6,X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_161]) ).
fof(c_0_286,plain,
! [X24,X25,X26] : lhs_atom112(X24,X25,X26),
inference(variable_rename,[status(thm)],[c_0_162]) ).
fof(c_0_287,plain,
! [X23,X24,X25] : lhs_atom110(X23,X24,X25),
inference(variable_rename,[status(thm)],[c_0_163]) ).
fof(c_0_288,plain,
! [X9,X10,X11] : lhs_atom106(X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_164]) ).
fof(c_0_289,plain,
! [X9,X10,X11] : lhs_atom105(X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_165]) ).
fof(c_0_290,plain,
! [X9,X10,X11] : lhs_atom104(X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_166]) ).
fof(c_0_291,plain,
! [X9,X10,X11] : lhs_atom102(X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_167]) ).
fof(c_0_292,plain,
! [X10,X11,X12] : lhs_atom90(X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_168]) ).
fof(c_0_293,plain,
! [X10,X11,X12] : lhs_atom89(X10,X11,X12),
inference(variable_rename,[status(thm)],[c_0_169]) ).
fof(c_0_294,plain,
! [X13,X14,X15] : lhs_atom75(X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_170]) ).
fof(c_0_295,plain,
! [X12,X13,X14] : lhs_atom74(X12,X13,X14),
inference(variable_rename,[status(thm)],[c_0_171]) ).
fof(c_0_296,plain,
! [X6,X7,X8] : lhs_atom68(X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_172]) ).
fof(c_0_297,plain,
! [X6,X7,X8] : lhs_atom60(X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_173]) ).
fof(c_0_298,plain,
! [X13,X14,X15] : lhs_atom59(X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_174]) ).
fof(c_0_299,plain,
! [X6,X7,X8] : lhs_atom55(X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_175]) ).
fof(c_0_300,plain,
! [X6,X7,X8] : lhs_atom54(X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_176]) ).
fof(c_0_301,plain,
! [X12,X13,X14] : lhs_atom44(X12,X13,X14),
inference(variable_rename,[status(thm)],[c_0_177]) ).
fof(c_0_302,plain,
! [X13,X14,X15] : lhs_atom40(X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_178]) ).
fof(c_0_303,plain,
! [X12,X13,X14] : lhs_atom39(X12,X13,X14),
inference(variable_rename,[status(thm)],[c_0_179]) ).
fof(c_0_304,plain,
! [X13,X14,X15] : lhs_atom38(X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_180]) ).
fof(c_0_305,plain,
! [X11,X12,X13] : lhs_atom36(X11,X12,X13),
inference(variable_rename,[status(thm)],[c_0_181]) ).
fof(c_0_306,plain,
! [X6,X7,X8] : lhs_atom34(X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_182]) ).
fof(c_0_307,plain,
! [X6,X7,X8] : lhs_atom32(X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_183]) ).
fof(c_0_308,plain,
! [X16,X17,X18] : lhs_atom30(X16,X17,X18),
inference(variable_rename,[status(thm)],[c_0_184]) ).
fof(c_0_309,plain,
! [X6,X7,X8] : lhs_atom22(X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_185]) ).
fof(c_0_310,plain,
! [X6,X7,X8] : lhs_atom21(X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_186]) ).
fof(c_0_311,plain,
! [X6,X7,X8] : lhs_atom20(X6,X7,X8),
inference(variable_rename,[status(thm)],[c_0_187]) ).
fof(c_0_312,plain,
! [X13,X14,X15] : lhs_atom12(X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_188]) ).
fof(c_0_313,plain,
! [X11,X12,X13] : lhs_atom7(X11,X12,X13),
inference(variable_rename,[status(thm)],[c_0_189]) ).
fof(c_0_314,plain,
! [X13,X14] : lhs_atom124(X13,X14),
inference(variable_rename,[status(thm)],[c_0_190]) ).
fof(c_0_315,plain,
! [X23,X24] : lhs_atom111(X23,X24),
inference(variable_rename,[status(thm)],[c_0_191]) ).
fof(c_0_316,plain,
! [X23,X24] : lhs_atom109(X23,X24),
inference(variable_rename,[status(thm)],[c_0_192]) ).
fof(c_0_317,plain,
! [X12,X13] : lhs_atom108(X12,X13),
inference(variable_rename,[status(thm)],[c_0_193]) ).
fof(c_0_318,plain,
! [X13,X14] : lhs_atom107(X13,X14),
inference(variable_rename,[status(thm)],[c_0_194]) ).
fof(c_0_319,plain,
! [X4,X5] : lhs_atom103(X4,X5),
inference(variable_rename,[status(thm)],[c_0_195]) ).
fof(c_0_320,plain,
! [X4,X5] : lhs_atom101(X4,X5),
inference(variable_rename,[status(thm)],[c_0_196]) ).
fof(c_0_321,plain,
! [X3,X4] : lhs_atom100(X3,X4),
inference(variable_rename,[status(thm)],[c_0_197]) ).
fof(c_0_322,plain,
! [X4,X5] : lhs_atom96(X4,X5),
inference(variable_rename,[status(thm)],[c_0_198]) ).
fof(c_0_323,plain,
! [X4,X5] : lhs_atom95(X4,X5),
inference(variable_rename,[status(thm)],[c_0_199]) ).
fof(c_0_324,plain,
! [X3,X4] : lhs_atom93(X3,X4),
inference(variable_rename,[status(thm)],[c_0_200]) ).
fof(c_0_325,plain,
! [X4,X5] : lhs_atom92(X4,X5),
inference(variable_rename,[status(thm)],[c_0_201]) ).
fof(c_0_326,plain,
! [X4,X5] : lhs_atom91(X4,X5),
inference(variable_rename,[status(thm)],[c_0_202]) ).
fof(c_0_327,plain,
! [X3,X4] : lhs_atom87(X3,X4),
inference(variable_rename,[status(thm)],[c_0_203]) ).
fof(c_0_328,plain,
! [X4,X5] : lhs_atom84(X4,X5),
inference(variable_rename,[status(thm)],[c_0_204]) ).
fof(c_0_329,plain,
! [X3,X4] : lhs_atom83(X3,X4),
inference(variable_rename,[status(thm)],[c_0_205]) ).
fof(c_0_330,plain,
! [X10,X11] : lhs_atom82(X10,X11),
inference(variable_rename,[status(thm)],[c_0_206]) ).
fof(c_0_331,plain,
! [X10,X11] : lhs_atom81(X10,X11),
inference(variable_rename,[status(thm)],[c_0_207]) ).
fof(c_0_332,plain,
! [X3,X4] : lhs_atom80(X3,X4),
inference(variable_rename,[status(thm)],[c_0_208]) ).
fof(c_0_333,plain,
! [X13,X14] : lhs_atom79(X13,X14),
inference(variable_rename,[status(thm)],[c_0_209]) ).
fof(c_0_334,plain,
! [X4,X5] : lhs_atom78(X4,X5),
inference(variable_rename,[status(thm)],[c_0_210]) ).
fof(c_0_335,plain,
! [X10,X11] : lhs_atom77(X10,X11),
inference(variable_rename,[status(thm)],[c_0_211]) ).
fof(c_0_336,plain,
! [X3,X4] : lhs_atom76(X3,X4),
inference(variable_rename,[status(thm)],[c_0_212]) ).
fof(c_0_337,plain,
! [X3,X4] : lhs_atom73(X3,X4),
inference(variable_rename,[status(thm)],[c_0_213]) ).
fof(c_0_338,plain,
! [X3,X4] : lhs_atom72(X3,X4),
inference(variable_rename,[status(thm)],[c_0_214]) ).
fof(c_0_339,plain,
! [X3,X4] : lhs_atom71(X3,X4),
inference(variable_rename,[status(thm)],[c_0_215]) ).
fof(c_0_340,plain,
! [X3,X4] : lhs_atom70(X3,X4),
inference(variable_rename,[status(thm)],[c_0_216]) ).
fof(c_0_341,plain,
! [X3,X4] : lhs_atom69(X3,X4),
inference(variable_rename,[status(thm)],[c_0_217]) ).
fof(c_0_342,plain,
! [X3,X4] : lhs_atom67(X3,X4),
inference(variable_rename,[status(thm)],[c_0_218]) ).
fof(c_0_343,plain,
! [X3,X4] : lhs_atom66(X3,X4),
inference(variable_rename,[status(thm)],[c_0_219]) ).
fof(c_0_344,plain,
! [X3,X4] : lhs_atom65(X3,X4),
inference(variable_rename,[status(thm)],[c_0_220]) ).
fof(c_0_345,plain,
! [X3,X4] : lhs_atom63(X3,X4),
inference(variable_rename,[status(thm)],[c_0_221]) ).
fof(c_0_346,plain,
! [X4,X5] : lhs_atom62(X4,X5),
inference(variable_rename,[status(thm)],[c_0_222]) ).
fof(c_0_347,plain,
! [X3,X4] : lhs_atom42(X3,X4),
inference(variable_rename,[status(thm)],[c_0_223]) ).
fof(c_0_348,plain,
! [X3,X4] : lhs_atom41(X3,X4),
inference(variable_rename,[status(thm)],[c_0_224]) ).
fof(c_0_349,plain,
! [X4,X5] : lhs_atom29(X4,X5),
inference(variable_rename,[status(thm)],[c_0_225]) ).
fof(c_0_350,plain,
! [X3,X4] : lhs_atom24(X3,X4),
inference(variable_rename,[status(thm)],[c_0_226]) ).
fof(c_0_351,plain,
! [X10,X11] : lhs_atom19(X10,X11),
inference(variable_rename,[status(thm)],[c_0_227]) ).
fof(c_0_352,plain,
! [X3,X4] : lhs_atom10(X3,X4),
inference(variable_rename,[status(thm)],[c_0_228]) ).
fof(c_0_353,plain,
! [X10,X11] : lhs_atom6(X10,X11),
inference(variable_rename,[status(thm)],[c_0_229]) ).
fof(c_0_354,plain,
! [X4,X5] : lhs_atom2(X4,X5),
inference(variable_rename,[status(thm)],[c_0_230]) ).
fof(c_0_355,plain,
! [X3,X4] : lhs_atom1(X3,X4),
inference(variable_rename,[status(thm)],[c_0_231]) ).
fof(c_0_356,plain,
! [X3] : lhs_atom97(X3),
inference(variable_rename,[status(thm)],[c_0_232]) ).
fof(c_0_357,plain,
! [X3] : lhs_atom88(X3),
inference(variable_rename,[status(thm)],[c_0_233]) ).
fof(c_0_358,plain,
! [X3] : lhs_atom50(X3),
inference(variable_rename,[status(thm)],[c_0_234]) ).
fof(c_0_359,plain,
lhs_atom123,
c_0_235 ).
fof(c_0_360,plain,
lhs_atom122,
c_0_236 ).
fof(c_0_361,plain,
lhs_atom121,
c_0_237 ).
fof(c_0_362,plain,
lhs_atom120,
c_0_238 ).
fof(c_0_363,plain,
lhs_atom119,
c_0_239 ).
fof(c_0_364,plain,
lhs_atom118,
c_0_240 ).
fof(c_0_365,plain,
lhs_atom117,
c_0_241 ).
fof(c_0_366,plain,
lhs_atom116,
c_0_242 ).
fof(c_0_367,plain,
lhs_atom115,
c_0_243 ).
fof(c_0_368,plain,
lhs_atom114,
c_0_244 ).
fof(c_0_369,plain,
lhs_atom113,
c_0_245 ).
fof(c_0_370,plain,
lhs_atom86,
c_0_246 ).
fof(c_0_371,plain,
lhs_atom31,
c_0_247 ).
cnf(c_0_372,plain,
lhs_atom98(X1,X2,X3,X4,X5,X6,X7),
inference(split_conjunct,[status(thm)],[c_0_248]) ).
cnf(c_0_373,plain,
lhs_atom51(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_249]) ).
cnf(c_0_374,plain,
lhs_atom28(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_250]) ).
cnf(c_0_375,plain,
lhs_atom27(X1,X2,X3,X4,X5,X6),
inference(split_conjunct,[status(thm)],[c_0_251]) ).
cnf(c_0_376,plain,
lhs_atom94(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_252]) ).
cnf(c_0_377,plain,
lhs_atom64(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_253]) ).
cnf(c_0_378,plain,
lhs_atom56(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_254]) ).
cnf(c_0_379,plain,
lhs_atom52(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_255]) ).
cnf(c_0_380,plain,
lhs_atom47(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_256]) ).
cnf(c_0_381,plain,
lhs_atom46(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_257]) ).
cnf(c_0_382,plain,
lhs_atom45(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_258]) ).
cnf(c_0_383,plain,
lhs_atom37(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_259]) ).
cnf(c_0_384,plain,
lhs_atom25(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_260]) ).
cnf(c_0_385,plain,
lhs_atom15(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_261]) ).
cnf(c_0_386,plain,
lhs_atom14(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_262]) ).
cnf(c_0_387,plain,
lhs_atom13(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_263]) ).
cnf(c_0_388,plain,
lhs_atom5(X1,X2,X3,X4,X5),
inference(split_conjunct,[status(thm)],[c_0_264]) ).
cnf(c_0_389,plain,
lhs_atom99(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_265]) ).
cnf(c_0_390,plain,
lhs_atom85(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_266]) ).
cnf(c_0_391,plain,
lhs_atom61(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_267]) ).
cnf(c_0_392,plain,
lhs_atom58(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_268]) ).
cnf(c_0_393,plain,
lhs_atom57(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_269]) ).
cnf(c_0_394,plain,
lhs_atom53(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_270]) ).
cnf(c_0_395,plain,
lhs_atom49(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_271]) ).
cnf(c_0_396,plain,
lhs_atom48(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_272]) ).
cnf(c_0_397,plain,
lhs_atom43(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_273]) ).
cnf(c_0_398,plain,
lhs_atom35(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_274]) ).
cnf(c_0_399,plain,
lhs_atom33(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_275]) ).
cnf(c_0_400,plain,
lhs_atom26(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_276]) ).
cnf(c_0_401,plain,
lhs_atom23(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_277]) ).
cnf(c_0_402,plain,
lhs_atom18(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_278]) ).
cnf(c_0_403,plain,
lhs_atom17(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_279]) ).
cnf(c_0_404,plain,
lhs_atom16(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_280]) ).
cnf(c_0_405,plain,
lhs_atom11(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_281]) ).
cnf(c_0_406,plain,
lhs_atom9(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_282]) ).
cnf(c_0_407,plain,
lhs_atom8(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_283]) ).
cnf(c_0_408,plain,
lhs_atom4(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_284]) ).
cnf(c_0_409,plain,
lhs_atom3(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_285]) ).
cnf(c_0_410,plain,
lhs_atom112(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_286]) ).
cnf(c_0_411,plain,
lhs_atom110(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_287]) ).
cnf(c_0_412,plain,
lhs_atom106(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_288]) ).
cnf(c_0_413,plain,
lhs_atom105(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_289]) ).
cnf(c_0_414,plain,
lhs_atom104(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_290]) ).
cnf(c_0_415,plain,
lhs_atom102(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_291]) ).
cnf(c_0_416,plain,
lhs_atom90(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_292]) ).
cnf(c_0_417,plain,
lhs_atom89(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_293]) ).
cnf(c_0_418,plain,
lhs_atom75(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_294]) ).
cnf(c_0_419,plain,
lhs_atom74(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_295]) ).
cnf(c_0_420,plain,
lhs_atom68(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_296]) ).
cnf(c_0_421,plain,
lhs_atom60(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_297]) ).
cnf(c_0_422,plain,
lhs_atom59(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_298]) ).
cnf(c_0_423,plain,
lhs_atom55(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_299]) ).
cnf(c_0_424,plain,
lhs_atom54(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_300]) ).
cnf(c_0_425,plain,
lhs_atom44(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_301]) ).
cnf(c_0_426,plain,
lhs_atom40(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_302]) ).
cnf(c_0_427,plain,
lhs_atom39(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_303]) ).
cnf(c_0_428,plain,
lhs_atom38(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_304]) ).
cnf(c_0_429,plain,
lhs_atom36(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_305]) ).
cnf(c_0_430,plain,
lhs_atom34(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_306]) ).
cnf(c_0_431,plain,
lhs_atom32(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_307]) ).
cnf(c_0_432,plain,
lhs_atom30(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_308]) ).
cnf(c_0_433,plain,
lhs_atom22(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_309]) ).
cnf(c_0_434,plain,
lhs_atom21(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_310]) ).
cnf(c_0_435,plain,
lhs_atom20(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_311]) ).
cnf(c_0_436,plain,
lhs_atom12(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_312]) ).
cnf(c_0_437,plain,
lhs_atom7(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_313]) ).
cnf(c_0_438,plain,
lhs_atom124(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_314]) ).
cnf(c_0_439,plain,
lhs_atom111(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_315]) ).
cnf(c_0_440,plain,
lhs_atom109(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_316]) ).
cnf(c_0_441,plain,
lhs_atom108(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_317]) ).
cnf(c_0_442,plain,
lhs_atom107(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_318]) ).
cnf(c_0_443,plain,
lhs_atom103(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_319]) ).
cnf(c_0_444,plain,
lhs_atom101(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_320]) ).
cnf(c_0_445,plain,
lhs_atom100(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_321]) ).
cnf(c_0_446,plain,
lhs_atom96(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_322]) ).
cnf(c_0_447,plain,
lhs_atom95(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_323]) ).
cnf(c_0_448,plain,
lhs_atom93(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_324]) ).
cnf(c_0_449,plain,
lhs_atom92(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_325]) ).
cnf(c_0_450,plain,
lhs_atom91(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_326]) ).
cnf(c_0_451,plain,
lhs_atom87(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_327]) ).
cnf(c_0_452,plain,
lhs_atom84(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_328]) ).
cnf(c_0_453,plain,
lhs_atom83(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_329]) ).
cnf(c_0_454,plain,
lhs_atom82(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_330]) ).
cnf(c_0_455,plain,
lhs_atom81(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_331]) ).
cnf(c_0_456,plain,
lhs_atom80(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_332]) ).
cnf(c_0_457,plain,
lhs_atom79(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_333]) ).
cnf(c_0_458,plain,
lhs_atom78(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_334]) ).
cnf(c_0_459,plain,
lhs_atom77(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_335]) ).
cnf(c_0_460,plain,
lhs_atom76(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_336]) ).
cnf(c_0_461,plain,
lhs_atom73(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_337]) ).
cnf(c_0_462,plain,
lhs_atom72(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_338]) ).
cnf(c_0_463,plain,
lhs_atom71(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_339]) ).
cnf(c_0_464,plain,
lhs_atom70(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_340]) ).
cnf(c_0_465,plain,
lhs_atom69(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_341]) ).
cnf(c_0_466,plain,
lhs_atom67(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_342]) ).
cnf(c_0_467,plain,
lhs_atom66(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_343]) ).
cnf(c_0_468,plain,
lhs_atom65(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_344]) ).
cnf(c_0_469,plain,
lhs_atom63(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_345]) ).
cnf(c_0_470,plain,
lhs_atom62(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_346]) ).
cnf(c_0_471,plain,
lhs_atom42(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_347]) ).
cnf(c_0_472,plain,
lhs_atom41(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_348]) ).
cnf(c_0_473,plain,
lhs_atom29(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_349]) ).
cnf(c_0_474,plain,
lhs_atom24(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_350]) ).
cnf(c_0_475,plain,
lhs_atom19(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_351]) ).
cnf(c_0_476,plain,
lhs_atom10(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_352]) ).
cnf(c_0_477,plain,
lhs_atom6(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_353]) ).
cnf(c_0_478,plain,
lhs_atom2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_354]) ).
cnf(c_0_479,plain,
lhs_atom1(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_355]) ).
cnf(c_0_480,plain,
lhs_atom97(X1),
inference(split_conjunct,[status(thm)],[c_0_356]) ).
cnf(c_0_481,plain,
lhs_atom88(X1),
inference(split_conjunct,[status(thm)],[c_0_357]) ).
cnf(c_0_482,plain,
lhs_atom50(X1),
inference(split_conjunct,[status(thm)],[c_0_358]) ).
cnf(c_0_483,plain,
lhs_atom123,
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_484,plain,
lhs_atom122,
inference(split_conjunct,[status(thm)],[c_0_360]) ).
cnf(c_0_485,plain,
lhs_atom121,
inference(split_conjunct,[status(thm)],[c_0_361]) ).
cnf(c_0_486,plain,
lhs_atom120,
inference(split_conjunct,[status(thm)],[c_0_362]) ).
cnf(c_0_487,plain,
lhs_atom119,
inference(split_conjunct,[status(thm)],[c_0_363]) ).
cnf(c_0_488,plain,
lhs_atom118,
inference(split_conjunct,[status(thm)],[c_0_364]) ).
cnf(c_0_489,plain,
lhs_atom117,
inference(split_conjunct,[status(thm)],[c_0_365]) ).
cnf(c_0_490,plain,
lhs_atom116,
inference(split_conjunct,[status(thm)],[c_0_366]) ).
cnf(c_0_491,plain,
lhs_atom115,
inference(split_conjunct,[status(thm)],[c_0_367]) ).
cnf(c_0_492,plain,
lhs_atom114,
inference(split_conjunct,[status(thm)],[c_0_368]) ).
cnf(c_0_493,plain,
lhs_atom113,
inference(split_conjunct,[status(thm)],[c_0_369]) ).
cnf(c_0_494,plain,
lhs_atom86,
inference(split_conjunct,[status(thm)],[c_0_370]) ).
cnf(c_0_495,plain,
lhs_atom31,
inference(split_conjunct,[status(thm)],[c_0_371]) ).
cnf(c_0_496,plain,
lhs_atom98(X1,X2,X3,X4,X5,X6,X7),
c_0_372,
[final] ).
cnf(c_0_497,plain,
lhs_atom51(X1,X2,X3,X4,X5,X6),
c_0_373,
[final] ).
cnf(c_0_498,plain,
lhs_atom28(X1,X2,X3,X4,X5,X6),
c_0_374,
[final] ).
cnf(c_0_499,plain,
lhs_atom27(X1,X2,X3,X4,X5,X6),
c_0_375,
[final] ).
cnf(c_0_500,plain,
lhs_atom94(X1,X2,X3,X4,X5),
c_0_376,
[final] ).
cnf(c_0_501,plain,
lhs_atom64(X1,X2,X3,X4,X5),
c_0_377,
[final] ).
cnf(c_0_502,plain,
lhs_atom56(X1,X2,X3,X4,X5),
c_0_378,
[final] ).
cnf(c_0_503,plain,
lhs_atom52(X1,X2,X3,X4,X5),
c_0_379,
[final] ).
cnf(c_0_504,plain,
lhs_atom47(X1,X2,X3,X4,X5),
c_0_380,
[final] ).
cnf(c_0_505,plain,
lhs_atom46(X1,X2,X3,X4,X5),
c_0_381,
[final] ).
cnf(c_0_506,plain,
lhs_atom45(X1,X2,X3,X4,X5),
c_0_382,
[final] ).
cnf(c_0_507,plain,
lhs_atom37(X1,X2,X3,X4,X5),
c_0_383,
[final] ).
cnf(c_0_508,plain,
lhs_atom25(X1,X2,X3,X4,X5),
c_0_384,
[final] ).
cnf(c_0_509,plain,
lhs_atom15(X1,X2,X3,X4,X5),
c_0_385,
[final] ).
cnf(c_0_510,plain,
lhs_atom14(X1,X2,X3,X4,X5),
c_0_386,
[final] ).
cnf(c_0_511,plain,
lhs_atom13(X1,X2,X3,X4,X5),
c_0_387,
[final] ).
cnf(c_0_512,plain,
lhs_atom5(X1,X2,X3,X4,X5),
c_0_388,
[final] ).
cnf(c_0_513,plain,
lhs_atom99(X1,X2,X3,X4),
c_0_389,
[final] ).
cnf(c_0_514,plain,
lhs_atom85(X1,X2,X3,X4),
c_0_390,
[final] ).
cnf(c_0_515,plain,
lhs_atom61(X1,X2,X3,X4),
c_0_391,
[final] ).
cnf(c_0_516,plain,
lhs_atom58(X1,X2,X3,X4),
c_0_392,
[final] ).
cnf(c_0_517,plain,
lhs_atom57(X1,X2,X3,X4),
c_0_393,
[final] ).
cnf(c_0_518,plain,
lhs_atom53(X1,X2,X3,X4),
c_0_394,
[final] ).
cnf(c_0_519,plain,
lhs_atom49(X1,X2,X3,X4),
c_0_395,
[final] ).
cnf(c_0_520,plain,
lhs_atom48(X1,X2,X3,X4),
c_0_396,
[final] ).
cnf(c_0_521,plain,
lhs_atom43(X1,X2,X3,X4),
c_0_397,
[final] ).
cnf(c_0_522,plain,
lhs_atom35(X1,X2,X3,X4),
c_0_398,
[final] ).
cnf(c_0_523,plain,
lhs_atom33(X1,X2,X3,X4),
c_0_399,
[final] ).
cnf(c_0_524,plain,
lhs_atom26(X1,X2,X3,X4),
c_0_400,
[final] ).
cnf(c_0_525,plain,
lhs_atom23(X1,X2,X3,X4),
c_0_401,
[final] ).
cnf(c_0_526,plain,
lhs_atom18(X1,X2,X3,X4),
c_0_402,
[final] ).
cnf(c_0_527,plain,
lhs_atom17(X1,X2,X3,X4),
c_0_403,
[final] ).
cnf(c_0_528,plain,
lhs_atom16(X1,X2,X3,X4),
c_0_404,
[final] ).
cnf(c_0_529,plain,
lhs_atom11(X1,X2,X3,X4),
c_0_405,
[final] ).
cnf(c_0_530,plain,
lhs_atom9(X1,X2,X3,X4),
c_0_406,
[final] ).
cnf(c_0_531,plain,
lhs_atom8(X1,X2,X3,X4),
c_0_407,
[final] ).
cnf(c_0_532,plain,
lhs_atom4(X1,X2,X3,X4),
c_0_408,
[final] ).
cnf(c_0_533,plain,
lhs_atom3(X1,X2,X3,X4),
c_0_409,
[final] ).
cnf(c_0_534,plain,
lhs_atom112(X1,X2,X3),
c_0_410,
[final] ).
cnf(c_0_535,plain,
lhs_atom110(X1,X2,X3),
c_0_411,
[final] ).
cnf(c_0_536,plain,
lhs_atom106(X1,X2,X3),
c_0_412,
[final] ).
cnf(c_0_537,plain,
lhs_atom105(X1,X2,X3),
c_0_413,
[final] ).
cnf(c_0_538,plain,
lhs_atom104(X1,X2,X3),
c_0_414,
[final] ).
cnf(c_0_539,plain,
lhs_atom102(X1,X2,X3),
c_0_415,
[final] ).
cnf(c_0_540,plain,
lhs_atom90(X1,X2,X3),
c_0_416,
[final] ).
cnf(c_0_541,plain,
lhs_atom89(X1,X2,X3),
c_0_417,
[final] ).
cnf(c_0_542,plain,
lhs_atom75(X1,X2,X3),
c_0_418,
[final] ).
cnf(c_0_543,plain,
lhs_atom74(X1,X2,X3),
c_0_419,
[final] ).
cnf(c_0_544,plain,
lhs_atom68(X1,X2,X3),
c_0_420,
[final] ).
cnf(c_0_545,plain,
lhs_atom60(X1,X2,X3),
c_0_421,
[final] ).
cnf(c_0_546,plain,
lhs_atom59(X1,X2,X3),
c_0_422,
[final] ).
cnf(c_0_547,plain,
lhs_atom55(X1,X2,X3),
c_0_423,
[final] ).
cnf(c_0_548,plain,
lhs_atom54(X1,X2,X3),
c_0_424,
[final] ).
cnf(c_0_549,plain,
lhs_atom44(X1,X2,X3),
c_0_425,
[final] ).
cnf(c_0_550,plain,
lhs_atom40(X1,X2,X3),
c_0_426,
[final] ).
cnf(c_0_551,plain,
lhs_atom39(X1,X2,X3),
c_0_427,
[final] ).
cnf(c_0_552,plain,
lhs_atom38(X1,X2,X3),
c_0_428,
[final] ).
cnf(c_0_553,plain,
lhs_atom36(X1,X2,X3),
c_0_429,
[final] ).
cnf(c_0_554,plain,
lhs_atom34(X1,X2,X3),
c_0_430,
[final] ).
cnf(c_0_555,plain,
lhs_atom32(X1,X2,X3),
c_0_431,
[final] ).
cnf(c_0_556,plain,
lhs_atom30(X1,X2,X3),
c_0_432,
[final] ).
cnf(c_0_557,plain,
lhs_atom22(X1,X2,X3),
c_0_433,
[final] ).
cnf(c_0_558,plain,
lhs_atom21(X1,X2,X3),
c_0_434,
[final] ).
cnf(c_0_559,plain,
lhs_atom20(X1,X2,X3),
c_0_435,
[final] ).
cnf(c_0_560,plain,
lhs_atom12(X1,X2,X3),
c_0_436,
[final] ).
cnf(c_0_561,plain,
lhs_atom7(X1,X2,X3),
c_0_437,
[final] ).
cnf(c_0_562,plain,
lhs_atom124(X1,X2),
c_0_438,
[final] ).
cnf(c_0_563,plain,
lhs_atom111(X1,X2),
c_0_439,
[final] ).
cnf(c_0_564,plain,
lhs_atom109(X1,X2),
c_0_440,
[final] ).
cnf(c_0_565,plain,
lhs_atom108(X1,X2),
c_0_441,
[final] ).
cnf(c_0_566,plain,
lhs_atom107(X1,X2),
c_0_442,
[final] ).
cnf(c_0_567,plain,
lhs_atom103(X1,X2),
c_0_443,
[final] ).
cnf(c_0_568,plain,
lhs_atom101(X1,X2),
c_0_444,
[final] ).
cnf(c_0_569,plain,
lhs_atom100(X1,X2),
c_0_445,
[final] ).
cnf(c_0_570,plain,
lhs_atom96(X1,X2),
c_0_446,
[final] ).
cnf(c_0_571,plain,
lhs_atom95(X1,X2),
c_0_447,
[final] ).
cnf(c_0_572,plain,
lhs_atom93(X1,X2),
c_0_448,
[final] ).
cnf(c_0_573,plain,
lhs_atom92(X1,X2),
c_0_449,
[final] ).
cnf(c_0_574,plain,
lhs_atom91(X1,X2),
c_0_450,
[final] ).
cnf(c_0_575,plain,
lhs_atom87(X1,X2),
c_0_451,
[final] ).
cnf(c_0_576,plain,
lhs_atom84(X1,X2),
c_0_452,
[final] ).
cnf(c_0_577,plain,
lhs_atom83(X1,X2),
c_0_453,
[final] ).
cnf(c_0_578,plain,
lhs_atom82(X1,X2),
c_0_454,
[final] ).
cnf(c_0_579,plain,
lhs_atom81(X1,X2),
c_0_455,
[final] ).
cnf(c_0_580,plain,
lhs_atom80(X1,X2),
c_0_456,
[final] ).
cnf(c_0_581,plain,
lhs_atom79(X1,X2),
c_0_457,
[final] ).
cnf(c_0_582,plain,
lhs_atom78(X1,X2),
c_0_458,
[final] ).
cnf(c_0_583,plain,
lhs_atom77(X1,X2),
c_0_459,
[final] ).
cnf(c_0_584,plain,
lhs_atom76(X1,X2),
c_0_460,
[final] ).
cnf(c_0_585,plain,
lhs_atom73(X1,X2),
c_0_461,
[final] ).
cnf(c_0_586,plain,
lhs_atom72(X1,X2),
c_0_462,
[final] ).
cnf(c_0_587,plain,
lhs_atom71(X1,X2),
c_0_463,
[final] ).
cnf(c_0_588,plain,
lhs_atom70(X1,X2),
c_0_464,
[final] ).
cnf(c_0_589,plain,
lhs_atom69(X1,X2),
c_0_465,
[final] ).
cnf(c_0_590,plain,
lhs_atom67(X1,X2),
c_0_466,
[final] ).
cnf(c_0_591,plain,
lhs_atom66(X1,X2),
c_0_467,
[final] ).
cnf(c_0_592,plain,
lhs_atom65(X1,X2),
c_0_468,
[final] ).
cnf(c_0_593,plain,
lhs_atom63(X1,X2),
c_0_469,
[final] ).
cnf(c_0_594,plain,
lhs_atom62(X1,X2),
c_0_470,
[final] ).
cnf(c_0_595,plain,
lhs_atom42(X1,X2),
c_0_471,
[final] ).
cnf(c_0_596,plain,
lhs_atom41(X1,X2),
c_0_472,
[final] ).
cnf(c_0_597,plain,
lhs_atom29(X1,X2),
c_0_473,
[final] ).
cnf(c_0_598,plain,
lhs_atom24(X1,X2),
c_0_474,
[final] ).
cnf(c_0_599,plain,
lhs_atom19(X1,X2),
c_0_475,
[final] ).
cnf(c_0_600,plain,
lhs_atom10(X1,X2),
c_0_476,
[final] ).
cnf(c_0_601,plain,
lhs_atom6(X1,X2),
c_0_477,
[final] ).
cnf(c_0_602,plain,
lhs_atom2(X1,X2),
c_0_478,
[final] ).
cnf(c_0_603,plain,
lhs_atom1(X1,X2),
c_0_479,
[final] ).
cnf(c_0_604,plain,
lhs_atom97(X1),
c_0_480,
[final] ).
cnf(c_0_605,plain,
lhs_atom88(X1),
c_0_481,
[final] ).
cnf(c_0_606,plain,
lhs_atom50(X1),
c_0_482,
[final] ).
cnf(c_0_607,plain,
lhs_atom123,
c_0_483,
[final] ).
cnf(c_0_608,plain,
lhs_atom122,
c_0_484,
[final] ).
cnf(c_0_609,plain,
lhs_atom121,
c_0_485,
[final] ).
cnf(c_0_610,plain,
lhs_atom120,
c_0_486,
[final] ).
cnf(c_0_611,plain,
lhs_atom119,
c_0_487,
[final] ).
cnf(c_0_612,plain,
lhs_atom118,
c_0_488,
[final] ).
cnf(c_0_613,plain,
lhs_atom117,
c_0_489,
[final] ).
cnf(c_0_614,plain,
lhs_atom116,
c_0_490,
[final] ).
cnf(c_0_615,plain,
lhs_atom115,
c_0_491,
[final] ).
cnf(c_0_616,plain,
lhs_atom114,
c_0_492,
[final] ).
cnf(c_0_617,plain,
lhs_atom113,
c_0_493,
[final] ).
cnf(c_0_618,plain,
lhs_atom86,
c_0_494,
[final] ).
cnf(c_0_619,plain,
lhs_atom31,
c_0_495,
[final] ).
% End CNF derivation
cnf(c_0_496_0,axiom,
c_Relation_Orel__comp(c_Relation_Orel__comp(X3,X2,X7,X4,X5),X1,X7,X5,X6) = c_Relation_Orel__comp(X3,c_Relation_Orel__comp(X2,X1,X4,X5,X6),X7,X4,X6),
inference(unfold_definition,[status(thm)],[c_0_496,def_lhs_atom98]) ).
cnf(c_0_497_0,axiom,
c_Product__Type_OSigma(c_Set_Oinsert(X2,X4,X6),c_COMBK(c_Set_Oinsert(X1,X3,X5),tc_fun(X5,tc_bool),X6),X6,X5) = c_Set_Oinsert(c_Pair(X2,X1,X6,X5),c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X4,c_COMBK(c_Set_Oinsert(X1,X3,X5),tc_fun(X5,tc_bool),X6),X6,X5),c_Product__Type_OSigma(c_Set_Oinsert(X2,X4,X6),c_COMBK(X3,tc_fun(X5,tc_bool),X6),X6,X5),tc_fun(tc_prod(X6,X5),tc_bool)),tc_prod(X6,X5)),
inference(unfold_definition,[status(thm)],[c_0_497,def_lhs_atom51]) ).
cnf(c_0_498_0,axiom,
c_Relation_Orel__comp(X3,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(tc_prod(X4,X5),tc_bool)),X6,X4,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X3,X2,X6,X4,X5),c_Relation_Orel__comp(X3,X1,X6,X4,X5),tc_fun(tc_prod(X6,X5),tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_498,def_lhs_atom28]) ).
cnf(c_0_499_0,axiom,
c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(tc_prod(X6,X4),tc_bool)),X3,X6,X4,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X2,X3,X6,X4,X5),c_Relation_Orel__comp(X1,X3,X6,X4,X5),tc_fun(tc_prod(X6,X5),tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_499,def_lhs_atom27]) ).
cnf(c_0_500_0,axiom,
c_Relation_Oconverse(c_Relation_Orel__comp(X2,X1,X4,X3,X5),X4,X5) = c_Relation_Orel__comp(c_Relation_Oconverse(X1,X3,X5),c_Relation_Oconverse(X2,X4,X3),X5,X3,X4),
inference(unfold_definition,[status(thm)],[c_0_500,def_lhs_atom94]) ).
cnf(c_0_501_0,axiom,
c_Set_Oimage(X1,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X4,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(X1,X3,X4,X5),c_Set_Oimage(X1,X2,X4,X5),tc_fun(X5,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_501,def_lhs_atom64]) ).
cnf(c_0_502_0,axiom,
c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X5,tc_bool)),c_COMBK(X1,tc_fun(X4,tc_bool),X5),X5,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X3,c_COMBK(X1,tc_fun(X4,tc_bool),X5),X5,X4),c_Product__Type_OSigma(X2,c_COMBK(X1,tc_fun(X4,tc_bool),X5),X5,X4),tc_fun(tc_prod(X5,X4),tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_502,def_lhs_atom56]) ).
cnf(c_0_503_0,axiom,
c_Set_Oimage(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) = c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5),
inference(unfold_definition,[status(thm)],[c_0_503,def_lhs_atom52]) ).
cnf(c_0_504_0,axiom,
c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X5,tc_bool)),c_COMBK(X1,tc_fun(X4,tc_bool),X5),X5,X4) = c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(X3,c_COMBK(X1,tc_fun(X4,tc_bool),X5),X5,X4),c_Product__Type_OSigma(X2,c_COMBK(X1,tc_fun(X4,tc_bool),X5),X5,X4),tc_fun(tc_prod(X5,X4),tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_504,def_lhs_atom47]) ).
cnf(c_0_505_0,axiom,
c_lessequals(c_Relation_OImage(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),X4,X5),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X1,X3,X4,X5),c_Relation_OImage(X1,X2,X4,X5),tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_505,def_lhs_atom46]) ).
cnf(c_0_506_0,axiom,
c_lessequals(c_Set_Oimage(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),X4,X5),c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(X1,X3,X4,X5),c_Set_Oimage(X1,X2,X4,X5),tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_506,def_lhs_atom45]) ).
cnf(c_0_507_0,axiom,
c_Relation_ORange(c_Set_Oinsert(c_Pair(X3,X2,X4,X5),X1,tc_prod(X4,X5)),X4,X5) = c_Set_Oinsert(X2,c_Relation_ORange(X1,X4,X5),X5),
inference(unfold_definition,[status(thm)],[c_0_507,def_lhs_atom37]) ).
cnf(c_0_508_0,axiom,
c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X5,tc_bool)),X3,X5,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X2,X3,X5,X4),c_Product__Type_OSigma(X1,X3,X5,X4),tc_fun(tc_prod(X5,X4),tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_508,def_lhs_atom25]) ).
cnf(c_0_509_0,axiom,
c_Relation_OImage(X1,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X4,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X1,X3,X4,X5),c_Relation_OImage(X1,X2,X4,X5),tc_fun(X5,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_509,def_lhs_atom15]) ).
cnf(c_0_510_0,axiom,
c_Relation_OImage(c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(tc_prod(X4,X5),tc_bool)),X3,X4,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X2,X3,X4,X5),c_Relation_OImage(X1,X3,X4,X5),tc_fun(X5,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_510,def_lhs_atom14]) ).
cnf(c_0_511_0,axiom,
c_Relation_ODomain(c_Set_Oinsert(c_Pair(X3,X2,X5,X4),X1,tc_prod(X5,X4)),X5,X4) = c_Set_Oinsert(X3,c_Relation_ODomain(X1,X5,X4),X5),
inference(unfold_definition,[status(thm)],[c_0_511,def_lhs_atom13]) ).
cnf(c_0_512_0,axiom,
c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X5,tc_bool)),X3,X5,X4) = c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(X2,X3,X5,X4),c_Product__Type_OSigma(X1,X3,X5,X4),tc_fun(tc_prod(X5,X4),tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_512,def_lhs_atom5]) ).
cnf(c_0_513_0,axiom,
c_Relation_Oconverse(c_Relation_Oinv__image(X2,X1,X3,X4),X4,X4) = c_Relation_Oinv__image(c_Relation_Oconverse(X2,X3,X3),X1,X3,X4),
inference(unfold_definition,[status(thm)],[c_0_513,def_lhs_atom99]) ).
cnf(c_0_514_0,axiom,
hAPP(c_COMBK(X2,X4,X3),X1) = X2,
inference(unfold_definition,[status(thm)],[c_0_514,def_lhs_atom85]) ).
cnf(c_0_515_0,axiom,
c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X2,X3,X4),c_Relation_ORange(X1,X3,X4),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_515,def_lhs_atom61]) ).
cnf(c_0_516_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_516,def_lhs_atom58]) ).
cnf(c_0_517_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_517,def_lhs_atom57]) ).
cnf(c_0_518_0,axiom,
c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Oconverse(X2,X3,X4),c_Relation_Oconverse(X1,X3,X4),tc_fun(tc_prod(X4,X3),tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_518,def_lhs_atom53]) ).
cnf(c_0_519_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_519,def_lhs_atom49]) ).
cnf(c_0_520_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),X1,tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_520,def_lhs_atom48]) ).
cnf(c_0_521_0,axiom,
c_lessequals(c_Relation_ODomain(c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(tc_prod(X4,X3),tc_bool)),X4,X3),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X2,X4,X3),c_Relation_ODomain(X1,X4,X3),tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_521,def_lhs_atom43]) ).
cnf(c_0_522_0,axiom,
c_lessequals(c_Relation_ORange(c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(X2,X3,X4),c_Relation_ORange(X1,X3,X4),tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_522,def_lhs_atom35]) ).
cnf(c_0_523_0,axiom,
c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(tc_prod(X4,X3),tc_bool)),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X2,X4,X3),c_Relation_ODomain(X1,X4,X3),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_523,def_lhs_atom33]) ).
cnf(c_0_524_0,axiom,
c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(X2,X3,X4),c_Relation_Oconverse(X1,X3,X4),tc_fun(tc_prod(X4,X3),tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_524,def_lhs_atom26]) ).
cnf(c_0_525_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_525,def_lhs_atom23]) ).
cnf(c_0_526_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X1,tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_526,def_lhs_atom18]) ).
cnf(c_0_527_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_527,def_lhs_atom17]) ).
cnf(c_0_528_0,axiom,
c_Set_Oinsert(X2,c_Set_Oinsert(X1,X3,X4),X4) = c_Set_Oinsert(X1,c_Set_Oinsert(X2,X3,X4),X4),
inference(unfold_definition,[status(thm)],[c_0_528,def_lhs_atom16]) ).
cnf(c_0_529_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X3,X4),c_Set_Oinsert(X1,X2,X4),tc_fun(X4,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),X4),
inference(unfold_definition,[status(thm)],[c_0_529,def_lhs_atom11]) ).
cnf(c_0_530_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X3,c_Set_Oinsert(X1,X2,X4),tc_fun(X4,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X4),
inference(unfold_definition,[status(thm)],[c_0_530,def_lhs_atom9]) ).
cnf(c_0_531_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,X3,X4),X2,tc_fun(X4,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X4),
inference(unfold_definition,[status(thm)],[c_0_531,def_lhs_atom8]) ).
cnf(c_0_532_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_532,def_lhs_atom4]) ).
cnf(c_0_533_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_533,def_lhs_atom3]) ).
cnf(c_0_534_0,axiom,
~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X3,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(unfold_definition,[status(thm)],[c_0_534,def_lhs_atom112]) ).
cnf(c_0_535_0,axiom,
~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X3,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(unfold_definition,[status(thm)],[c_0_535,def_lhs_atom110]) ).
cnf(c_0_536_0,axiom,
c_Relation_ORange(X1,X2,X3) = c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X3),X3,X2),
inference(unfold_definition,[status(thm)],[c_0_536,def_lhs_atom106]) ).
cnf(c_0_537_0,axiom,
c_Relation_ODomain(c_Relation_Oconverse(X1,X2,X3),X3,X2) = c_Relation_ORange(X1,X2,X3),
inference(unfold_definition,[status(thm)],[c_0_537,def_lhs_atom105]) ).
cnf(c_0_538_0,axiom,
c_Relation_Oconverse(c_Relation_Oconverse(X1,X3,X2),X2,X3) = X1,
inference(unfold_definition,[status(thm)],[c_0_538,def_lhs_atom104]) ).
cnf(c_0_539_0,axiom,
c_Relation_ORange(c_Relation_Oconverse(X1,X3,X2),X2,X3) = c_Relation_ODomain(X1,X3,X2),
inference(unfold_definition,[status(thm)],[c_0_539,def_lhs_atom102]) ).
cnf(c_0_540_0,axiom,
c_Relation_Orel__comp(X1,c_Relation_OId(X2),X3,X2,X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_540,def_lhs_atom90]) ).
cnf(c_0_541_0,axiom,
c_Relation_Orel__comp(c_Relation_OId(X3),X1,X3,X3,X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_541,def_lhs_atom89]) ).
cnf(c_0_542_0,axiom,
c_in(c_Pair(X1,X1,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3)),
inference(unfold_definition,[status(thm)],[c_0_542,def_lhs_atom75]) ).
cnf(c_0_543_0,axiom,
c_in(c_Pair(X2,X2,X3,X3),c_Transitive__Closure_Ortrancl(X1,X3),tc_prod(X3,X3)),
inference(unfold_definition,[status(thm)],[c_0_543,def_lhs_atom74]) ).
cnf(c_0_544_0,axiom,
c_Relation_OImage(c_Relation_OId__on(X2,X3),X1,X3,X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_544,def_lhs_atom68]) ).
cnf(c_0_545_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_545,def_lhs_atom60]) ).
cnf(c_0_546_0,axiom,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
inference(unfold_definition,[status(thm)],[c_0_546,def_lhs_atom59]) ).
cnf(c_0_547_0,axiom,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_547,def_lhs_atom55]) ).
cnf(c_0_548_0,axiom,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_548,def_lhs_atom54]) ).
cnf(c_0_549_0,axiom,
c_lessequals(X2,c_Set_Oinsert(X1,X2,X3),tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_549,def_lhs_atom44]) ).
cnf(c_0_550_0,axiom,
c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
inference(unfold_definition,[status(thm)],[c_0_550,def_lhs_atom40]) ).
cnf(c_0_551_0,axiom,
c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
inference(unfold_definition,[status(thm)],[c_0_551,def_lhs_atom39]) ).
cnf(c_0_552_0,axiom,
c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
inference(unfold_definition,[status(thm)],[c_0_552,def_lhs_atom38]) ).
cnf(c_0_553_0,axiom,
c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X2,X3),c_Transitive__Closure_Ortrancl(X1,X3),tc_fun(tc_prod(X3,X3),tc_bool)),X3) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(tc_prod(X3,X3),tc_bool)),X3),
inference(unfold_definition,[status(thm)],[c_0_553,def_lhs_atom36]) ).
cnf(c_0_554_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_554,def_lhs_atom34]) ).
cnf(c_0_555_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_555,def_lhs_atom32]) ).
cnf(c_0_556_0,axiom,
c_Relation_OField(c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(tc_prod(X3,X3),tc_bool)),X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OField(X2,X3),c_Relation_OField(X1,X3),tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_556,def_lhs_atom30]) ).
cnf(c_0_557_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_557,def_lhs_atom22]) ).
cnf(c_0_558_0,axiom,
c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_558,def_lhs_atom21]) ).
cnf(c_0_559_0,axiom,
c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_559,def_lhs_atom20]) ).
cnf(c_0_560_0,axiom,
c_Set_Oinsert(X1,c_Set_Oinsert(X1,X2,X3),X3) = c_Set_Oinsert(X1,X2,X3),
inference(unfold_definition,[status(thm)],[c_0_560,def_lhs_atom12]) ).
cnf(c_0_561_0,axiom,
c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X2,X3),c_Transitive__Closure_Ortrancl(X1,X3),tc_fun(tc_prod(X3,X3),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(tc_prod(X3,X3),tc_bool)),X3),tc_fun(tc_prod(X3,X3),tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_561,def_lhs_atom7]) ).
cnf(c_0_562_0,axiom,
c_fequal(X1,X1,X2),
inference(unfold_definition,[status(thm)],[c_0_562,def_lhs_atom124]) ).
cnf(c_0_563_0,axiom,
~ c_in(c_Pair(X1,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X2,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(unfold_definition,[status(thm)],[c_0_563,def_lhs_atom111]) ).
cnf(c_0_564_0,axiom,
~ c_in(c_Pair(X1,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X2,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(unfold_definition,[status(thm)],[c_0_564,def_lhs_atom109]) ).
cnf(c_0_565_0,axiom,
c_in(c_Pair(X1,X1,X2,X2),c_Relation_OId(X2),tc_prod(X2,X2)),
inference(unfold_definition,[status(thm)],[c_0_565,def_lhs_atom108]) ).
cnf(c_0_566_0,axiom,
c_in(c_Pair(X1,X1,X2,X2),c_Relation_OId(X2),tc_prod(X2,X2)),
inference(unfold_definition,[status(thm)],[c_0_566,def_lhs_atom107]) ).
cnf(c_0_567_0,axiom,
c_Relation_ORange(c_Relation_OId__on(X1,X2),X2,X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_567,def_lhs_atom103]) ).
cnf(c_0_568_0,axiom,
c_Relation_Oconverse(c_Relation_OId__on(X1,X2),X2,X2) = c_Relation_OId__on(X1,X2),
inference(unfold_definition,[status(thm)],[c_0_568,def_lhs_atom101]) ).
cnf(c_0_569_0,axiom,
c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X1,X2,X2),X2) = c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X1,X2),X2,X2),
inference(unfold_definition,[status(thm)],[c_0_569,def_lhs_atom100]) ).
cnf(c_0_570_0,axiom,
c_Relation_Orefl__on(X1,c_Relation_OId__on(X1,X2),X2),
inference(unfold_definition,[status(thm)],[c_0_570,def_lhs_atom96]) ).
cnf(c_0_571_0,axiom,
c_Relation_Osym(c_Relation_OId__on(X1,X2),X2),
inference(unfold_definition,[status(thm)],[c_0_571,def_lhs_atom95]) ).
cnf(c_0_572_0,axiom,
c_Relation_ORange(c_Transitive__Closure_Otrancl(X1,X2),X2,X2) = c_Relation_ORange(X1,X2,X2),
inference(unfold_definition,[status(thm)],[c_0_572,def_lhs_atom93]) ).
cnf(c_0_573_0,axiom,
c_Relation_ODomain(c_Relation_OId__on(X1,X2),X2,X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_573,def_lhs_atom92]) ).
cnf(c_0_574_0,axiom,
c_Relation_OImage(c_Relation_OId(X2),X1,X2,X2) = X1,
inference(unfold_definition,[status(thm)],[c_0_574,def_lhs_atom91]) ).
cnf(c_0_575_0,axiom,
c_Relation_ODomain(c_Transitive__Closure_Otrancl(X1,X2),X2,X2) = c_Relation_ODomain(X1,X2,X2),
inference(unfold_definition,[status(thm)],[c_0_575,def_lhs_atom87]) ).
cnf(c_0_576_0,axiom,
c_lessequals(c_Relation_OId__on(X1,X2),c_Product__Type_OSigma(X1,c_COMBK(X1,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_576,def_lhs_atom84]) ).
cnf(c_0_577_0,axiom,
c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),X1,X2,X2,X2),
inference(unfold_definition,[status(thm)],[c_0_577,def_lhs_atom83]) ).
cnf(c_0_578_0,axiom,
c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(unfold_definition,[status(thm)],[c_0_578,def_lhs_atom82]) ).
cnf(c_0_579_0,axiom,
c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(unfold_definition,[status(thm)],[c_0_579,def_lhs_atom81]) ).
cnf(c_0_580_0,axiom,
c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X1,X2,X2),X2) = c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X1,X2),X2,X2),
inference(unfold_definition,[status(thm)],[c_0_580,def_lhs_atom80]) ).
cnf(c_0_581_0,axiom,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_581,def_lhs_atom79]) ).
cnf(c_0_582_0,axiom,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_582,def_lhs_atom78]) ).
cnf(c_0_583_0,axiom,
c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X1,X2),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(unfold_definition,[status(thm)],[c_0_583,def_lhs_atom77]) ).
cnf(c_0_584_0,axiom,
c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(unfold_definition,[status(thm)],[c_0_584,def_lhs_atom76]) ).
cnf(c_0_585_0,axiom,
c_Transitive__Closure_Otrancl(X1,X2) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),X1,X2,X2,X2),
inference(unfold_definition,[status(thm)],[c_0_585,def_lhs_atom73]) ).
cnf(c_0_586_0,axiom,
c_Transitive__Closure_Otrancl(X1,X2) = c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),
inference(unfold_definition,[status(thm)],[c_0_586,def_lhs_atom72]) ).
cnf(c_0_587_0,axiom,
c_lessequals(c_Transitive__Closure_Otrancl(X1,X2),c_Product__Type_OSigma(c_Relation_OField(X1,X2),c_COMBK(c_Relation_OField(X1,X2),tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_587,def_lhs_atom71]) ).
cnf(c_0_588_0,axiom,
c_Transitive__Closure_Ortrancl(X1,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X2),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),X1,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_588,def_lhs_atom70]) ).
cnf(c_0_589_0,axiom,
c_Transitive__Closure_Ortrancl(X1,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X1,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_589,def_lhs_atom69]) ).
cnf(c_0_590_0,axiom,
c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X1,c_Relation_Oconverse(X1,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
inference(unfold_definition,[status(thm)],[c_0_590,def_lhs_atom67]) ).
cnf(c_0_591_0,axiom,
c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_Oconverse(X1,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
inference(unfold_definition,[status(thm)],[c_0_591,def_lhs_atom66]) ).
cnf(c_0_592_0,axiom,
c_Transitive__Closure_Otrancl(X1,X2) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X1,X2),X1,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_592,def_lhs_atom65]) ).
cnf(c_0_593_0,axiom,
c_Relation_OField(X1,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X1,X2,X2),c_Relation_ORange(X1,X2,X2),tc_fun(X2,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_593,def_lhs_atom63]) ).
cnf(c_0_594_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_fun(X2,tc_bool)) = X1,
inference(unfold_definition,[status(thm)],[c_0_594,def_lhs_atom62]) ).
cnf(c_0_595_0,axiom,
c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(unfold_definition,[status(thm)],[c_0_595,def_lhs_atom42]) ).
cnf(c_0_596_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X1,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(unfold_definition,[status(thm)],[c_0_596,def_lhs_atom41]) ).
cnf(c_0_597_0,axiom,
c_Relation_Otrans(c_Relation_OId__on(X1,X2),X2),
inference(unfold_definition,[status(thm)],[c_0_597,def_lhs_atom29]) ).
cnf(c_0_598_0,axiom,
c_Relation_OField(c_Relation_Oconverse(X1,X2,X2),X2) = c_Relation_OField(X1,X2),
inference(unfold_definition,[status(thm)],[c_0_598,def_lhs_atom24]) ).
cnf(c_0_599_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X1,X2),c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(unfold_definition,[status(thm)],[c_0_599,def_lhs_atom19]) ).
cnf(c_0_600_0,axiom,
c_Relation_Otrans(c_Transitive__Closure_Ortrancl(X1,X2),X2),
inference(unfold_definition,[status(thm)],[c_0_600,def_lhs_atom10]) ).
cnf(c_0_601_0,axiom,
c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(unfold_definition,[status(thm)],[c_0_601,def_lhs_atom6]) ).
cnf(c_0_602_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,X1,tc_fun(X2,tc_bool)) = X1,
inference(unfold_definition,[status(thm)],[c_0_602,def_lhs_atom2]) ).
cnf(c_0_603_0,axiom,
c_Relation_Otrans(c_Transitive__Closure_Otrancl(X1,X2),X2),
inference(unfold_definition,[status(thm)],[c_0_603,def_lhs_atom1]) ).
cnf(c_0_604_0,axiom,
c_Relation_Oconverse(c_Relation_OId(X1),X1,X1) = c_Relation_OId(X1),
inference(unfold_definition,[status(thm)],[c_0_604,def_lhs_atom97]) ).
cnf(c_0_605_0,axiom,
c_Relation_Osym(c_Relation_OId(X1),X1),
inference(unfold_definition,[status(thm)],[c_0_605,def_lhs_atom88]) ).
cnf(c_0_606_0,axiom,
c_Relation_Otrans(c_Relation_OId(X1),X1),
inference(unfold_definition,[status(thm)],[c_0_606,def_lhs_atom50]) ).
cnf(c_0_607_0,axiom,
class_HOL_Oord(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_607,def_lhs_atom123]) ).
cnf(c_0_608_0,axiom,
class_Orderings_Oorder(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_608,def_lhs_atom122]) ).
cnf(c_0_609_0,axiom,
class_Lattices_Olattice(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_609,def_lhs_atom121]) ).
cnf(c_0_610_0,axiom,
class_Orderings_Opreorder(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_610,def_lhs_atom120]) ).
cnf(c_0_611_0,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_611,def_lhs_atom119]) ).
cnf(c_0_612_0,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_612,def_lhs_atom118]) ).
cnf(c_0_613_0,axiom,
class_Lattices_Olower__semilattice(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_613,def_lhs_atom117]) ).
cnf(c_0_614_0,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_614,def_lhs_atom116]) ).
cnf(c_0_615_0,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
inference(unfold_definition,[status(thm)],[c_0_615,def_lhs_atom115]) ).
cnf(c_0_616_0,axiom,
v_a____ != v_b____,
inference(unfold_definition,[status(thm)],[c_0_616,def_lhs_atom114]) ).
cnf(c_0_617_0,axiom,
c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_617,def_lhs_atom113]) ).
cnf(c_0_618_0,axiom,
c_Relation_ORange(v_r,t_a,t_b) = c_Relation_ODomain(c_Relation_Oconverse(v_r,t_a,t_b),t_b,t_a),
inference(unfold_definition,[status(thm)],[c_0_618,def_lhs_atom86]) ).
cnf(c_0_619_0,axiom,
c_Relation_OField(v_r,t_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(v_r,t_a,t_a),c_Relation_ORange(v_r,t_a,t_a),tc_fun(t_a,tc_bool)),
inference(unfold_definition,[status(thm)],[c_0_619,def_lhs_atom31]) ).
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0_001,axiom,
! [X25,X17,X23,X7,X26,X15,X3] :
( c_in(c_Pair(X7,c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X7,X23,X17,X25,X3,X15,X26),X3,X26),X17,tc_prod(X3,X26))
| ~ c_in(c_Pair(X7,X23,X3,X15),c_Relation_Orel__comp(X17,X25,X3,X26,X15),tc_prod(X3,X15)) ),
file('<stdin>',cls_rel__compEpair_0) ).
fof(c_0_1_002,axiom,
! [X25,X17,X23,X7,X26,X15,X3] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X7,X23,X17,X25,X3,X15,X26),X23,X26,X15),X25,tc_prod(X26,X15))
| ~ c_in(c_Pair(X7,X23,X3,X15),c_Relation_Orel__comp(X17,X25,X3,X26,X15),tc_prod(X3,X15)) ),
file('<stdin>',cls_rel__compEpair_1) ).
fof(c_0_2_003,axiom,
! [X10,X17,X27,X22,X15,X3] :
( hAPP(X22,c_List_Osko__Recdef__Xcuts__eq__1__1(X22,X27,X17,X10,X3,X15)) != hAPP(X27,c_List_Osko__Recdef__Xcuts__eq__1__1(X22,X27,X17,X10,X3,X15))
| c_Recdef_Ocut(X22,X17,X10,X3,X15) = c_Recdef_Ocut(X27,X17,X10,X3,X15) ),
file('<stdin>',cls_cuts__eq_2) ).
fof(c_0_3_004,axiom,
! [X11,X24,X3] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X24,X11,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X24,X24,X3,X3,X3),c_Relation_Orel__comp(X11,X24,X3,X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)),X11,tc_fun(tc_prod(X3,X3),tc_bool)),X3) ),
file('<stdin>',cls_wf__union__merge_1) ).
fof(c_0_4_005,axiom,
! [X10,X17,X27,X22,X15,X3] :
( c_Recdef_Ocut(X22,X17,X10,X3,X15) = c_Recdef_Ocut(X27,X17,X10,X3,X15)
| c_in(c_Pair(c_List_Osko__Recdef__Xcuts__eq__1__1(X22,X27,X17,X10,X3,X15),X10,X3,X3),X17,tc_prod(X3,X3)) ),
file('<stdin>',cls_cuts__eq_1) ).
fof(c_0_5_006,axiom,
! [X11,X24,X3] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X24,X24,X3,X3,X3),c_Relation_Orel__comp(X11,X24,X3,X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)),X11,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X24,X11,tc_fun(tc_prod(X3,X3),tc_bool)),X3) ),
file('<stdin>',cls_wf__union__merge_0) ).
fof(c_0_6_007,axiom,
! [X38,X21,X19,X18,X15,X3] :
( c_lessequals(c_Product__Type_OSigma(X18,X19,X3,X15),c_Product__Type_OSigma(X21,X38,X3,X15),tc_fun(tc_prod(X3,X15),tc_bool))
| ~ c_lessequals(hAPP(X19,c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(X18,X19,X38,X3,X15)),hAPP(X38,c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(X18,X19,X38,X3,X15)),tc_fun(X15,tc_bool))
| ~ c_lessequals(X18,X21,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Sigma__mono_1) ).
fof(c_0_7_008,axiom,
! [X22,X19,X18,X15,X3] :
( c_in(X22,c_FuncSet_OPi(X18,X19,X3,X15),tc_fun(X3,X15))
| ~ c_in(hAPP(X22,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X18,X19,X22,X3,X15)),hAPP(X19,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X18,X19,X22,X3,X15)),X15) ),
file('<stdin>',cls_Pi__I_H_1) ).
fof(c_0_8_009,axiom,
! [X22,X19,X18,X15,X3] :
( c_in(X22,c_FuncSet_OPi(X18,X19,X3,X15),tc_fun(X3,X15))
| ~ c_in(hAPP(X22,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X18,X19,X22,X3,X15)),hAPP(X19,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X18,X19,X22,X3,X15)),X15) ),
file('<stdin>',cls_Pi__I_1) ).
fof(c_0_9_010,axiom,
! [X22,X19,X18,X15,X3] :
( c_in(X22,c_FuncSet_OPi(X18,c_COMBK(X19,tc_fun(X15,tc_bool),X3),X3,X15),tc_fun(X3,X15))
| ~ c_in(hAPP(X22,c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X18,X19,X22,X3,X15)),X19,X15) ),
file('<stdin>',cls_funcsetI_1) ).
fof(c_0_10_011,axiom,
! [X25,X17,X21,X19,X18,X26,X15,X3] :
( c_lessequals(c_Relation_Orel__comp(X17,X25,X3,X15,X26),c_Product__Type_OSigma(X18,c_COMBK(X21,tc_fun(X26,tc_bool),X3),X3,X26),tc_fun(tc_prod(X3,X26),tc_bool))
| ~ c_lessequals(X25,c_Product__Type_OSigma(X19,c_COMBK(X21,tc_fun(X26,tc_bool),X15),X15,X26),tc_fun(tc_prod(X15,X26),tc_bool))
| ~ c_lessequals(X17,c_Product__Type_OSigma(X18,c_COMBK(X19,tc_fun(X15,tc_bool),X3),X3,X15),tc_fun(tc_prod(X3,X15),tc_bool)) ),
file('<stdin>',cls_rel__comp__subset__Sigma_0) ).
fof(c_0_11_012,axiom,
! [X17,X6,X18,X15,X3] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X18,X6,X17,X15,X3),X6,X15,X3),X17,tc_prod(X15,X3))
| ~ c_in(X6,c_Relation_OImage(X17,X18,X15,X3),X3) ),
file('<stdin>',cls_Image__iff_1) ).
fof(c_0_12_013,axiom,
! [X17,X6,X18,X15,X3] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X18,X6,X17,X15,X3),X6,X15,X3),X17,tc_prod(X15,X3))
| ~ c_in(X6,c_Relation_OImage(X17,X18,X15,X3),X3) ),
file('<stdin>',cls_ImageE_0) ).
fof(c_0_13_014,axiom,
! [X35,X25,X36,X17,X26,X15,X3] :
( c_lessequals(c_Relation_Orel__comp(X36,X35,X3,X15,X26),c_Relation_Orel__comp(X17,X25,X3,X15,X26),tc_fun(tc_prod(X3,X26),tc_bool))
| ~ c_lessequals(X35,X25,tc_fun(tc_prod(X15,X26),tc_bool))
| ~ c_lessequals(X36,X17,tc_fun(tc_prod(X3,X15),tc_bool)) ),
file('<stdin>',cls_rel__comp__mono_0) ).
fof(c_0_14_015,axiom,
! [X25,X17,X3] :
( c_lessequals(c_Transitive__Closure_Ortrancl(X17,X3),X25,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Ortrancl(X17,X3),X25,tc_fun(tc_prod(X3,X3),tc_bool)),X17,X3,X3,X3),X25,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(c_Relation_OId(X3),X25,tc_fun(tc_prod(X3,X3),tc_bool)) ),
file('<stdin>',cls_rtrancl__Int__subset_0) ).
fof(c_0_15_016,axiom,
! [X25,X17,X3] :
( c_lessequals(c_Transitive__Closure_Otrancl(X17,X3),X25,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Otrancl(X17,X3),X25,tc_fun(tc_prod(X3,X3),tc_bool)),X17,X3,X3,X3),X25,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(X17,X25,tc_fun(tc_prod(X3,X3),tc_bool)) ),
file('<stdin>',cls_trancl__Int__subset_0) ).
fof(c_0_16_017,axiom,
! [X25,X17,X23,X6,X7,X26,X15,X3] :
( c_in(c_Pair(X7,X23,X3,X26),c_Relation_Orel__comp(X17,X25,X3,X15,X26),tc_prod(X3,X26))
| ~ c_in(c_Pair(X6,X23,X15,X26),X25,tc_prod(X15,X26))
| ~ c_in(c_Pair(X7,X6,X3,X15),X17,tc_prod(X3,X15)) ),
file('<stdin>',cls_rel__compI_0) ).
fof(c_0_17_018,axiom,
! [X12,X10,X17,X27,X22,X15,X3] :
( c_Recdef_Ocut(X22,X17,X10,X3,X15) != c_Recdef_Ocut(X27,X17,X10,X3,X15)
| hAPP(X22,X12) = hAPP(X27,X12)
| ~ c_in(c_Pair(X12,X10,X3,X3),X17,tc_prod(X3,X3)) ),
file('<stdin>',cls_cuts__eq_0) ).
fof(c_0_18_019,axiom,
! [X11,X24,X3] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X24,X11,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_lessequals(c_Relation_Orel__comp(X24,X11,X3,X3,X3),X24,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Wellfounded_Owf(X11,X3)
| ~ c_Wellfounded_Owf(X24,X3) ),
file('<stdin>',cls_wf__union__compatible_0) ).
fof(c_0_19_020,axiom,
! [X24,X3] :
( c_Wellfounded_Owf(X24,X3)
| ~ c_Wellfounded_Owf(c_Relation_Orel__comp(X24,X24,X3,X3,X3),X3) ),
file('<stdin>',cls_wf__comp__self_1) ).
fof(c_0_20_021,axiom,
! [X38,X21,X19,X18,X15,X3] :
( c_lessequals(c_Product__Type_OSigma(X18,X19,X3,X15),c_Product__Type_OSigma(X21,X38,X3,X15),tc_fun(tc_prod(X3,X15),tc_bool))
| c_in(c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(X18,X19,X38,X3,X15),X18,X3)
| ~ c_lessequals(X18,X21,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Sigma__mono_0) ).
fof(c_0_21_022,axiom,
! [X12,X10,X6,X7,X8] :
( c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X8,X7,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X7,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X12
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X6 ),
file('<stdin>',cls_in__above_14) ).
fof(c_0_22_023,axiom,
! [X12,X10,X6,X7,X8] :
( c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X8,X7,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X12
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X6 ),
file('<stdin>',cls_in__below_14) ).
fof(c_0_23_024,axiom,
! [X22,X19,X18,X15,X3] :
( c_in(X22,c_FuncSet_OPi(X18,c_COMBK(X19,tc_fun(X15,tc_bool),X3),X3,X15),tc_fun(X3,X15))
| c_in(c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X18,X19,X22,X3,X15),X18,X3) ),
file('<stdin>',cls_funcsetI_0) ).
fof(c_0_24_025,axiom,
! [X10,X17,X22,X7,X15,X3] :
( hAPP(c_Recdef_Ocut(X22,X17,X7,X3,X15),X10) = hAPP(X22,X10)
| ~ c_in(c_Pair(X10,X7,X3,X3),X17,tc_prod(X3,X3)) ),
file('<stdin>',cls_cut__apply_0) ).
fof(c_0_25_026,axiom,
! [X10,X22,X7,X24,X15,X3] :
( hAPP(c_Recdef_Ocut(X22,X24,X7,X3,X15),X10) = hAPP(X22,X10)
| ~ c_in(c_Pair(X10,X7,X3,X3),X24,tc_prod(X3,X3)) ),
file('<stdin>',cls_tfl__cut__apply_0) ).
fof(c_0_26_027,axiom,
! [X17,X6,X18,X15,X3] :
( c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X18,X6,X17,X15,X3),X18,X15)
| ~ c_in(X6,c_Relation_OImage(X17,X18,X15,X3),X3) ),
file('<stdin>',cls_Image__iff_0) ).
fof(c_0_27_028,axiom,
! [X17,X6,X18,X15,X3] :
( c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X18,X6,X17,X15,X3),X18,X15)
| ~ c_in(X6,c_Relation_OImage(X17,X18,X15,X3),X3) ),
file('<stdin>',cls_ImageE_1) ).
fof(c_0_28_029,axiom,
! [X20,X10,X17,X3] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X17,X10,X20,X3),X20,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3))
| c_in(c_Pair(X10,X20,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(c_Pair(X10,X20,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_converse__tranclE_1) ).
fof(c_0_29_030,axiom,
! [X17,X18,X3] :
( c_Relation_Orefl__on(X18,X17,X3)
| ~ c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1(X18,X17,X3),c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1(X18,X17,X3),X3,X3),X17,tc_prod(X3,X3))
| ~ c_lessequals(X17,c_Product__Type_OSigma(X18,c_COMBK(X18,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
file('<stdin>',cls_refl__onI_1) ).
fof(c_0_30_031,axiom,
! [X17,X18,X3] :
( c_Relation_Orefl__on(X18,X17,X3)
| ~ c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1(X18,X17,X3),c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1(X18,X17,X3),X3,X3),X17,tc_prod(X3,X3))
| ~ c_lessequals(X17,c_Product__Type_OSigma(X18,c_COMBK(X18,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
file('<stdin>',cls_refl__on__def_3) ).
fof(c_0_31_032,axiom,
! [X20,X10,X17,X3] :
( c_in(c_Pair(X10,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X17,X10,X20,X3),X3,X3),X17,tc_prod(X3,X3))
| c_in(c_Pair(X10,X20,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(c_Pair(X10,X20,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_converse__tranclE_0) ).
fof(c_0_32_033,axiom,
! [X22,X19,X18,X15,X3] :
( c_in(X22,c_FuncSet_OPi(X18,X19,X3,X15),tc_fun(X3,X15))
| c_in(c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X18,X19,X22,X3,X15),X18,X3) ),
file('<stdin>',cls_Pi__I_H_0) ).
fof(c_0_33_034,axiom,
! [X22,X19,X18,X15,X3] :
( c_in(X22,c_FuncSet_OPi(X18,X19,X3,X15),tc_fun(X3,X15))
| c_in(c_FuncSet_Osko__FuncSet__XPi__I__1__1(X18,X19,X22,X3,X15),X18,X3) ),
file('<stdin>',cls_Pi__I_0) ).
fof(c_0_34_035,axiom,
! [X10,X21,X19,X18,X15,X3] :
( c_lessequals(X18,X19,tc_fun(X15,tc_bool))
| ~ c_lessequals(c_Product__Type_OSigma(X18,c_COMBK(X21,tc_fun(X3,tc_bool),X15),X15,X3),c_Product__Type_OSigma(X19,c_COMBK(X21,tc_fun(X3,tc_bool),X15),X15,X3),tc_fun(tc_prod(X15,X3),tc_bool))
| ~ c_in(X10,X21,X3) ),
file('<stdin>',cls_Times__subset__cancel2_0) ).
fof(c_0_35_036,axiom,
! [X17,X18,X3] :
( c_lessequals(X17,c_Relation_Orel__comp(c_Relation_Oconverse(X17,X3,X3),X17,X3,X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Relation_Orefl__on(X18,X17,X3) ),
file('<stdin>',cls_refl__on__comp__subset_0) ).
fof(c_0_36_037,axiom,
! [X17,X3] :
( c_lessequals(c_Relation_Orel__comp(c_Relation_Oconverse(X17,X3,X3),X17,X3,X3,X3),X17,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Relation_Otrans(X17,X3)
| ~ c_Relation_Osym(X17,X3) ),
file('<stdin>',cls_sym__trans__comp__subset_0) ).
fof(c_0_37_038,axiom,
! [X12,X10,X17,X3] :
( ~ c_in(c_Pair(X10,X12,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3))
| ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X12,X10,X3,X3),X17,tc_prod(X3,X3)),X3) ),
file('<stdin>',cls_wf__insert_1) ).
fof(c_0_38_039,axiom,
! [X12,X10,X6,X7,X8] :
( c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X8,X7,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X7
| ~ c_in(c_Pair(X10,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X12
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X6 ),
file('<stdin>',cls_in__below_10) ).
fof(c_0_39_040,axiom,
! [X12,X10,X6,X7,X8] :
( c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X8,X7,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X12 = X7
| X10 = X12
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X6 ),
file('<stdin>',cls_in__below_8) ).
fof(c_0_40_041,axiom,
! [X12,X10,X6,X7,X8] :
( c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X8,X7,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X12 = X6
| ~ c_in(c_Pair(X7,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X12
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X6 ),
file('<stdin>',cls_in__above_10) ).
fof(c_0_41_042,axiom,
! [X12,X10,X6,X7,X8] :
( c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X8,X7,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X6
| X10 = X12
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X6 ),
file('<stdin>',cls_in__above_8) ).
fof(c_0_42_043,axiom,
! [X12,X10,X6,X8] :
( ~ c_in(c_Pair(X6,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X12
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X10 = X6
| c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X8,X10,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_in__below_13) ).
fof(c_0_43_044,axiom,
! [X16,X10,X7,X8] :
( ~ c_in(c_Pair(X16,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X16 = X10
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X10
| c_in(c_Pair(X16,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X8,X7,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X16,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_in__below_12) ).
fof(c_0_44_045,axiom,
! [X16,X10,X7,X8] :
( ~ c_in(c_Pair(X16,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X7,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X16 = X10
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X10
| c_in(c_Pair(X16,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X8,X7,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_in__above_13) ).
fof(c_0_45_046,axiom,
! [X12,X10,X6,X8] :
( ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X12
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X10 = X6
| c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X8,X10,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_in__above_12) ).
fof(c_0_46_047,axiom,
! [X17,X3] :
( c_lessequals(c_Relation_Orel__comp(X17,X17,X3,X3,X3),X17,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Relation_Otrans(X17,X3) ),
file('<stdin>',cls_trans__O__subset_0) ).
fof(c_0_47_048,axiom,
! [X12,X10,X24,X3] :
( c_in(c_Pair(X10,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X24,X10,X12,X3),X3,X3),c_Transitive__Closure_Ortrancl(X24,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X10,X12,X3,X3),c_Transitive__Closure_Otrancl(X24,X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_tranclD2_0) ).
fof(c_0_48_049,axiom,
! [X12,X10,X24,X3] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X24,X10,X12,X3),X12,X3,X3),c_Transitive__Closure_Ortrancl(X24,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X10,X12,X3,X3),c_Transitive__Closure_Otrancl(X24,X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_tranclD_1) ).
fof(c_0_49_050,axiom,
! [X12,X10,X24,X3] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X24,X10,X12,X3),X12,X3,X3),X24,tc_prod(X3,X3))
| ~ c_in(c_Pair(X10,X12,X3,X3),c_Transitive__Closure_Otrancl(X24,X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_tranclD2_1) ).
fof(c_0_50_051,axiom,
! [X12,X10,X24,X3] :
( c_in(c_Pair(X10,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X24,X10,X12,X3),X3,X3),X24,tc_prod(X3,X3))
| ~ c_in(c_Pair(X10,X12,X3,X3),c_Transitive__Closure_Otrancl(X24,X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_tranclD_0) ).
fof(c_0_51_052,axiom,
! [X17,X23,X6,X7,X3] :
( c_in(c_Pair(X7,X23,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X6,X23,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X7,X6,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_rtrancl__trans_0) ).
fof(c_0_52_053,axiom,
! [X17,X23,X6,X7,X3] :
( c_in(c_Pair(X7,X23,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X6,X23,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X7,X6,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_trancl__rtrancl__trancl_0) ).
fof(c_0_53_054,axiom,
! [X20,X12,X10,X17,X3] :
( c_in(c_Pair(X10,X20,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X12,X20,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X10,X12,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_rtrancl__trancl__trancl_0) ).
fof(c_0_54_055,axiom,
! [X17,X23,X6,X7,X3] :
( c_in(c_Pair(X7,X23,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X6,X23,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X7,X6,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_trancl__trans_0) ).
fof(c_0_55_056,axiom,
! [X17,X6,X7,X18,X3] :
( c_in(X7,X18,X3)
| X7 = X6
| ~ c_lessequals(X17,c_Product__Type_OSigma(X18,c_COMBK(X18,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_in(c_Pair(X7,X6,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_trancl__subset__Sigma__aux_0) ).
fof(c_0_56_057,axiom,
! [X17,X23,X6,X7,X3] :
( c_in(c_Pair(X7,X23,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X6,X23,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(c_Pair(X7,X6,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_rtrancl__into__trancl1_0) ).
fof(c_0_57_058,axiom,
! [X17,X23,X6,X7,X3] :
( c_in(c_Pair(X7,X23,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X6,X23,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X7,X6,X3,X3),X17,tc_prod(X3,X3)) ),
file('<stdin>',cls_rtrancl__into__trancl2_0) ).
fof(c_0_58_059,axiom,
! [X17,X23,X6,X7,X3] :
( c_in(c_Pair(X7,X23,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X6,X23,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(c_Pair(X7,X6,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_rtrancl_Ortrancl__into__rtrancl_0) ).
fof(c_0_59_060,axiom,
! [X17,X23,X6,X7,X3] :
( c_in(c_Pair(X7,X23,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X6,X23,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X7,X6,X3,X3),X17,tc_prod(X3,X3)) ),
file('<stdin>',cls_converse__rtrancl__into__rtrancl_0) ).
fof(c_0_60_061,axiom,
! [X17,X23,X6,X7,X3] :
( c_in(c_Pair(X7,X23,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X6,X23,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X7,X6,X3,X3),X17,tc_prod(X3,X3)) ),
file('<stdin>',cls_trancl__into__trancl2_0) ).
fof(c_0_61_062,axiom,
! [X17,X23,X6,X7,X3] :
( c_in(c_Pair(X7,X23,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X6,X23,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(c_Pair(X7,X6,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_Transitive__Closure_Otrancl__into__trancl_0) ).
fof(c_0_62_063,axiom,
! [X24,X3] :
( c_Wellfounded_Owf(c_Relation_Orel__comp(X24,X24,X3,X3,X3),X3)
| ~ c_Wellfounded_Owf(X24,X3) ),
file('<stdin>',cls_wf__comp__self_0) ).
fof(c_0_63_064,axiom,
! [X17,X18,X3] :
( c_lessequals(c_Transitive__Closure_Otrancl(X17,X3),c_Product__Type_OSigma(X18,c_COMBK(X18,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(X17,c_Product__Type_OSigma(X18,c_COMBK(X18,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
file('<stdin>',cls_trancl__subset__Sigma_0) ).
fof(c_0_64_065,axiom,
! [X23,X6,X7,X24,X3] :
( c_in(c_Pair(X7,X23,X3,X3),c_Transitive__Closure_Otrancl(X24,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X6,X23,X3,X3),X24,tc_prod(X3,X3))
| ~ c_in(c_Pair(X7,X6,X3,X3),X24,tc_prod(X3,X3)) ),
file('<stdin>',cls_r__r__into__trancl_0) ).
fof(c_0_65_066,axiom,
! [X17,X23,X6,X7,X3] :
( c_in(c_Pair(X7,X23,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(c_Pair(X6,X23,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(c_Pair(X7,X6,X3,X3),X17,tc_prod(X3,X3))
| ~ c_Relation_Otrans(X17,X3) ),
file('<stdin>',cls_transD_0) ).
fof(c_0_66_067,axiom,
! [X20,X12,X10,X17,X3] :
( c_in(c_Pair(X10,X20,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(c_Pair(X12,X20,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(c_Pair(X10,X12,X3,X3),X17,tc_prod(X3,X3))
| ~ c_Relation_Otrans(X17,X3) ),
file('<stdin>',cls_trans__def_0) ).
fof(c_0_67_068,axiom,
! [X12,X10,X17,X22,X15,X3] :
( c_in(c_Pair(hAPP(X22,X10),hAPP(X22,X12),X15,X15),X17,tc_prod(X15,X15))
| ~ c_in(c_Pair(X10,X12,X3,X3),c_Relation_Oinv__image(X17,X22,X15,X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_in__inv__image_0) ).
fof(c_0_68_069,axiom,
! [X17,X3] :
( c_Relation_Orel__comp(c_Relation_Oconverse(X17,X3,X3),X17,X3,X3,X3) != X17
| c_Equiv__Relations_Oequiv(c_Relation_ODomain(X17,X3,X3),X17,X3) ),
file('<stdin>',cls_comp__equivI_0) ).
fof(c_0_69_070,axiom,
! [X12,X10,X17,X22,X15,X3] :
( c_in(c_Pair(X10,X12,X3,X3),c_Relation_Oinv__image(X17,X22,X15,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(hAPP(X22,X10),hAPP(X22,X12),X15,X15),X17,tc_prod(X15,X15)) ),
file('<stdin>',cls_in__inv__image_1) ).
fof(c_0_70_071,axiom,
! [X17,X21,X19,X18,X15,X3] :
( c_lessequals(c_Relation_OImage(X17,X21,X3,X15),X19,tc_fun(X15,tc_bool))
| ~ c_lessequals(X17,c_Product__Type_OSigma(X18,c_COMBK(X19,tc_fun(X15,tc_bool),X3),X3,X15),tc_fun(tc_prod(X3,X15),tc_bool)) ),
file('<stdin>',cls_Image__subset_0) ).
fof(c_0_71_072,axiom,
! [X17,X19,X18,X3] :
( c_Wellfounded_Owf(X17,X3)
| c_in(c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1(X18,X19,X17,X3),X19,X3)
| ~ c_lessequals(X17,c_Product__Type_OSigma(X18,c_COMBK(X19,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
file('<stdin>',cls_wfI_3) ).
fof(c_0_72_073,axiom,
! [X17,X19,X18,X3] :
( c_Wellfounded_Owf(X17,X3)
| c_in(c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1(X18,X19,X17,X3),X18,X3)
| ~ c_lessequals(X17,c_Product__Type_OSigma(X18,c_COMBK(X19,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
file('<stdin>',cls_wfI_2) ).
fof(c_0_73_074,axiom,
! [X12,X10,X17,X3] :
( c_in(c_Pair(X10,X12,X3,X3),c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X17,X3),X3,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X10,X12,X3,X3),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X17,X3,X3),X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_trancl__converseD_0) ).
fof(c_0_74_075,axiom,
! [X12,X10,X17,X3] :
( c_in(c_Pair(X10,X12,X3,X3),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X17,X3,X3),X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X10,X12,X3,X3),c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X17,X3),X3,X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_trancl__converseI_0) ).
fof(c_0_75_076,axiom,
! [X22,X19,X18,X15,X3] :
( c_lessequals(c_Set_Oimage(X22,X18,X3,X15),X19,tc_fun(X15,tc_bool))
| ~ c_in(X22,c_FuncSet_OPi(X18,c_COMBK(X19,tc_fun(X15,tc_bool),X3),X3,X15),tc_fun(X3,X15)) ),
file('<stdin>',cls_funcset__image_0) ).
fof(c_0_76_077,axiom,
! [X12,X10,X8] :
( ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X12,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X12
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('<stdin>',cls_notin__Lin__iff_1) ).
fof(c_0_77_078,axiom,
! [X6,X7,X8] :
( ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X7,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('<stdin>',cls_Lin__irrefl_0) ).
fof(c_0_78_079,axiom,
! [X10,X21,X19,X18,X15,X3] :
( c_lessequals(c_Product__Type_OSigma(X18,c_COMBK(X21,tc_fun(X3,tc_bool),X15),X15,X3),c_Product__Type_OSigma(X19,c_COMBK(X21,tc_fun(X3,tc_bool),X15),X15,X3),tc_fun(tc_prod(X15,X3),tc_bool))
| ~ c_lessequals(X18,X19,tc_fun(X15,tc_bool))
| ~ c_in(X10,X21,X3) ),
file('<stdin>',cls_Times__subset__cancel2_1) ).
fof(c_0_79_080,axiom,
! [X12,X10,X17,X3] :
( c_in(c_Pair(X12,X10,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X10,X12,X3,X3),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X17,X3,X3),X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_rtrancl__converseD_0) ).
fof(c_0_80_081,axiom,
! [X12,X10,X17,X3] :
( c_Wellfounded_Owf(X17,X3)
| ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X12,X10,X3,X3),X17,tc_prod(X3,X3)),X3) ),
file('<stdin>',cls_wf__insert_0) ).
fof(c_0_81_082,axiom,
! [X10,X17,X7,X3] :
( ~ c_in(c_Pair(X10,X7,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(c_Pair(X7,X10,X3,X3),X17,tc_prod(X3,X3))
| ~ c_Wellfounded_Owf(X17,X3) ),
file('<stdin>',cls_wf__asym_0) ).
fof(c_0_82_083,axiom,
! [X17,X7,X15,X3] :
( c_in(c_Pair(X7,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X7,X17,X3,X15),X3,X15),X17,tc_prod(X3,X15))
| ~ c_in(X7,c_Relation_ODomain(X17,X3,X15),X3) ),
file('<stdin>',cls_Domain__iff_0) ).
fof(c_0_83_084,axiom,
! [X17,X7,X15,X3] :
( c_in(c_Pair(X7,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X7,X17,X3,X15),X3,X15),X17,tc_prod(X3,X15))
| ~ c_in(X7,c_Relation_ODomain(X17,X3,X15),X3) ),
file('<stdin>',cls_DomainE_0) ).
fof(c_0_84_085,axiom,
! [X17,X7,X15,X3] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X7,X17,X3,X15),X7,X15,X3),X17,tc_prod(X15,X3))
| ~ c_in(X7,c_Relation_ORange(X17,X15,X3),X3) ),
file('<stdin>',cls_Range__iff_0) ).
fof(c_0_85_086,axiom,
! [X17,X6,X15,X3] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X6,X17,X3,X15),X6,X15,X3),X17,tc_prod(X15,X3))
| ~ c_in(X6,c_Relation_ORange(X17,X15,X3),X3) ),
file('<stdin>',cls_RangeE_0) ).
fof(c_0_86_087,axiom,
! [X12,X10,X6,X7,X8] :
( c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X12 = X6
| X10 = X6
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X8,X7,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X6 ),
file('<stdin>',cls_in__above_3) ).
fof(c_0_87_088,axiom,
! [X16,X10,X7,X8] :
( X16 = X10
| ~ c_in(c_Pair(X16,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X8,X7,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X10
| c_in(c_Pair(X16,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X16 = X7 ),
file('<stdin>',cls_in__above_2) ).
fof(c_0_88_089,axiom,
! [X12,X10,X6,X7,X8] :
( c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X7
| X12 = X7
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X8,X7,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X6 ),
file('<stdin>',cls_in__below_3) ).
fof(c_0_89_090,axiom,
! [X12,X10,X6,X8] :
( X12 = X10
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X8,X10,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X10 = X6
| c_in(c_Pair(X6,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X12 = X6 ),
file('<stdin>',cls_in__below_2) ).
fof(c_0_90_091,axiom,
! [X12,X10,X7,X8] :
( ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X8,X7,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X10
| c_in(c_Pair(X7,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_in__above_1) ).
fof(c_0_91_092,axiom,
! [X16,X10,X6,X8] :
( ~ c_in(c_Pair(X16,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X8,X10,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X10 = X6
| c_in(c_Pair(X16,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_in__below_1) ).
fof(c_0_92_093,axiom,
! [X17,X2,X18,X3] :
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_in(X2,c_Equiv__Relations_Oquotient(X18,X17,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X17,c_Product__Type_OSigma(X18,c_COMBK(X18,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Finite__Set_Ofinite(X18,X3) ),
file('<stdin>',cls_finite__equiv__class_0) ).
fof(c_0_93_094,axiom,
! [X12,X10,X17,X3] :
( c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X12,X10,X3,X3),X17,tc_prod(X3,X3)),X3)
| c_in(c_Pair(X10,X12,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3))
| ~ c_Wellfounded_Owf(X17,X3) ),
file('<stdin>',cls_wf__insert_2) ).
fof(c_0_94_095,axiom,
! [X6,X7,X19,X18,X15,X3] :
( c_in(X6,hAPP(X19,X7),X15)
| ~ c_in(c_Pair(X7,X6,X3,X15),c_Product__Type_OSigma(X18,X19,X3,X15),tc_prod(X3,X15)) ),
file('<stdin>',cls_SigmaD2_0) ).
fof(c_0_95_096,axiom,
! [X12,X10,X17,X3] :
( c_in(c_Pair(X10,X12,X3,X3),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X17,X3,X3),X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X12,X10,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_rtrancl__converseI_0) ).
fof(c_0_96_097,axiom,
! [X12,X10,X17,X1,X2,X18,X3] :
( X2 = X1
| ~ c_in(c_Pair(X10,X12,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(X12,X1,X3)
| ~ c_in(X10,X2,X3)
| ~ c_in(X1,c_Equiv__Relations_Oquotient(X18,X17,X3),tc_fun(X3,tc_bool))
| ~ c_in(X2,c_Equiv__Relations_Oquotient(X18,X17,X3),tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X18,X17,X3) ),
file('<stdin>',cls_quotient__eqI_0) ).
fof(c_0_97_098,axiom,
! [X12,X10,X6,X7,X8] :
( c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X8,X7,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X12 = X6
| X10 = X6
| X10 = X12
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X6 ),
file('<stdin>',cls_in__above_4) ).
fof(c_0_98_099,axiom,
! [X12,X10,X6,X7,X8] :
( c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X8,X7,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X7
| X12 = X7
| X10 = X12
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X6 ),
file('<stdin>',cls_in__below_4) ).
fof(c_0_99_100,axiom,
! [X16,X10,X7,X8] :
( ~ c_in(c_Pair(X16,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X16 = X10
| X16 = X10
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X10
| c_in(c_Pair(X16,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X8,X7,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_in__above_7) ).
fof(c_0_100_101,axiom,
! [X12,X10,X6,X8] :
( X10 = X6
| X10 = X12
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X10 = X6
| c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X8,X10,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_in__above_6) ).
fof(c_0_101_102,axiom,
! [X12,X10,X6,X8] :
( ~ c_in(c_Pair(X6,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X12 = X10
| X10 = X12
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X10 = X6
| c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X8,X10,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_in__below_7) ).
fof(c_0_102_103,axiom,
! [X16,X10,X7,X8] :
( X10 = X7
| X16 = X10
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X10
| c_in(c_Pair(X16,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X8,X7,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X16,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_in__below_6) ).
fof(c_0_103_104,axiom,
! [X16,X10,X8] :
( ~ c_in(c_Pair(X16,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X16 = X10
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X16 = X10
| c_in(c_Pair(X16,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X8,X16,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_in__above_11) ).
fof(c_0_104_105,axiom,
! [X12,X10,X7,X8] :
( ~ c_in(c_Pair(X7,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X12
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X10
| c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X8,X7,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_in__above_9) ).
fof(c_0_105_106,axiom,
! [X16,X10,X8] :
( ~ c_in(c_Pair(X10,X16,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X16
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X10 = X16
| c_in(c_Pair(X10,X16,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X8,X10,X16),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_in__below_11) ).
fof(c_0_106_107,axiom,
! [X16,X10,X6,X8] :
( ~ c_in(c_Pair(X16,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X16 = X10
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X10 = X6
| c_in(c_Pair(X16,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X8,X10,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_in__below_9) ).
fof(c_0_107_108,axiom,
! [X6,X7,X19,X18,X15,X3] :
( c_in(X7,X18,X3)
| ~ c_in(c_Pair(X7,X6,X3,X15),c_Product__Type_OSigma(X18,X19,X3,X15),tc_prod(X3,X15)) ),
file('<stdin>',cls_SigmaD1_0) ).
fof(c_0_108_109,axiom,
! [X17,X18,X3] :
( c_Relation_Orefl__on(X18,X17,X3)
| c_in(c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1(X18,X17,X3),X18,X3)
| ~ c_lessequals(X17,c_Product__Type_OSigma(X18,c_COMBK(X18,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
file('<stdin>',cls_refl__on__def_2) ).
fof(c_0_109_110,axiom,
! [X17,X18,X3] :
( c_Relation_Orefl__on(X18,X17,X3)
| c_in(c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1(X18,X17,X3),X18,X3)
| ~ c_lessequals(X17,c_Product__Type_OSigma(X18,c_COMBK(X18,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
file('<stdin>',cls_refl__onI_0) ).
fof(c_0_110_111,axiom,
! [X17,X6,X7,X15,X3] :
( c_in(c_Pair(X6,X7,X15,X3),X17,tc_prod(X15,X3))
| ~ c_in(c_Pair(X7,X6,X3,X15),c_Relation_Oconverse(X17,X15,X3),tc_prod(X3,X15)) ),
file('<stdin>',cls_converseD_0) ).
fof(c_0_111_112,axiom,
! [X10,X17,X3] :
( ~ c_in(c_Pair(X10,X10,X3,X3),X17,tc_prod(X3,X3))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X17,X3),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X17,X3),X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_irrefl__trancl__rD_0) ).
fof(c_0_112_113,axiom,
! [X17,X6,X7,X15,X3] :
( c_in(c_Pair(X6,X7,X15,X3),c_Relation_Oconverse(X17,X3,X15),tc_prod(X15,X3))
| ~ c_in(c_Pair(X7,X6,X3,X15),X17,tc_prod(X3,X15)) ),
file('<stdin>',cls_converseI_0) ).
fof(c_0_113_114,axiom,
! [X17,X6,X7,X15,X3] :
( c_in(c_Pair(X7,X6,X3,X15),c_Relation_Oconverse(X17,X15,X3),tc_prod(X3,X15))
| ~ c_in(c_Pair(X6,X7,X15,X3),X17,tc_prod(X15,X3)) ),
file('<stdin>',cls_converse__iff_1) ).
fof(c_0_114_115,axiom,
! [X10,X22,X19,X18,X15,X3] :
( c_in(hAPP(X22,X10),X19,X15)
| ~ c_in(X10,X18,X3)
| ~ c_in(X22,c_FuncSet_OPi(X18,c_COMBK(X19,tc_fun(X15,tc_bool),X3),X3,X15),tc_fun(X3,X15)) ),
file('<stdin>',cls_funcset__mem_0) ).
fof(c_0_115_116,axiom,
! [X6,X7,X24,X3] :
( c_in(c_Pair(X7,X6,X3,X3),c_Transitive__Closure_Otrancl(X24,X3),tc_prod(X3,X3))
| X7 = X6
| ~ c_in(c_Pair(X7,X6,X3,X3),c_Transitive__Closure_Ortrancl(X24,X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_rtranclD_0) ).
fof(c_0_116_117,axiom,
! [X12,X10,X24,X3] :
( c_in(c_Pair(X10,X12,X3,X3),c_Transitive__Closure_Otrancl(X24,X3),tc_prod(X3,X3))
| X10 = X12
| ~ c_in(c_Pair(X10,X12,X3,X3),c_Transitive__Closure_Ortrancl(X24,X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_rtrancl__eq__or__trancl_0) ).
fof(c_0_117_118,axiom,
! [X12,X10,X24,X3] :
( c_in(c_Pair(X10,X12,X3,X3),c_Transitive__Closure_Ortrancl(X24,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X10,X12,X3,X3),c_Transitive__Closure_Otrancl(X24,X3),tc_prod(X3,X3))
| X10 = X12 ),
file('<stdin>',cls_rtrancl__eq__or__trancl_2) ).
fof(c_0_118_119,axiom,
! [X17,X6,X7,X3] :
( c_in(c_Pair(X7,X6,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X7,X6,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_trancl__into__rtrancl_0) ).
fof(c_0_119_120,axiom,
! [X17,X6,X7,X18,X15,X3] :
( c_in(X6,c_Relation_OImage(X17,X18,X3,X15),X15)
| ~ c_in(c_Pair(X7,X6,X3,X15),X17,tc_prod(X3,X15))
| ~ c_in(X7,X18,X3) ),
file('<stdin>',cls_rev__ImageI_0) ).
fof(c_0_120_121,axiom,
! [X10,X17,X6,X18,X15,X3] :
( c_in(X6,c_Relation_OImage(X17,X18,X15,X3),X3)
| ~ c_in(c_Pair(X10,X6,X15,X3),X17,tc_prod(X15,X3))
| ~ c_in(X10,X18,X15) ),
file('<stdin>',cls_Image__iff_2) ).
fof(c_0_121_122,axiom,
! [X17,X6,X7,X3] :
( c_in(c_Pair(X7,X6,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X7,X6,X3,X3),X17,tc_prod(X3,X3)) ),
file('<stdin>',cls_trancl_Or__into__trancl_0) ).
fof(c_0_122_123,axiom,
! [X12,X10,X17,X3] :
( c_in(c_Pair(X12,X10,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(c_Pair(X10,X12,X3,X3),X17,tc_prod(X3,X3))
| ~ c_Relation_Osym(X17,X3) ),
file('<stdin>',cls_sym__def_0) ).
fof(c_0_123_124,axiom,
! [X17,X6,X7,X3] :
( c_in(c_Pair(X6,X7,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(c_Pair(X7,X6,X3,X3),X17,tc_prod(X3,X3))
| ~ c_Relation_Osym(X17,X3) ),
file('<stdin>',cls_symD_0) ).
fof(c_0_124_125,axiom,
! [X20,X12,X10,X8] :
( c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X12 = X20
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X8,X20),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_in__mktop_2) ).
fof(c_0_125_126,axiom,
! [X20,X12,X10,X8] :
( c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X20
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X8,X20),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_in__mkbot_2) ).
fof(c_0_126_127,axiom,
! [X20,X12,X10,X8] :
( c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X8,X20),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X12
| X10 = X20 ),
file('<stdin>',cls_in__mktop_5) ).
fof(c_0_127_128,axiom,
! [X20,X12,X10,X8] :
( c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X8,X20),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X12 = X20
| X10 = X20 ),
file('<stdin>',cls_in__mktop_3) ).
fof(c_0_128_129,axiom,
! [X20,X12,X10,X8] :
( c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X8,X20),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X12
| X12 = X20 ),
file('<stdin>',cls_in__mkbot_5) ).
fof(c_0_129_130,axiom,
! [X20,X12,X10,X8] :
( c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X8,X20),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X20
| X12 = X20 ),
file('<stdin>',cls_in__mkbot_3) ).
fof(c_0_130_131,axiom,
! [X12,X16,X17,X31,X3] :
( ~ c_in(X12,X31,X3)
| ~ c_in(c_Pair(X12,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X31,X17,X3),X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(X16,X31,X3)
| ~ c_Wellfounded_Owf(X17,X3) ),
file('<stdin>',cls_wf__eq__minimal_1) ).
fof(c_0_131_132,axiom,
! [X12,X10,X24,X31,X3] :
( ~ c_in(X12,X31,X3)
| ~ c_in(c_Pair(X12,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X31,X24,X3),X3,X3),X24,tc_prod(X3,X3))
| ~ c_in(X10,X31,X3)
| ~ c_Wellfounded_Owf(X24,X3) ),
file('<stdin>',cls_wfE__min_1) ).
fof(c_0_132_133,axiom,
! [X12,X17,X7,X29,X3] :
( hBOOL(hAPP(X29,X7))
| hBOOL(hAPP(X29,X12))
| ~ c_in(c_Pair(X12,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X29,X17,X3),X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(X7,c_Wellfounded_Oacc(X17,X3),X3) ),
file('<stdin>',cls_acc__induct_1) ).
fof(c_0_133_134,axiom,
! [X12,X17,X7,X29,X3] :
( hBOOL(hAPP(X29,X7))
| hBOOL(hAPP(X29,X12))
| ~ c_in(c_Pair(X12,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X29,X17,X3),X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(X7,c_Wellfounded_Oacc(X17,X3),X3) ),
file('<stdin>',cls_acc__induct__rule_1) ).
fof(c_0_134_135,axiom,
! [X12,X16,X10,X17,X18,X3] :
( ~ c_in(X12,X10,X3)
| ~ c_in(X16,X10,X3)
| ~ c_in(X10,c_Equiv__Relations_Oquotient(X18,X17,X3),tc_fun(X3,tc_bool))
| ~ c_in(X10,c_Equiv__Relations_Oquotient(X18,X17,X3),tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X18,X17,X3)
| c_in(c_Pair(X16,X12,X3,X3),X17,tc_prod(X3,X3)) ),
file('<stdin>',cls_quotient__eq__iff_0) ).
fof(c_0_135_136,axiom,
! [X16,X10,X17,X18,X3] :
( c_in(c_Pair(X16,X10,X3,X3),X17,tc_prod(X3,X3))
| c_in(c_Pair(X10,X16,X3,X3),X17,tc_prod(X3,X3))
| X10 = X16
| ~ c_in(X16,X18,X3)
| ~ c_in(X10,X18,X3)
| ~ c_Relation_Ototal__on(X18,X17,X3) ),
file('<stdin>',cls_total__on__def_0) ).
fof(c_0_136_137,axiom,
! [X17,X18,X3] :
( c_Relation_Orel__comp(c_Relation_Oconverse(X17,X3,X3),X17,X3,X3,X3) = X17
| ~ c_Equiv__Relations_Oequiv(X18,X17,X3) ),
file('<stdin>',cls_equiv__comp__eq_0) ).
fof(c_0_137_138,axiom,
! [X36,X17,X37,X18,X15,X3] :
( c_lessequals(c_Relation_OImage(X36,X37,X3,X15),c_Relation_OImage(X17,X18,X3,X15),tc_fun(X15,tc_bool))
| ~ c_lessequals(X37,X18,tc_fun(X3,tc_bool))
| ~ c_lessequals(X36,X17,tc_fun(tc_prod(X3,X15),tc_bool)) ),
file('<stdin>',cls_Image__mono_0) ).
fof(c_0_138_139,axiom,
! [X10,X21,X19,X18,X15,X3] :
( c_Product__Type_OSigma(X18,c_COMBK(X21,tc_fun(X3,tc_bool),X15),X15,X3) != c_Product__Type_OSigma(X19,c_COMBK(X21,tc_fun(X3,tc_bool),X15),X15,X3)
| ~ c_in(X10,X21,X3)
| X18 = X19 ),
file('<stdin>',cls_Times__eq__cancel2_0) ).
fof(c_0_139_140,axiom,
! [X12,X10,X8] :
( c_in(c_Pair(X12,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X12
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('<stdin>',cls_notin__Lin__iff_0) ).
fof(c_0_140_141,axiom,
! [X6,X7,X19,X18,X15,X3] :
( c_in(c_Pair(X7,X6,X3,X15),c_Product__Type_OSigma(X18,X19,X3,X15),tc_prod(X3,X15))
| ~ c_in(X6,hAPP(X19,X7),X15)
| ~ c_in(X7,X18,X3) ),
file('<stdin>',cls_mem__Sigma__iff_2) ).
fof(c_0_141_142,axiom,
! [X6,X7,X19,X18,X15,X3] :
( c_in(c_Pair(X7,X6,X3,X15),c_Product__Type_OSigma(X18,X19,X3,X15),tc_prod(X3,X15))
| ~ c_in(X6,hAPP(X19,X7),X15)
| ~ c_in(X7,X18,X3) ),
file('<stdin>',cls_SigmaI_0) ).
fof(c_0_142_143,axiom,
! [X10,X6,X7,X8] :
( ~ c_in(c_Pair(X10,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X8,X7,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X6 ),
file('<stdin>',cls_in__above_0) ).
fof(c_0_143_144,axiom,
! [X10,X6,X7,X8] :
( ~ c_in(c_Pair(X10,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X8,X7,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X6 ),
file('<stdin>',cls_in__below_0) ).
fof(c_0_144_145,axiom,
! [X30,X10,X17,X29] :
( hBOOL(hAPP(X29,X10))
| c_in(X30,c_Wellfounded_Oacc(X17,t_a),t_a)
| ~ c_in(c_Pair(X30,v_sko__Wellfounded__Xacc__Xinduct__1(X29,X17),t_a,t_a),X17,tc_prod(t_a,t_a))
| ~ c_in(X10,c_Wellfounded_Oacc(X17,t_a),t_a) ),
file('<stdin>',cls_acc_Oinduct_0) ).
fof(c_0_145_146,axiom,
! [X30,X10,X17,X29] :
( hBOOL(hAPP(X29,X10))
| c_in(X30,c_Wellfounded_Oacc(X17,t_a),t_a)
| ~ c_in(c_Pair(X30,v_sko__Wellfounded__Xacc__Xinducts__1(X29,X17),t_a,t_a),X17,tc_prod(t_a,t_a))
| ~ c_in(X10,c_Wellfounded_Oacc(X17,t_a),t_a) ),
file('<stdin>',cls_acc_Oinducts_0) ).
fof(c_0_146_147,axiom,
! [X22,X19,X18,X15,X3] :
( c_lessequals(c_Set_Oimage(X22,X18,X3,X15),c_Set_Oimage(X22,X19,X3,X15),tc_fun(X15,tc_bool))
| ~ c_lessequals(X18,X19,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_image__mono_0) ).
fof(c_0_147_148,axiom,
! [X10,X22,X18,X15,X3] :
( ~ c_lessequals(X10,X18,tc_fun(X15,tc_bool))
| c_lessequals(c_Set_Oimage(X22,X10,X15,X3),c_Set_Oimage(X22,X18,X15,X3),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__image__iff_2) ).
fof(c_0_148_149,axiom,
! [X17,X6,X7,X3] :
( c_in(X6,c_Wellfounded_Oacc(X17,X3),X3)
| ~ c_in(c_Pair(X6,X7,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(X7,c_Wellfounded_Oacc(X17,X3),X3) ),
file('<stdin>',cls_acc__downwards_0) ).
fof(c_0_149_150,axiom,
! [X17,X6,X7,X3] :
( c_in(X6,c_Wellfounded_Oacc(X17,X3),X3)
| ~ c_in(X7,c_Wellfounded_Oacc(X17,X3),X3)
| ~ c_in(c_Pair(X6,X7,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_acc__downwards__aux_0) ).
fof(c_0_150_151,axiom,
! [X12,X10,X17,X29] :
( hBOOL(hAPP(X29,X10))
| hBOOL(hAPP(X29,X12))
| ~ c_in(c_Pair(X12,v_sko__Wellfounded__Xacc__Xinducts__1(X29,X17),t_a,t_a),X17,tc_prod(t_a,t_a))
| ~ c_in(X10,c_Wellfounded_Oacc(X17,t_a),t_a) ),
file('<stdin>',cls_acc_Oinducts_1) ).
fof(c_0_151_152,axiom,
! [X12,X10,X17,X29] :
( hBOOL(hAPP(X29,X10))
| hBOOL(hAPP(X29,X12))
| ~ c_in(c_Pair(X12,v_sko__Wellfounded__Xacc__Xinduct__1(X29,X17),t_a,t_a),X17,tc_prod(t_a,t_a))
| ~ c_in(X10,c_Wellfounded_Oacc(X17,t_a),t_a) ),
file('<stdin>',cls_acc_Oinduct_1) ).
fof(c_0_152_153,axiom,
! [X17,X6,X7,X3] :
( c_in(X7,c_Wellfounded_Oacc(X17,X3),X3)
| ~ c_in(c_Pair(X7,X6,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(X6,c_Wellfounded_Oacc(X17,X3),X3) ),
file('<stdin>',cls_acc__downward_0) ).
fof(c_0_153_154,axiom,
! [X12,X17,X7,X3] :
( c_in(X12,c_Wellfounded_Oacc(X17,X3),X3)
| ~ c_in(c_Pair(X12,X7,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(X7,c_Wellfounded_Oacc(X17,X3),X3) ),
file('<stdin>',cls_acc_Ocases_0) ).
fof(c_0_154_155,axiom,
! [X12,X10,X24,X3] :
( X10 = X12
| ~ c_in(c_Pair(X10,X12,X3,X3),c_Transitive__Closure_Ortrancl(X24,X3),tc_prod(X3,X3))
| c_in(X10,c_Relation_ODomain(X24,X3,X3),X3) ),
file('<stdin>',cls_Not__Domain__rtrancl_0) ).
fof(c_0_155_156,axiom,
! [X10,X22,X19,X18,X15,X3] :
( c_in(hAPP(X22,X10),hAPP(X19,X10),X15)
| ~ c_in(X10,X18,X3)
| ~ c_in(X22,c_FuncSet_OPi(X18,X19,X3,X15),tc_fun(X3,X15)) ),
file('<stdin>',cls_Pi__mem_0) ).
fof(c_0_156_157,axiom,
! [X10,X22,X19,X18,X15,X3] :
( ~ c_in(X10,X18,X3)
| c_in(hAPP(X22,X10),hAPP(X19,X10),X15)
| ~ c_in(X22,c_FuncSet_OPi(X18,X19,X3,X15),tc_fun(X3,X15)) ),
file('<stdin>',cls_PiE_0) ).
fof(c_0_157_158,axiom,
! [X17,X3] :
( c_Nitpick_Orefl_H(X17,X3)
| ~ c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X17,X3),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X17,X3),X3,X3),X17,tc_prod(X3,X3)) ),
file('<stdin>',cls_Nitpick_Orefl_H__def_1) ).
fof(c_0_158_159,axiom,
! [X10,X22,X19,X18,X15,X3] :
( c_in(hAPP(X22,X10),X19,X3)
| ~ c_in(X10,X18,X15)
| ~ c_lessequals(c_Set_Oimage(X22,X18,X15,X3),X19,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_image__subset__iff_0) ).
fof(c_0_159_160,axiom,
! [X10,X17,X7,X15,X3] :
( c_in(X7,c_Relation_ORange(X17,X15,X3),X3)
| ~ c_in(c_Pair(X10,X7,X15,X3),X17,tc_prod(X15,X3)) ),
file('<stdin>',cls_Range__iff_1) ).
fof(c_0_160_161,axiom,
! [X17,X6,X7,X15,X3] :
( c_in(X6,c_Relation_ORange(X17,X3,X15),X15)
| ~ c_in(c_Pair(X7,X6,X3,X15),X17,tc_prod(X3,X15)) ),
file('<stdin>',cls_RangeI_0) ).
fof(c_0_161_162,axiom,
! [X10,X17,X7,X15,X3] :
( c_in(X7,c_Relation_ODomain(X17,X3,X15),X3)
| ~ c_in(c_Pair(X7,X10,X3,X15),X17,tc_prod(X3,X15)) ),
file('<stdin>',cls_Domain__iff_1) ).
fof(c_0_162_163,axiom,
! [X17,X6,X7,X15,X3] :
( c_in(X7,c_Relation_ODomain(X17,X3,X15),X3)
| ~ c_in(c_Pair(X7,X6,X3,X15),X17,tc_prod(X3,X15)) ),
file('<stdin>',cls_DomainI_0) ).
fof(c_0_163_164,axiom,
! [X9] :
( v_thesis____
| ~ c_in(X9,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X9,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_that_0) ).
fof(c_0_164_165,axiom,
! [X12,X10,X17,X18,X3] :
( c_in(X12,X18,X3)
| ~ c_in(c_Pair(X10,X12,X3,X3),X17,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X18,X17,X3) ),
file('<stdin>',cls_equiv__class__eq__iff_2) ).
fof(c_0_165_166,axiom,
! [X12,X10,X17,X18,X3] :
( c_in(X10,X18,X3)
| ~ c_in(c_Pair(X10,X12,X3,X3),X17,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X18,X17,X3) ),
file('<stdin>',cls_equiv__class__eq__iff_1) ).
fof(c_0_166_167,axiom,
! [X12,X10,X17,X18,X3] :
( c_in(X12,X18,X3)
| ~ c_in(c_Pair(X10,X12,X3,X3),X17,tc_prod(X3,X3))
| ~ c_Relation_Orefl__on(X18,X17,X3) ),
file('<stdin>',cls_refl__onD2_0) ).
fof(c_0_167_168,axiom,
! [X12,X10,X17,X18,X3] :
( c_in(X10,X18,X3)
| ~ c_in(c_Pair(X10,X12,X3,X3),X17,tc_prod(X3,X3))
| ~ c_Relation_Orefl__on(X18,X17,X3) ),
file('<stdin>',cls_refl__onD1_0) ).
fof(c_0_168_169,axiom,
! [X17,X18,X3] :
( c_lessequals(X17,c_Product__Type_OSigma(X18,c_COMBK(X18,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Equiv__Relations_Oequiv(X18,X17,X3) ),
file('<stdin>',cls_equiv__type_0) ).
fof(c_0_169_170,axiom,
! [X17,X18,X3] :
( c_lessequals(X17,c_Product__Type_OSigma(X18,c_COMBK(X18,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Relation_Orefl__on(X18,X17,X3) ),
file('<stdin>',cls_refl__on__def_0) ).
fof(c_0_170_171,axiom,
! [X12,X10,X18,X3] :
( c_in(X10,X18,X3)
| ~ c_in(c_Pair(X10,X12,X3,X3),c_Relation_OId__on(X18,X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_Id__on__iff_1) ).
fof(c_0_171_172,axiom,
! [X12,X10,X18,X3] :
( X10 = X12
| ~ c_in(c_Pair(X10,X12,X3,X3),c_Relation_OId__on(X18,X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_Id__on__iff_0) ).
fof(c_0_172_173,axiom,
! [X22,X19,X18,X15,X3] :
( c_Finite__Set_Ofinite(X19,X15)
| ~ c_lessequals(X19,c_Set_Oimage(X22,X18,X3,X15),tc_fun(X15,tc_bool))
| ~ c_Finite__Set_Ofinite(X18,X3) ),
file('<stdin>',cls_finite__surj_0) ).
fof(c_0_173_174,axiom,
! [X17,X7,X3] :
( ~ c_in(c_Pair(X7,X7,X3,X3),X17,tc_prod(X3,X3))
| ~ c_Wellfounded_Owf(X17,X3) ),
file('<stdin>',cls_wf__irrefl_0) ).
fof(c_0_174_175,axiom,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3),c_Lattices_Olower__semilattice__class_Oinf(X10,X20,X3),X3),c_Lattices_Olower__semilattice__class_Oinf(X10,c_Lattices_Oupper__semilattice__class_Osup(X12,X20,X3),X3),X3) ),
file('<stdin>',cls_distrib__inf__le_0) ).
fof(c_0_175_176,axiom,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Olower__semilattice__class_Oinf(X12,X20,X3),X3),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),c_Lattices_Oupper__semilattice__class_Osup(X10,X20,X3),X3),X3) ),
file('<stdin>',cls_distrib__sup__le_0) ).
fof(c_0_176_177,axiom,
! [X6,X7,X3] :
( X7 = X6
| ~ c_in(c_Pair(X7,X6,X3,X3),c_Relation_OId(X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_pair__in__Id__conv_0) ).
fof(c_0_177_178,axiom,
! [X10,X22,X18,X15,X3] :
( c_Set_Oinsert(hAPP(X22,X10),c_Set_Oimage(X22,X18,X3,X15),X15) = c_Set_Oimage(X22,X18,X3,X15)
| ~ c_in(X10,X18,X3) ),
file('<stdin>',cls_insert__image_0) ).
fof(c_0_178_179,axiom,
! [X10,X17,X3] :
( c_in(X10,c_Wellfounded_Oacc(X17,X3),X3)
| c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X17,X10,X3),X10,X3,X3),X17,tc_prod(X3,X3)) ),
file('<stdin>',cls_acc_OaccI_0) ).
fof(c_0_179_180,axiom,
! [X10,X24,X3] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X24,X10,X3),X10,X3,X3),X24,tc_prod(X3,X3))
| c_in(X10,c_Wellfounded_Oacc(X24,X3),X3) ),
file('<stdin>',cls_not__acc__down_0) ).
fof(c_0_180_181,axiom,
! [X16,X10,X8] :
( X16 = X10
| X10 = X16
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X10 = X16
| c_in(c_Pair(X10,X16,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X8,X10,X16),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_in__below_5) ).
fof(c_0_181_182,axiom,
! [X16,X10,X8] :
( X16 = X10
| X16 = X10
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X16 = X10
| c_in(c_Pair(X16,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X8,X16,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_in__above_5) ).
fof(c_0_182_183,axiom,
! [X17,X2,X18,X3] :
( c_in(c_List_Osko__Equiv__Relations__XquotientE__1__1(X18,X2,X17,X3),X18,X3)
| ~ c_in(X2,c_Equiv__Relations_Oquotient(X18,X17,X3),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_quotientE_1) ).
fof(c_0_183_184,axiom,
! [X21,X19,X18,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)),X21,tc_fun(X3,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X18,c_Lattices_Oupper__semilattice__class_Osup(X19,X21,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| c_lessequals(X21,X18,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__Int__assoc__eq_0) ).
fof(c_0_184_185,axiom,
! [X10,X11,X24,X3] :
( c_in(X10,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X24,X11,tc_fun(tc_prod(X3,X3),tc_bool)),X3),tc_prod(X3,X3))
| ~ c_in(X10,c_Transitive__Closure_Ortrancl(X11,X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_in__rtrancl__UnI_1) ).
fof(c_0_185_186,axiom,
! [X10,X11,X24,X3] :
( c_in(X10,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X24,X11,tc_fun(tc_prod(X3,X3),tc_bool)),X3),tc_prod(X3,X3))
| ~ c_in(X10,c_Transitive__Closure_Ortrancl(X24,X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_in__rtrancl__UnI_0) ).
fof(c_0_186_187,axiom,
! [X13,X6,X14,X7,X15,X3] :
( c_Pair(X7,X6,X3,X15) != c_Pair(X14,X13,X3,X15)
| X6 = X13 ),
file('<stdin>',cls_Pair__eq_1) ).
fof(c_0_187_188,axiom,
! [X13,X6,X14,X7,X15,X3] :
( c_Pair(X7,X6,X3,X15) != c_Pair(X14,X13,X3,X15)
| X7 = X14 ),
file('<stdin>',cls_Pair__eq_0) ).
fof(c_0_188_189,axiom,
! [X10,X24,X3] :
( c_in(X10,c_Relation_ODomain(X24,X3,X3),X3)
| c_in(c_Pair(X10,X10,X3,X3),c_Transitive__Closure_Ortrancl(X24,X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_Not__Domain__rtrancl_1) ).
fof(c_0_189_190,axiom,
! [X10,X17,X18,X3] :
( c_in(c_Pair(X10,X10,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(X10,X18,X3)
| ~ c_Relation_Orefl__on(X18,X17,X3) ),
file('<stdin>',cls_refl__on__def_1) ).
fof(c_0_190_191,axiom,
! [X17,X7,X18,X3] :
( c_in(c_Pair(X7,X7,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(X7,X18,X3)
| ~ c_Relation_Orefl__on(X18,X17,X3) ),
file('<stdin>',cls_refl__onD_0) ).
fof(c_0_191_192,axiom,
! [X10,X18,X3] :
( c_in(c_Pair(X10,X10,X3,X3),c_Relation_OId__on(X18,X3),tc_prod(X3,X3))
| ~ c_in(X10,X18,X3) ),
file('<stdin>',cls_Id__on__eqI_0) ).
fof(c_0_192_193,axiom,
! [X10,X22,X18,X43,X3] :
( ~ c_in(X10,X18,X43)
| c_in(hAPP(X22,X10),c_Set_Oimage(X22,X18,X43,X3),X3) ),
file('<stdin>',cls_rev__image__eqI_0) ).
fof(c_0_193_194,axiom,
! [X10,X22,X18,X15,X3] :
( ~ c_in(X10,X18,X15)
| c_in(hAPP(X22,X10),c_Set_Oimage(X22,X18,X15,X3),X3) ),
file('<stdin>',cls_image__iff_2) ).
fof(c_0_194_195,axiom,
! [X10,X22,X18,X15,X3] :
( c_in(hAPP(X22,X10),c_Set_Oimage(X22,X18,X15,X3),X3)
| ~ c_in(X10,X18,X15) ),
file('<stdin>',cls_image__eqI_0) ).
fof(c_0_195_196,axiom,
! [X10,X22,X18,X15,X3] :
( c_in(hAPP(X22,X10),c_Set_Oimage(X22,X18,X3,X15),X15)
| ~ c_in(X10,X18,X3) ),
file('<stdin>',cls_imageI_0) ).
fof(c_0_196_197,axiom,
! [X25,X17,X19,X18,X3] :
( c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(X18,X19,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X17,X25,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Relation_Orefl__on(X19,X25,X3)
| ~ c_Relation_Orefl__on(X18,X17,X3) ),
file('<stdin>',cls_refl__on__Un_0) ).
fof(c_0_197_198,axiom,
! [X25,X17,X19,X18,X3] :
( c_Relation_Orefl__on(c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X17,X25,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Relation_Orefl__on(X19,X25,X3)
| ~ c_Relation_Orefl__on(X18,X17,X3) ),
file('<stdin>',cls_refl__on__Int_0) ).
fof(c_0_198_199,axiom,
! [X23,X18,X3] :
( X23 = c_Pair(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X18,X23,X3),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X18,X23,X3),X3,X3)
| ~ c_in(X23,c_Relation_OId__on(X18,X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_Id__onE_1) ).
fof(c_0_199_200,axiom,
! [X38,X21,X19,X18,X3] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X18,X19,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X21,X38,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X19,X38,tc_fun(X3,tc_bool))
| ~ c_lessequals(X18,X21,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__mono_0) ).
fof(c_0_200_201,axiom,
! [X38,X21,X19,X18,X3] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X21,X38,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X19,X38,tc_fun(X3,tc_bool))
| ~ c_lessequals(X18,X21,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Int__mono_0) ).
fof(c_0_201_202,axiom,
! [X10,X17,X3] :
( c_in(c_Pair(X10,X10,X3,X3),X17,tc_prod(X3,X3))
| ~ c_Nitpick_Orefl_H(X17,X3) ),
file('<stdin>',cls_Nitpick_Orefl_H__def_0) ).
fof(c_0_202_203,axiom,
! [X12,X10,X8] :
( X10 = X12
| X12 = X10
| c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X8,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_in__mkbot_4) ).
fof(c_0_203_204,axiom,
! [X16,X10,X8] :
( X16 = X10
| X16 = X10
| c_in(c_Pair(X16,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X8,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_in__mktop_4) ).
fof(c_0_204_205,axiom,
! [X6,X7] :
( c_in(c_Pair(X7,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X7,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X7 = X6 ),
file('<stdin>',cls_complete__Lin_1) ).
fof(c_0_205_206,axiom,
! [X10,X19,X18,X3] :
( hBOOL(hAPP(X19,X10))
| hBOOL(hAPP(X18,X10))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X18,X19,tc_fun(X3,tc_bool)),X10)) ),
file('<stdin>',cls_sup1E_0) ).
fof(c_0_206_207,axiom,
! [X21,X19,X18,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)),X21,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X18,c_Lattices_Oupper__semilattice__class_Osup(X19,X21,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X21,X18,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__Int__assoc__eq_1) ).
fof(c_0_207_208,axiom,
! [X10,X19,X18,X3] :
( hBOOL(hAPP(X19,X10))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)),X10)) ),
file('<stdin>',cls_inf1E_1) ).
fof(c_0_208_209,axiom,
! [X10,X19,X18,X3] :
( hBOOL(hAPP(X18,X10))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)),X10)) ),
file('<stdin>',cls_inf1E_0) ).
fof(c_0_209_210,axiom,
! [X17,X7,X29,X3] :
( hBOOL(hAPP(X29,X7))
| ~ hBOOL(hAPP(X29,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X29,X17,X3)))
| ~ c_in(X7,c_Wellfounded_Oacc(X17,X3),X3) ),
file('<stdin>',cls_acc__induct__rule_2) ).
fof(c_0_210_211,axiom,
! [X17,X7,X29,X3] :
( hBOOL(hAPP(X29,X7))
| ~ hBOOL(hAPP(X29,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X29,X17,X3)))
| ~ c_in(X7,c_Wellfounded_Oacc(X17,X3),X3) ),
file('<stdin>',cls_acc__induct_2) ).
fof(c_0_211_212,axiom,
! [X17,X22,X15,X3] :
( c_Relation_Otrans(c_Relation_Oinv__image(X17,X22,X3,X15),X15)
| ~ c_Relation_Otrans(X17,X3) ),
file('<stdin>',cls_trans__inv__image_0) ).
fof(c_0_212_213,axiom,
! [X40,X41,X15,X3] :
( c_Finite__Set_Ofinite(c_Set_Oimage(X40,X41,X3,X15),X15)
| ~ c_Finite__Set_Ofinite(X41,X3) ),
file('<stdin>',cls_finite__imageI_0) ).
fof(c_0_213_214,axiom,
! [X17,X22,X15,X3] :
( c_Wellfounded_Owf(c_Relation_Oinv__image(X17,X22,X3,X15),X15)
| ~ c_Wellfounded_Owf(X17,X3) ),
file('<stdin>',cls_wf__inv__image_0) ).
fof(c_0_214_215,axiom,
! [X17,X22,X15,X3] :
( c_Relation_Osym(c_Relation_Oinv__image(X17,X22,X3,X15),X15)
| ~ c_Relation_Osym(X17,X3) ),
file('<stdin>',cls_sym__inv__image_0) ).
fof(c_0_215_216,axiom,
! [X25,X17,X15,X3] :
( c_lessequals(c_Relation_ODomain(X17,X3,X15),c_Relation_ODomain(X25,X3,X15),tc_fun(X3,tc_bool))
| ~ c_lessequals(X17,X25,tc_fun(tc_prod(X3,X15),tc_bool)) ),
file('<stdin>',cls_Domain__mono_0) ).
fof(c_0_216_217,axiom,
! [X25,X17,X28,X3] :
( c_in(X28,c_Transitive__Closure_Otrancl(X25,X3),tc_prod(X3,X3))
| ~ c_lessequals(X17,X25,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_in(X28,c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_trancl__mono_0) ).
fof(c_0_217_218,axiom,
! [X7,X21,X19,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X7,X19,X3),X21,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X7,c_Lattices_Olower__semilattice__class_Oinf(X19,X21,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X7,X21,X3) ),
file('<stdin>',cls_Int__insert__left_0) ).
fof(c_0_218_219,axiom,
! [X7,X19,X18,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(X18,c_Set_Oinsert(X7,X19,X3),tc_fun(X3,tc_bool)) = c_Set_Oinsert(X7,c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X7,X18,X3) ),
file('<stdin>',cls_Int__insert__right_0) ).
fof(c_0_219_220,axiom,
! [X11,X24,X3] :
( c_Transitive__Closure_Ortrancl(X11,X3) = c_Transitive__Closure_Ortrancl(X24,X3)
| ~ c_lessequals(X11,c_Transitive__Closure_Ortrancl(X24,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(X24,X11,tc_fun(tc_prod(X3,X3),tc_bool)) ),
file('<stdin>',cls_rtrancl__subset_0) ).
fof(c_0_220_221,axiom,
! [X21,X19,X18,X3] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X18,X19,tc_fun(X3,tc_bool)),X21,tc_fun(X3,tc_bool))
| ~ c_lessequals(X19,X21,tc_fun(X3,tc_bool))
| ~ c_lessequals(X18,X21,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__subset__iff_2) ).
fof(c_0_221_222,axiom,
! [X21,X19,X18,X3] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X18,X19,tc_fun(X3,tc_bool)),X21,tc_fun(X3,tc_bool))
| ~ c_lessequals(X19,X21,tc_fun(X3,tc_bool))
| ~ c_lessequals(X18,X21,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__least_0) ).
fof(c_0_222_223,axiom,
! [X21,X19,X18,X3] :
( c_lessequals(X21,c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X21,X19,tc_fun(X3,tc_bool))
| ~ c_lessequals(X21,X18,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Int__greatest_0) ).
fof(c_0_223_224,axiom,
! [X21,X19,X18,X3] :
( c_lessequals(X21,c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X21,X19,tc_fun(X3,tc_bool))
| ~ c_lessequals(X21,X18,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Int__subset__iff_2) ).
fof(c_0_224_225,axiom,
! [X8] :
( c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Relation_Oconverse(X8,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('<stdin>',cls_converse__in__Lin_0) ).
fof(c_0_225_226,axiom,
! [X21,X19,X18,X3] :
( c_lessequals(X21,X19,tc_fun(X3,tc_bool))
| ~ c_lessequals(X21,c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Int__subset__iff_1) ).
fof(c_0_226_227,axiom,
! [X21,X19,X18,X3] :
( c_lessequals(X21,X18,tc_fun(X3,tc_bool))
| ~ c_lessequals(X21,c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Int__subset__iff_0) ).
fof(c_0_227_228,axiom,
! [X21,X19,X18,X3] :
( c_lessequals(X18,X21,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X18,X19,tc_fun(X3,tc_bool)),X21,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__subset__iff_0) ).
fof(c_0_228_229,axiom,
! [X21,X19,X18,X3] :
( c_lessequals(X19,X21,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X18,X19,tc_fun(X3,tc_bool)),X21,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__subset__iff_1) ).
fof(c_0_229_230,axiom,
! [X28,X3] :
( X28 = c_Pair(c_ATP__Linkup_Osko__Relation__XIdE__1__1(X28,X3),c_ATP__Linkup_Osko__Relation__XIdE__1__1(X28,X3),X3,X3)
| ~ c_in(X28,c_Relation_OId(X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_IdE_0) ).
fof(c_0_230_231,axiom,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Odistrib__lattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X12,X20,X3),X10,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X12,X10,X3),c_Lattices_Olower__semilattice__class_Oinf(X20,X10,X3),X3) ),
file('<stdin>',cls_inf__sup__distrib2_0) ).
fof(c_0_231_232,axiom,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Odistrib__lattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X10,c_Lattices_Oupper__semilattice__class_Osup(X12,X20,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3),c_Lattices_Olower__semilattice__class_Oinf(X10,X20,X3),X3) ),
file('<stdin>',cls_inf__sup__distrib1_0) ).
fof(c_0_232_233,axiom,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Odistrib__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X12,X20,X3),X10,X3) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X12,X10,X3),c_Lattices_Oupper__semilattice__class_Osup(X20,X10,X3),X3) ),
file('<stdin>',cls_sup__inf__distrib2_0) ).
fof(c_0_233_234,axiom,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Odistrib__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Olower__semilattice__class_Oinf(X12,X20,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),c_Lattices_Oupper__semilattice__class_Osup(X10,X20,X3),X3) ),
file('<stdin>',cls_sup__inf__distrib1_0) ).
fof(c_0_234_235,axiom,
! [X23,X19,X18,X3] :
( c_in(X23,X19,X3)
| c_in(X23,X18,X3)
| ~ c_in(X23,c_Lattices_Oupper__semilattice__class_Osup(X18,X19,tc_fun(X3,tc_bool)),X3) ),
file('<stdin>',cls_UnE_0) ).
fof(c_0_235_236,axiom,
! [X10,X19,X18,X3] :
( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)),X10))
| ~ hBOOL(hAPP(X19,X10))
| ~ hBOOL(hAPP(X18,X10)) ),
file('<stdin>',cls_inf1I_0) ).
fof(c_0_236_237,axiom,
! [X25,X17,X3] :
( c_lessequals(c_Transitive__Closure_Ortrancl(X17,X3),c_Transitive__Closure_Ortrancl(X25,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(X17,c_Transitive__Closure_Ortrancl(X25,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
file('<stdin>',cls_rtrancl__subset__rtrancl_0) ).
fof(c_0_237_238,axiom,
! [X10,X19,X18,X3] :
( c_lessequals(X18,X19,tc_fun(X3,tc_bool))
| c_in(X10,X18,X3)
| ~ c_lessequals(X18,c_Set_Oinsert(X10,X19,X3),tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__insert__iff_1) ).
fof(c_0_238_239,axiom,
! [X10,X19,X18,X3] :
( c_lessequals(X18,X19,tc_fun(X3,tc_bool))
| ~ c_lessequals(X18,c_Set_Oinsert(X10,X19,X3),tc_fun(X3,tc_bool))
| c_in(X10,X18,X3) ),
file('<stdin>',cls_subset__insert_0) ).
fof(c_0_239_240,axiom,
! [X12,X10,X18,X3] :
( hBOOL(hAPP(X18,X10))
| X12 = X10
| ~ hBOOL(hAPP(c_Set_Oinsert(X12,X18,X3),X10)) ),
file('<stdin>',cls_insert__code_0) ).
fof(c_0_240_241,axiom,
! [X7,X38,X21,X3] :
( c_lessequals(c_Set_Oinsert(X7,X21,X3),c_Set_Oinsert(X7,X38,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X21,X38,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_insert__mono_0) ).
fof(c_0_241_242,axiom,
! [X12,X10,X8] :
( c_in(c_Arrow__Order__Mirabelle_Obelow(X8,X10,X12),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X10 = X12 ),
file('<stdin>',cls_below__Lin_0) ).
fof(c_0_242_243,axiom,
! [X12,X10,X8] :
( c_in(c_Arrow__Order__Mirabelle_Oabove(X8,X10,X12),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X10 = X12 ),
file('<stdin>',cls_above__Lin_0) ).
fof(c_0_243_244,axiom,
! [X8] :
( c_in(c_Relation_Oconverse(X8,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('<stdin>',cls_converse__in__Lin_1) ).
fof(c_0_244_245,axiom,
! [X10,X19,X18,X3] :
( c_lessequals(c_Set_Oinsert(X10,X18,X3),X19,tc_fun(X3,tc_bool))
| ~ c_lessequals(X18,X19,tc_fun(X3,tc_bool))
| ~ c_in(X10,X19,X3) ),
file('<stdin>',cls_insert__subset_2) ).
fof(c_0_245_246,axiom,
! [X25,X17,X3] :
( c_lessequals(c_Transitive__Closure_Ortrancl(X17,X3),c_Transitive__Closure_Ortrancl(X25,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(X17,X25,tc_fun(tc_prod(X3,X3),tc_bool)) ),
file('<stdin>',cls_rtrancl__mono_0) ).
fof(c_0_246_247,axiom,
! [X10,X19,X18,X3] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X18,X19,tc_fun(X3,tc_bool)),X10))
| ~ hBOOL(hAPP(X19,X10)) ),
file('<stdin>',cls_sup1CI_0) ).
fof(c_0_247_248,axiom,
! [X10,X19,X18,X3] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X18,X19,tc_fun(X3,tc_bool)),X10))
| ~ hBOOL(hAPP(X18,X10)) ),
file('<stdin>',cls_sup1CI_1) ).
fof(c_0_248_249,axiom,
! [X21,X18,X3] :
( c_in(c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X18,X21,X3),X21,tc_fun(X3,tc_bool))
| ~ c_in(X18,c_Complete__Lattice_OSup__class_OSup(X21,tc_fun(X3,tc_bool)),X3) ),
file('<stdin>',cls_UnionE_1) ).
fof(c_0_249_250,axiom,
! [X23,X19,X18,X3] :
( c_in(X23,X19,X3)
| ~ c_in(X23,c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)),X3) ),
file('<stdin>',cls_IntE_1) ).
fof(c_0_250_251,axiom,
! [X23,X19,X18,X3] :
( c_in(X23,X18,X3)
| ~ c_in(X23,c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)),X3) ),
file('<stdin>',cls_IntE_0) ).
fof(c_0_251_252,axiom,
! [X21,X18,X3] :
( c_in(X18,c_Complete__Lattice_OInf__class_OInf(X21,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X18,c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X18,X21,X3),X3) ),
file('<stdin>',cls_InterI_1) ).
fof(c_0_252_253,axiom,
! [X23,X19,X18,X3] :
( c_in(X23,c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X23,X19,X3)
| ~ c_in(X23,X18,X3) ),
file('<stdin>',cls_Int__iff_2) ).
fof(c_0_253_254,axiom,
! [X23,X19,X18,X3] :
( c_in(X23,c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X23,X19,X3)
| ~ c_in(X23,X18,X3) ),
file('<stdin>',cls_IntI_0) ).
fof(c_0_254_255,axiom,
! [X2,X21,X18,X3] :
( c_in(X18,X2,X3)
| ~ c_in(X2,X21,tc_fun(X3,tc_bool))
| ~ c_in(X18,c_Complete__Lattice_OInf__class_OInf(X21,tc_fun(X3,tc_bool)),X3) ),
file('<stdin>',cls_InterD_0) ).
fof(c_0_255_256,axiom,
! [X10,X17,X3] :
( c_in(X10,c_Wellfounded_Oacc(X17,X3),X3)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X17,X10,X3),c_Wellfounded_Oacc(X17,X3),X3) ),
file('<stdin>',cls_acc_OaccI_1) ).
fof(c_0_256_257,axiom,
! [X10,X24,X3] :
( ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X24,X10,X3),c_Wellfounded_Oacc(X24,X3),X3)
| c_in(X10,c_Wellfounded_Oacc(X24,X3),X3) ),
file('<stdin>',cls_not__acc__down_1) ).
fof(c_0_257_258,axiom,
! [X10,X19,X18,X3] :
( c_lessequals(X18,X19,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X10,X18,X3),X19,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_insert__subset_1) ).
fof(c_0_258_259,axiom,
! [X17,X3] :
( c_Wellfounded_Owf(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X17,X3),X3,X3),X3)
| ~ c_Wellfounded_Owf(c_Relation_Oconverse(X17,X3,X3),X3) ),
file('<stdin>',cls_wf__converse__trancl_0) ).
fof(c_0_259_260,axiom,
! [X10,X19,X18,X3] :
( c_lessequals(X18,c_Set_Oinsert(X10,X19,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X18,X19,tc_fun(X3,tc_bool))
| c_in(X10,X18,X3) ),
file('<stdin>',cls_subset__insert__iff_2) ).
fof(c_0_260_261,axiom,
! [X10,X19,X18,X3] :
( c_lessequals(X18,c_Set_Oinsert(X10,X19,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X18,X19,tc_fun(X3,tc_bool))
| c_in(X10,X18,X3) ),
file('<stdin>',cls_subset__insert_1) ).
fof(c_0_261_262,axiom,
! [X21,X18,X3] :
( c_in(X18,c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X18,X21,X3),X3)
| ~ c_in(X18,c_Complete__Lattice_OSup__class_OSup(X21,tc_fun(X3,tc_bool)),X3) ),
file('<stdin>',cls_UnionE_0) ).
fof(c_0_262_263,axiom,
! [X17,X7,X29,X3] :
( hBOOL(hAPP(X29,X7))
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X29,X17,X3),c_Wellfounded_Oacc(X17,X3),X3)
| ~ c_in(X7,c_Wellfounded_Oacc(X17,X3),X3) ),
file('<stdin>',cls_acc__induct_0) ).
fof(c_0_263_264,axiom,
! [X17,X7,X29,X3] :
( hBOOL(hAPP(X29,X7))
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X29,X17,X3),c_Wellfounded_Oacc(X17,X3),X3)
| ~ c_in(X7,c_Wellfounded_Oacc(X17,X3),X3) ),
file('<stdin>',cls_acc__induct__rule_0) ).
fof(c_0_264_265,axiom,
! [X10,X19,X18,X3] :
( c_in(X10,X19,X3)
| ~ c_lessequals(c_Set_Oinsert(X10,X18,X3),X19,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_insert__subset_0) ).
fof(c_0_265_266,axiom,
! [X10,X6,X7,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X7,X6,X3),X10,X3)
| ~ c_lessequals(X6,X10,X3)
| ~ c_lessequals(X7,X10,X3) ),
file('<stdin>',cls_le__supI_0) ).
fof(c_0_266_267,axiom,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X12,X20,X3),X10,X3)
| ~ c_lessequals(X20,X10,X3)
| ~ c_lessequals(X12,X10,X3) ),
file('<stdin>',cls_sup__least_0) ).
fof(c_0_267_268,axiom,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X20,X3)
| ~ c_lessequals(X12,X20,X3)
| ~ c_lessequals(X10,X20,X3) ),
file('<stdin>',cls_le__sup__iff_2) ).
fof(c_0_268_269,axiom,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X10,c_Lattices_Olower__semilattice__class_Oinf(X12,X20,X3),X3)
| ~ c_lessequals(X10,X20,X3)
| ~ c_lessequals(X10,X12,X3) ),
file('<stdin>',cls_inf__greatest_0) ).
fof(c_0_269_270,axiom,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X10,c_Lattices_Olower__semilattice__class_Oinf(X12,X20,X3),X3)
| ~ c_lessequals(X10,X20,X3)
| ~ c_lessequals(X10,X12,X3) ),
file('<stdin>',cls_le__inf__iff_2) ).
fof(c_0_270_271,axiom,
! [X10,X6,X7,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X10,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,X3),X3)
| ~ c_lessequals(X10,X6,X3)
| ~ c_lessequals(X10,X7,X3) ),
file('<stdin>',cls_le__infI_0) ).
fof(c_0_271_272,axiom,
! [X2,X21,X18,X3] :
( c_in(X18,c_Complete__Lattice_OSup__class_OSup(X21,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X18,X2,X3)
| ~ c_in(X2,X21,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_UnionI_0) ).
fof(c_0_272_273,axiom,
! [X25,X17,X3] :
( c_lessequals(c_Relation_OField(X17,X3),c_Relation_OField(X25,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X17,X25,tc_fun(tc_prod(X3,X3),tc_bool)) ),
file('<stdin>',cls_mono__Field_0) ).
fof(c_0_273_274,axiom,
! [X33,X34,X3] :
( c_lessequals(c_Wellfounded_Oacc(X33,X3),c_Wellfounded_Oacc(X34,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X34,X33,tc_fun(tc_prod(X3,X3),tc_bool)) ),
file('<stdin>',cls_acc__subset_0) ).
fof(c_0_274_275,axiom,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X20,X3) = c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Oupper__semilattice__class_Osup(X12,X20,X3),X3) ),
file('<stdin>',cls_sup__assoc_0) ).
fof(c_0_275_276,axiom,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Oupper__semilattice__class_Osup(X12,X20,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X12,c_Lattices_Oupper__semilattice__class_Osup(X10,X20,X3),X3) ),
file('<stdin>',cls_sup__left__commute_0) ).
fof(c_0_276_277,axiom,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Oupper__semilattice__class_Osup(X12,X20,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X12,c_Lattices_Oupper__semilattice__class_Osup(X10,X20,X3),X3) ),
file('<stdin>',cls_inf__sup__aci_I7_J_0) ).
fof(c_0_277_278,axiom,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X20,X3) = c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Oupper__semilattice__class_Osup(X12,X20,X3),X3) ),
file('<stdin>',cls_inf__sup__aci_I6_J_0) ).
fof(c_0_278_279,axiom,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3),X20,X3) = c_Lattices_Olower__semilattice__class_Oinf(X10,c_Lattices_Olower__semilattice__class_Oinf(X12,X20,X3),X3) ),
file('<stdin>',cls_inf__sup__aci_I2_J_0) ).
fof(c_0_279_280,axiom,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X10,c_Lattices_Olower__semilattice__class_Oinf(X12,X20,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X12,c_Lattices_Olower__semilattice__class_Oinf(X10,X20,X3),X3) ),
file('<stdin>',cls_inf__sup__aci_I3_J_0) ).
fof(c_0_280_281,axiom,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X10,c_Lattices_Olower__semilattice__class_Oinf(X12,X20,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X12,c_Lattices_Olower__semilattice__class_Oinf(X10,X20,X3),X3) ),
file('<stdin>',cls_inf__left__commute_0) ).
fof(c_0_281_282,axiom,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3),X20,X3) = c_Lattices_Olower__semilattice__class_Oinf(X10,c_Lattices_Olower__semilattice__class_Oinf(X12,X20,X3),X3) ),
file('<stdin>',cls_inf__assoc_0) ).
fof(c_0_282_283,axiom,
! [X23,X18,X3] :
( c_in(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X18,X23,X3),X18,X3)
| ~ c_in(X23,c_Relation_OId__on(X18,X3),tc_prod(X3,X3)) ),
file('<stdin>',cls_Id__onE_0) ).
fof(c_0_283_284,axiom,
! [X10,X8] :
( c_in(c_Arrow__Order__Mirabelle_Omktop(X8,X10),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('<stdin>',cls_mktop__Lin_0) ).
fof(c_0_284_285,axiom,
! [X10,X8] :
( c_in(c_Arrow__Order__Mirabelle_Omkbot(X8,X10),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('<stdin>',cls_mkbot__Lin_0) ).
fof(c_0_285_286,axiom,
! [X21,X19,X18,X3] :
( c_lessequals(X18,X21,tc_fun(X3,tc_bool))
| ~ c_lessequals(X19,X21,tc_fun(X3,tc_bool))
| ~ c_lessequals(X18,X19,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__trans_0) ).
fof(c_0_286_287,axiom,
! [X7,X19,X18,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(X18,c_Set_Oinsert(X7,X19,X3),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool))
| c_in(X7,X18,X3) ),
file('<stdin>',cls_Int__insert__right_1) ).
fof(c_0_287_288,axiom,
! [X7,X21,X19,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X7,X19,X3),X21,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X19,X21,tc_fun(X3,tc_bool))
| c_in(X7,X21,X3) ),
file('<stdin>',cls_Int__insert__left_1) ).
fof(c_0_288_289,axiom,
! [X25,X17,X3] :
( c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X17,X25,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Relation_Osym(X25,X3)
| ~ c_Relation_Osym(X17,X3) ),
file('<stdin>',cls_sym__Un_0) ).
fof(c_0_289_290,axiom,
! [X25,X17,X3] :
( c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X17,X25,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Relation_Osym(X25,X3)
| ~ c_Relation_Osym(X17,X3) ),
file('<stdin>',cls_sym__Int_0) ).
fof(c_0_290_291,axiom,
! [X25,X17,X3] :
( c_Relation_Otrans(c_Lattices_Olower__semilattice__class_Oinf(X17,X25,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Relation_Otrans(X25,X3)
| ~ c_Relation_Otrans(X17,X3) ),
file('<stdin>',cls_trans__Int_0) ).
fof(c_0_291_292,axiom,
! [X10,X6,X7,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X10,X7,X3)
| ~ c_lessequals(X10,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,X3),X3) ),
file('<stdin>',cls_le__infE_0) ).
fof(c_0_292_293,axiom,
! [X10,X6,X7,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X10,X6,X3)
| ~ c_lessequals(X10,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,X3),X3) ),
file('<stdin>',cls_le__infE_1) ).
fof(c_0_293_294,axiom,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X10,X12,X3)
| ~ c_lessequals(X10,c_Lattices_Olower__semilattice__class_Oinf(X12,X20,X3),X3) ),
file('<stdin>',cls_le__inf__iff_0) ).
fof(c_0_294_295,axiom,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X10,X20,X3)
| ~ c_lessequals(X10,c_Lattices_Olower__semilattice__class_Oinf(X12,X20,X3),X3) ),
file('<stdin>',cls_le__inf__iff_1) ).
fof(c_0_295_296,axiom,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X12,X20,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X20,X3) ),
file('<stdin>',cls_le__sup__iff_1) ).
fof(c_0_296_297,axiom,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X10,X20,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X20,X3) ),
file('<stdin>',cls_le__sup__iff_0) ).
fof(c_0_297_298,axiom,
! [X10,X6,X7,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X6,X10,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X7,X6,X3),X10,X3) ),
file('<stdin>',cls_le__supE_1) ).
fof(c_0_298_299,axiom,
! [X10,X6,X7,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X7,X10,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X7,X6,X3),X10,X3) ),
file('<stdin>',cls_le__supE_0) ).
fof(c_0_299_300,axiom,
! [X6,X7,X18,X3] :
( c_in(X7,X18,X3)
| X7 = X6
| ~ c_in(X7,c_Set_Oinsert(X6,X18,X3),X3) ),
file('<stdin>',cls_insertE_0) ).
fof(c_0_300_301,axiom,
! [X21,X18,X3] :
( c_in(X18,c_Complete__Lattice_OInf__class_OInf(X21,tc_fun(X3,tc_bool)),X3)
| c_in(c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X18,X21,X3),X21,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_InterI_0) ).
fof(c_0_301_302,axiom,
! [X17,X18,X3] :
( c_Relation_Orefl__on(X18,X17,X3)
| ~ c_Relation_Orefl__on(X18,c_Relation_Oconverse(X17,X3,X3),X3) ),
file('<stdin>',cls_refl__on__converse_0) ).
fof(c_0_302_303,axiom,
! [X17,X18,X3] :
( c_Relation_Ototal__on(X18,X17,X3)
| ~ c_Relation_Ototal__on(X18,c_Relation_Oconverse(X17,X3,X3),X3) ),
file('<stdin>',cls_total__on__converse_0) ).
fof(c_0_303_304,axiom,
! [X6,X19,X18,X3] :
( c_lessequals(X18,c_Set_Oinsert(X6,X19,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X18,X19,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__insertI2_0) ).
fof(c_0_304_305,axiom,
! [X17,X3] :
( c_Relation_Otrans(c_Lattices_Oupper__semilattice__class_Osup(X17,c_Relation_OId(X3),tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Relation_Otrans(X17,X3) ),
file('<stdin>',cls_trans__reflclI_0) ).
fof(c_0_305_306,axiom,
! [X23,X19,X18,X3] :
( c_in(X23,c_Lattices_Oupper__semilattice__class_Osup(X18,X19,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X23,X18,X3) ),
file('<stdin>',cls_UnCI_1) ).
fof(c_0_306_307,axiom,
! [X23,X19,X18,X3] :
( c_in(X23,c_Lattices_Oupper__semilattice__class_Osup(X18,X19,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X23,X19,X3) ),
file('<stdin>',cls_UnCI_0) ).
fof(c_0_307_308,axiom,
! [X36,X17,X3] :
( c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X17,X36,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Wellfounded_Owf(X17,X3) ),
file('<stdin>',cls_wf__Int1_0) ).
fof(c_0_308_309,axiom,
! [X36,X17,X3] :
( c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X36,X17,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Wellfounded_Owf(X17,X3) ),
file('<stdin>',cls_wf__Int2_0) ).
fof(c_0_309_310,axiom,
! [X12,X10,X18,X3] :
( hBOOL(hAPP(c_Set_Oinsert(X12,X18,X3),X10))
| ~ hBOOL(hAPP(X18,X10)) ),
file('<stdin>',cls_insert__code_2) ).
fof(c_0_310_311,axiom,
! [X10,X19,X18,X3] :
( c_Set_Oinsert(X10,X18,X3) != c_Set_Oinsert(X10,X19,X3)
| c_in(X10,X19,X3)
| c_in(X10,X18,X3)
| X18 = X19 ),
file('<stdin>',cls_insert__ident_0) ).
fof(c_0_311_312,axiom,
! [X10,X17,X29] :
( hBOOL(hAPP(X29,X10))
| ~ hBOOL(hAPP(X29,v_sko__Wellfounded__Xacc__Xinduct__1(X29,X17)))
| ~ c_in(X10,c_Wellfounded_Oacc(X17,t_a),t_a) ),
file('<stdin>',cls_acc_Oinduct_2) ).
fof(c_0_312_313,axiom,
! [X10,X17,X29] :
( hBOOL(hAPP(X29,X10))
| ~ hBOOL(hAPP(X29,v_sko__Wellfounded__Xacc__Xinducts__1(X29,X17)))
| ~ c_in(X10,c_Wellfounded_Oacc(X17,t_a),t_a) ),
file('<stdin>',cls_acc_Oinducts_2) ).
fof(c_0_313_314,axiom,
! [X42,X41,X3] :
( c_Finite__Set_Ofinite(X41,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X41,X42,tc_fun(X3,tc_bool)),X3) ),
file('<stdin>',cls_finite__Un_0) ).
fof(c_0_314_315,axiom,
! [X42,X41,X3] :
( c_Finite__Set_Ofinite(X42,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X41,X42,tc_fun(X3,tc_bool)),X3) ),
file('<stdin>',cls_finite__Un_1) ).
fof(c_0_315_316,axiom,
! [X19,X18,X3] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X18,tc_fun(X3,tc_bool)),X19,tc_fun(X3,tc_bool))
| ~ c_in(X19,X18,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Inter__lower_0) ).
fof(c_0_316_317,axiom,
! [X19,X18,X3] :
( c_lessequals(X19,c_Complete__Lattice_OSup__class_OSup(X18,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_in(X19,X18,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Union__upper_0) ).
fof(c_0_317_318,axiom,
! [X10,X24,X31,X3] :
( c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X31,X24,X3),X31,X3)
| ~ c_in(X10,X31,X3)
| ~ c_Wellfounded_Owf(X24,X3) ),
file('<stdin>',cls_wfE__min_0) ).
fof(c_0_318_319,axiom,
! [X16,X17,X31,X3] :
( c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X31,X17,X3),X31,X3)
| ~ c_in(X16,X31,X3)
| ~ c_Wellfounded_Owf(X17,X3) ),
file('<stdin>',cls_wf__eq__minimal_0) ).
fof(c_0_319_320,axiom,
! [X32,X19,X18,X3] :
( c_in(X32,X19,X3)
| ~ c_in(X32,X18,X3)
| ~ c_lessequals(X18,X19,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__iff_0) ).
fof(c_0_320_321,axiom,
! [X10,X19,X18,X3] :
( c_in(X10,X19,X3)
| ~ c_lessequals(X18,X19,tc_fun(X3,tc_bool))
| ~ c_in(X10,X18,X3) ),
file('<stdin>',cls_set__rev__mp_0) ).
fof(c_0_321_322,axiom,
! [X23,X19,X18,X3] :
( c_in(X23,X19,X3)
| ~ c_in(X23,X18,X3)
| ~ c_lessequals(X18,X19,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subsetD_0) ).
fof(c_0_322_323,axiom,
! [X10,X19,X18,X3] :
( c_in(X10,X19,X3)
| ~ c_in(X10,X18,X3)
| ~ c_lessequals(X18,X19,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_set__mp_0) ).
fof(c_0_323_324,axiom,
! [X10,X6,X7,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,X3),X10,X3)
| ~ c_lessequals(X7,X10,X3) ),
file('<stdin>',cls_le__infI1_0) ).
fof(c_0_324_325,axiom,
! [X10,X6,X7,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,X3),X10,X3)
| ~ c_lessequals(X6,X10,X3) ),
file('<stdin>',cls_le__infI2_0) ).
fof(c_0_325_326,axiom,
! [X10,X6,X7,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X10,c_Lattices_Oupper__semilattice__class_Osup(X7,X6,X3),X3)
| ~ c_lessequals(X10,X6,X3) ),
file('<stdin>',cls_le__supI2_0) ).
fof(c_0_326_327,axiom,
! [X10,X6,X7,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X10,c_Lattices_Oupper__semilattice__class_Osup(X7,X6,X3),X3)
| ~ c_lessequals(X10,X7,X3) ),
file('<stdin>',cls_le__supI1_0) ).
fof(c_0_327_328,axiom,
! [X6,X7,X18,X3] :
( c_in(X7,c_Set_Oinsert(X6,X18,X3),X3)
| ~ c_in(X7,X18,X3) ),
file('<stdin>',cls_insert__iff_2) ).
fof(c_0_328_329,axiom,
! [X6,X7,X19,X3] :
( c_in(X7,c_Set_Oinsert(X6,X19,X3),X3)
| ~ c_in(X7,X19,X3) ),
file('<stdin>',cls_insertCI_0) ).
fof(c_0_329_330,axiom,
! [X17,X18,X3] :
( c_Relation_Orefl__on(X18,c_Relation_Oconverse(X17,X3,X3),X3)
| ~ c_Relation_Orefl__on(X18,X17,X3) ),
file('<stdin>',cls_refl__on__converse_1) ).
fof(c_0_330_331,axiom,
! [X17,X18,X3] :
( c_Relation_Ototal__on(X18,c_Relation_Oconverse(X17,X3,X3),X3)
| ~ c_Relation_Ototal__on(X18,X17,X3) ),
file('<stdin>',cls_total__on__converse_1) ).
fof(c_0_331_332,axiom,
! [X19,X18,X3] :
( X18 = X19
| ~ c_lessequals(X19,X18,tc_fun(X3,tc_bool))
| ~ c_lessequals(X18,X19,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_set__eq__subset_2) ).
fof(c_0_332_333,axiom,
! [X19,X18,X3] :
( X18 = X19
| ~ c_lessequals(X19,X18,tc_fun(X3,tc_bool))
| ~ c_lessequals(X18,X19,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_equalityI_0) ).
fof(c_0_333_334,axiom,
! [X17,X28,X3] :
( c_Wellfounded_Owf(X28,X3)
| ~ c_lessequals(X28,X17,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Wellfounded_Owf(X17,X3) ),
file('<stdin>',cls_wf__subset_0) ).
fof(c_0_334_335,axiom,
! [X10,X27,X22,X15,X3] :
( ~ class_HOL_Oord(X15)
| c_lessequals(hAPP(X22,X10),hAPP(X27,X10),X15)
| ~ c_lessequals(X22,X27,tc_fun(X3,X15)) ),
file('<stdin>',cls_le__funD_0) ).
fof(c_0_335_336,axiom,
! [X20,X12,X10,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X10,X20,X3)
| ~ c_lessequals(X12,X20,X3)
| ~ c_lessequals(X10,X12,X3) ),
file('<stdin>',cls_order__trans_0) ).
fof(c_0_336_337,axiom,
! [X20,X12,X10,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X20,X10,X3)
| ~ c_lessequals(X20,X12,X3)
| ~ c_lessequals(X12,X10,X3) ),
file('<stdin>',cls_xt1_I6_J_0) ).
fof(c_0_337_338,axiom,
! [X17,X28,X3] :
( c_in(X28,c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(X28,X17,tc_prod(X3,X3)) ),
file('<stdin>',cls_r__into__rtrancl_0) ).
fof(c_0_338_339,axiom,
! [X17,X28,X3] :
( c_in(X28,c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(X28,X17,tc_prod(X3,X3)) ),
file('<stdin>',cls_r__into__trancl_H_0) ).
fof(c_0_339_340,axiom,
! [X10,X39,X3] :
( c_Finite__Set_Ofinite(c_Complete__Lattice_OInf__class_OInf(X39,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X10,X3)
| ~ c_in(X10,X39,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_finite__Inter_0) ).
fof(c_0_340_341,axiom,
! [X17,X18,X3] :
( c_Complete__Lattice_OSup__class_OSup(c_Equiv__Relations_Oquotient(X18,X17,X3),tc_fun(X3,tc_bool)) = X18
| ~ c_Equiv__Relations_Oequiv(X18,X17,X3) ),
file('<stdin>',cls_Union__quotient_0) ).
fof(c_0_341_342,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3) ),
file('<stdin>',cls_sup__left__idem_0) ).
fof(c_0_342_343,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3) ),
file('<stdin>',cls_inf__sup__aci_I8_J_0) ).
fof(c_0_343_344,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X10,c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3) ),
file('<stdin>',cls_inf__sup__aci_I4_J_0) ).
fof(c_0_344_345,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X10,c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3) ),
file('<stdin>',cls_inf__left__idem_0) ).
fof(c_0_345_346,axiom,
! [X42,X41,X3] :
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X41,X42,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X42,X3)
| ~ c_Finite__Set_Ofinite(X41,X3) ),
file('<stdin>',cls_finite__Un_2) ).
fof(c_0_346_347,axiom,
! [X42,X41,X3] :
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X41,X42,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X42,X3)
| ~ c_Finite__Set_Ofinite(X41,X3) ),
file('<stdin>',cls_finite__UnI_0) ).
fof(c_0_347_348,axiom,
! [X7,X18,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X7,X18,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X7,c_Complete__Lattice_OInf__class_OInf(X18,X3),X3) ),
file('<stdin>',cls_Inf__insert_0) ).
fof(c_0_348_349,axiom,
! [X7,X18,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X7,X18,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X7,c_Complete__Lattice_OSup__class_OSup(X18,X3),X3) ),
file('<stdin>',cls_Sup__insert_0) ).
fof(c_0_349_350,axiom,
! [X17,X3] :
( c_Relation_Otrans(X17,X3)
| ~ c_Relation_Otrans(c_Relation_Oconverse(X17,X3,X3),X3) ),
file('<stdin>',cls_trans__converse_0) ).
fof(c_0_350_351,axiom,
! [X7,X18,X3] :
( c_Finite__Set_Ofinite(X18,X3)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X7,X18,X3),X3) ),
file('<stdin>',cls_finite__insert_0) ).
fof(c_0_351_352,axiom,
! [X17,X3] :
( c_Relation_Osym(X17,X3)
| ~ c_Relation_Osym(c_Relation_Oconverse(X17,X3,X3),X3) ),
file('<stdin>',cls_sym__converse_0) ).
fof(c_0_352_353,axiom,
! [X19,X18,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X18,X19,tc_fun(X3,tc_bool)) != X19
| c_lessequals(X18,X19,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_subset__Un__eq_1) ).
fof(c_0_353_354,axiom,
! [X19,X18,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)) = X18
| ~ c_lessequals(X18,X19,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Int__absorb2_0) ).
fof(c_0_354_355,axiom,
! [X19,X18,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)) = X19
| ~ c_lessequals(X19,X18,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Int__absorb1_0) ).
fof(c_0_355_356,axiom,
! [X19,X18,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X18,X19,tc_fun(X3,tc_bool)) = X19
| ~ c_lessequals(X18,X19,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__absorb1_0) ).
fof(c_0_356_357,axiom,
! [X19,X18,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X18,X19,tc_fun(X3,tc_bool)) = X18
| ~ c_lessequals(X19,X18,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_Un__absorb2_0) ).
fof(c_0_357_358,axiom,
! [X10,X31,X29,X3] :
( hBOOL(hAPP(X31,X10))
| ~ c_lessequals(X29,X31,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X29,X10)) ),
file('<stdin>',cls_rev__predicate1D_0) ).
fof(c_0_358_359,axiom,
! [X10,X31,X29,X3] :
( hBOOL(hAPP(X31,X10))
| ~ hBOOL(hAPP(X29,X10))
| ~ c_lessequals(X29,X31,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_predicate1D_0) ).
fof(c_0_359_360,axiom,
! [X42,X41,X3] :
( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X41,X42,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X42,X3) ),
file('<stdin>',cls_finite__Int_1) ).
fof(c_0_360_361,axiom,
! [X42,X41,X3] :
( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X41,X42,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X41,X3) ),
file('<stdin>',cls_finite__Int_0) ).
fof(c_0_361_362,axiom,
! [X17,X3] :
( c_Wellfounded_Owf(X17,X3)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X17,X3),c_Wellfounded_Oacc(X17,X3),X3) ),
file('<stdin>',cls_acc__wfI_0) ).
fof(c_0_362_363,axiom,
! [X17,X3] :
( c_Wellfounded_Owf(X17,X3)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X17,X3),c_Wellfounded_Oacc(X17,X3),X3) ),
file('<stdin>',cls_wf__acc__iff_1) ).
fof(c_0_363_364,axiom,
! [X12,X10,X3] :
( ~ class_Orderings_Oorder(X3)
| X10 = X12
| ~ c_lessequals(X10,X12,X3)
| ~ c_lessequals(X12,X10,X3) ),
file('<stdin>',cls_order__antisym__conv_0) ).
fof(c_0_364_365,axiom,
! [X12,X10,X3] :
( ~ class_Orderings_Oorder(X3)
| X10 = X12
| ~ c_lessequals(X12,X10,X3)
| ~ c_lessequals(X10,X12,X3) ),
file('<stdin>',cls_order__antisym_0) ).
fof(c_0_365_366,axiom,
! [X12,X10,X3] :
( ~ class_Orderings_Oorder(X3)
| X10 = X12
| ~ c_lessequals(X12,X10,X3)
| ~ c_lessequals(X10,X12,X3) ),
file('<stdin>',cls_order__eq__iff_2) ).
fof(c_0_366_367,axiom,
! [X10,X18,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X18,X3),X10,X3)
| ~ c_in(X10,X18,X3) ),
file('<stdin>',cls_Inf__lower_0) ).
fof(c_0_367_368,axiom,
! [X10,X18,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_lessequals(X10,c_Complete__Lattice_OSup__class_OSup(X18,X3),X3)
| ~ c_in(X10,X18,X3) ),
file('<stdin>',cls_Sup__upper_0) ).
fof(c_0_368_369,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3),X3) = X10 ),
file('<stdin>',cls_sup__inf__absorb_0) ).
fof(c_0_369_370,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X10,c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X3) = X10 ),
file('<stdin>',cls_inf__sup__absorb_0) ).
fof(c_0_370_371,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X10,c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X3) ),
file('<stdin>',cls_sup__ge1_0) ).
fof(c_0_371_372,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X12,c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X3) ),
file('<stdin>',cls_sup__ge2_0) ).
fof(c_0_372_373,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(X12,c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X3) ),
file('<stdin>',cls_inf__sup__ord_I4_J_0) ).
fof(c_0_373_374,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(X10,c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X3) ),
file('<stdin>',cls_inf__sup__ord_I3_J_0) ).
fof(c_0_374_375,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3),X10,X3) ),
file('<stdin>',cls_inf__sup__ord_I1_J_0) ).
fof(c_0_375_376,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3),X12,X3) ),
file('<stdin>',cls_inf__sup__ord_I2_J_0) ).
fof(c_0_376_377,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3),X12,X3) ),
file('<stdin>',cls_inf__le2_0) ).
fof(c_0_377_378,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3),X10,X3) ),
file('<stdin>',cls_inf__le1_0) ).
fof(c_0_378_379,axiom,
! [X19,X18,X3] :
( c_Finite__Set_Ofinite(X18,X3)
| ~ c_Finite__Set_Ofinite(X19,X3)
| ~ c_lessequals(X18,X19,tc_fun(X3,tc_bool)) ),
file('<stdin>',cls_finite__subset_0) ).
fof(c_0_379_380,axiom,
! [X19,X18,X3] :
( c_Finite__Set_Ofinite(X18,X3)
| ~ c_lessequals(X18,X19,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X19,X3) ),
file('<stdin>',cls_rev__finite__subset_0) ).
fof(c_0_380_381,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3) != X10
| c_lessequals(X10,X12,X3) ),
file('<stdin>',cls_le__iff__inf_1) ).
fof(c_0_381_382,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3) != X12
| c_lessequals(X10,X12,X3) ),
file('<stdin>',cls_le__iff__sup_1) ).
fof(c_0_382_383,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3) = X10
| ~ c_lessequals(X10,X12,X3) ),
file('<stdin>',cls_le__iff__inf_0) ).
fof(c_0_383_384,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3) = X12
| ~ c_lessequals(X12,X10,X3) ),
file('<stdin>',cls_inf__absorb2_0) ).
fof(c_0_384_385,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3) = X10
| ~ c_lessequals(X12,X10,X3) ),
file('<stdin>',cls_sup__absorb1_0) ).
fof(c_0_385_386,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3) = X12
| ~ c_lessequals(X10,X12,X3) ),
file('<stdin>',cls_le__iff__sup_0) ).
fof(c_0_386_387,axiom,
! [X6,X7] :
( c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X7,X6),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X6 ),
file('<stdin>',cls_complete__Lin_0) ).
fof(c_0_387_388,axiom,
! [X17,X3] :
( c_Relation_Otrans(c_Relation_Oconverse(X17,X3,X3),X3)
| ~ c_Relation_Otrans(X17,X3) ),
file('<stdin>',cls_trans__converse_1) ).
fof(c_0_388_389,axiom,
! [X7,X18,X3] :
( c_Finite__Set_Ofinite(c_Set_Oinsert(X7,X18,X3),X3)
| ~ c_Finite__Set_Ofinite(X18,X3) ),
file('<stdin>',cls_finite__insert_1) ).
fof(c_0_389_390,axiom,
! [X17,X3] :
( c_Relation_Osym(c_Relation_Oconverse(X17,X3,X3),X3)
| ~ c_Relation_Osym(X17,X3) ),
file('<stdin>',cls_sym__converse_1) ).
fof(c_0_390_391,axiom,
! [X7,X18,X3] :
( c_Set_Oinsert(X7,X18,X3) = X18
| ~ c_in(X7,X18,X3) ),
file('<stdin>',cls_insert__absorb_0) ).
fof(c_0_391_392,axiom,
! [X17,X18,X3] :
( c_Relation_Orefl__on(X18,X17,X3)
| ~ c_Equiv__Relations_Oequiv(X18,X17,X3) ),
file('<stdin>',cls_equiv_Orefl__on_0) ).
fof(c_0_392_393,axiom,
! [X12,X10,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X12,X10,X3)
| c_lessequals(X10,X12,X3) ),
file('<stdin>',cls_linorder__linear_0) ).
fof(c_0_393_394,axiom,
! [X10,X11,X3] :
( hBOOL(hAPP(X11,X10))
| ~ c_in(X10,X11,X3) ),
file('<stdin>',cls_mem__def_0) ).
fof(c_0_394_395,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3) = c_Lattices_Olower__semilattice__class_Oinf(X12,X10,X3) ),
file('<stdin>',cls_inf__commute_0) ).
fof(c_0_395_396,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3) = c_Lattices_Olower__semilattice__class_Oinf(X12,X10,X3) ),
file('<stdin>',cls_inf__sup__aci_I1_J_0) ).
fof(c_0_396_397,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3) = c_Lattices_Oupper__semilattice__class_Osup(X12,X10,X3) ),
file('<stdin>',cls_sup__commute_0) ).
fof(c_0_397_398,axiom,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3) = c_Lattices_Oupper__semilattice__class_Osup(X12,X10,X3) ),
file('<stdin>',cls_inf__sup__aci_I5_J_0) ).
fof(c_0_398_399,axiom,
! [X10,X17,X3] :
( c_in(X10,c_Wellfounded_Oacc(X17,X3),X3)
| ~ c_Wellfounded_Owf(X17,X3) ),
file('<stdin>',cls_acc__wfD_0) ).
fof(c_0_399_400,axiom,
! [X10,X11,X3] :
( c_in(X10,X11,X3)
| ~ hBOOL(hAPP(X11,X10)) ),
file('<stdin>',cls_mem__def_1) ).
fof(c_0_400_401,axiom,
! [X17,X3] :
( c_Relation_Oconverse(X17,X3,X3) != X17
| c_Relation_Osym(X17,X3) ),
file('<stdin>',cls_sym__conv__converse__eq_1) ).
fof(c_0_401_402,axiom,
! [X17,X18,X3] :
( c_Relation_Otrans(X17,X3)
| ~ c_Equiv__Relations_Oequiv(X18,X17,X3) ),
file('<stdin>',cls_equiv_Otrans_0) ).
fof(c_0_402_403,axiom,
! [X17,X18,X3] :
( c_Relation_Osym(X17,X3)
| ~ c_Equiv__Relations_Oequiv(X18,X17,X3) ),
file('<stdin>',cls_equiv_Osym_0) ).
fof(c_0_403_404,axiom,
! [X1,X2,X3] :
( X2 = X1
| ~ c_fequal(X2,X1,X3) ),
file('<stdin>',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(c_0_404_405,axiom,
! [X17,X3] :
( c_Relation_Oconverse(X17,X3,X3) = X17
| ~ c_Relation_Osym(X17,X3) ),
file('<stdin>',cls_sym__conv__converse__eq_0) ).
fof(c_0_405_406,axiom,
! [X17,X3] :
( c_Relation_Osym(c_Transitive__Closure_Ortrancl(X17,X3),X3)
| ~ c_Relation_Osym(X17,X3) ),
file('<stdin>',cls_sym__rtrancl_0) ).
fof(c_0_406_407,axiom,
! [X17,X3] :
( c_Relation_Osym(c_Transitive__Closure_Otrancl(X17,X3),X3)
| ~ c_Relation_Osym(X17,X3) ),
file('<stdin>',cls_sym__trancl_0) ).
fof(c_0_407_408,axiom,
! [X17,X3] :
( c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X17,X3),X3)
| ~ c_Wellfounded_Owf(X17,X3) ),
file('<stdin>',cls_wf__trancl_0) ).
fof(c_0_408_409,axiom,
! [X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,X10,X3) = X10 ),
file('<stdin>',cls_sup__idem_0) ).
fof(c_0_409_410,axiom,
! [X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X10,X10,X3) = X10 ),
file('<stdin>',cls_inf__idem_0) ).
fof(c_0_410_411,axiom,
! [X10,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X10,X10,X3) ),
file('<stdin>',cls_order__eq__refl_0) ).
fof(c_0_411_412,axiom,
! [X10,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X10,X10,X3) ),
file('<stdin>',cls_order__eq__iff_0) ).
fof(c_0_412_413,axiom,
! [X4,X5] :
( class_Finite__Set_Ofinite_Ofinite(tc_prod(X4,X5))
| ~ class_Finite__Set_Ofinite_Ofinite(X5)
| ~ class_Finite__Set_Ofinite_Ofinite(X4) ),
file('<stdin>',clsarity_prod__Finite__Set_Ofinite_Ofinite) ).
fof(c_0_413_414,axiom,
! [X4,X5] :
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X4,X5))
| ~ class_Finite__Set_Ofinite_Ofinite(X5)
| ~ class_Finite__Set_Ofinite_Ofinite(X4) ),
file('<stdin>',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
fof(c_0_414_415,axiom,
! [X17,X3] :
( c_Transitive__Closure_Otrancl(X17,X3) = X17
| ~ c_Relation_Otrans(X17,X3) ),
file('<stdin>',cls_trancl__id_0) ).
fof(c_0_415_416,axiom,
! [X4,X5] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X4,X5))
| ~ class_Complete__Lattice_Ocomplete__lattice(X5) ),
file('<stdin>',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
fof(c_0_416_417,axiom,
! [X4,X5] :
( class_Lattices_Oupper__semilattice(tc_fun(X4,X5))
| ~ class_Lattices_Olattice(X5) ),
file('<stdin>',clsarity_fun__Lattices_Oupper__semilattice) ).
fof(c_0_417_418,axiom,
! [X4,X5] :
( class_Lattices_Olower__semilattice(tc_fun(X4,X5))
| ~ class_Lattices_Olattice(X5) ),
file('<stdin>',clsarity_fun__Lattices_Olower__semilattice) ).
fof(c_0_418_419,axiom,
! [X4,X5] :
( class_Lattices_Odistrib__lattice(tc_fun(X4,X5))
| ~ class_Lattices_Odistrib__lattice(X5) ),
file('<stdin>',clsarity_fun__Lattices_Odistrib__lattice) ).
fof(c_0_419_420,axiom,
! [X4,X5] :
( class_Orderings_Opreorder(tc_fun(X4,X5))
| ~ class_Orderings_Opreorder(X5) ),
file('<stdin>',clsarity_fun__Orderings_Opreorder) ).
fof(c_0_420_421,axiom,
! [X4,X5] :
( class_Lattices_Olattice(tc_fun(X4,X5))
| ~ class_Lattices_Olattice(X5) ),
file('<stdin>',clsarity_fun__Lattices_Olattice) ).
fof(c_0_421_422,axiom,
! [X4,X5] :
( class_Orderings_Oorder(tc_fun(X4,X5))
| ~ class_Orderings_Oorder(X5) ),
file('<stdin>',clsarity_fun__Orderings_Oorder) ).
fof(c_0_422_423,axiom,
! [X4,X5] :
( class_HOL_Oord(tc_fun(X4,X5))
| ~ class_HOL_Oord(X5) ),
file('<stdin>',clsarity_fun__HOL_Oord) ).
fof(c_0_423_424,axiom,
! [X18,X3] :
( ~ class_Finite__Set_Ofinite_Ofinite(X3)
| c_Finite__Set_Ofinite(X18,X3) ),
file('<stdin>',cls_finite_0) ).
fof(c_0_424_425,plain,
! [X25,X17,X23,X7,X26,X15,X3] :
( c_in(c_Pair(X7,c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X7,X23,X17,X25,X3,X15,X26),X3,X26),X17,tc_prod(X3,X26))
| ~ c_in(c_Pair(X7,X23,X3,X15),c_Relation_Orel__comp(X17,X25,X3,X26,X15),tc_prod(X3,X15)) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_425_426,plain,
! [X25,X17,X23,X7,X26,X15,X3] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X7,X23,X17,X25,X3,X15,X26),X23,X26,X15),X25,tc_prod(X26,X15))
| ~ c_in(c_Pair(X7,X23,X3,X15),c_Relation_Orel__comp(X17,X25,X3,X26,X15),tc_prod(X3,X15)) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_426_427,axiom,
! [X10,X17,X27,X22,X15,X3] :
( hAPP(X22,c_List_Osko__Recdef__Xcuts__eq__1__1(X22,X27,X17,X10,X3,X15)) != hAPP(X27,c_List_Osko__Recdef__Xcuts__eq__1__1(X22,X27,X17,X10,X3,X15))
| c_Recdef_Ocut(X22,X17,X10,X3,X15) = c_Recdef_Ocut(X27,X17,X10,X3,X15) ),
c_0_2 ).
fof(c_0_427_428,plain,
! [X11,X24,X3] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X24,X11,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X24,X24,X3,X3,X3),c_Relation_Orel__comp(X11,X24,X3,X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)),X11,tc_fun(tc_prod(X3,X3),tc_bool)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_428_429,axiom,
! [X10,X17,X27,X22,X15,X3] :
( c_Recdef_Ocut(X22,X17,X10,X3,X15) = c_Recdef_Ocut(X27,X17,X10,X3,X15)
| c_in(c_Pair(c_List_Osko__Recdef__Xcuts__eq__1__1(X22,X27,X17,X10,X3,X15),X10,X3,X3),X17,tc_prod(X3,X3)) ),
c_0_4 ).
fof(c_0_429_430,plain,
! [X11,X24,X3] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X24,X24,X3,X3,X3),c_Relation_Orel__comp(X11,X24,X3,X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)),X11,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X24,X11,tc_fun(tc_prod(X3,X3),tc_bool)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_430_431,plain,
! [X38,X21,X19,X18,X15,X3] :
( c_lessequals(c_Product__Type_OSigma(X18,X19,X3,X15),c_Product__Type_OSigma(X21,X38,X3,X15),tc_fun(tc_prod(X3,X15),tc_bool))
| ~ c_lessequals(hAPP(X19,c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(X18,X19,X38,X3,X15)),hAPP(X38,c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(X18,X19,X38,X3,X15)),tc_fun(X15,tc_bool))
| ~ c_lessequals(X18,X21,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_431_432,plain,
! [X22,X19,X18,X15,X3] :
( c_in(X22,c_FuncSet_OPi(X18,X19,X3,X15),tc_fun(X3,X15))
| ~ c_in(hAPP(X22,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X18,X19,X22,X3,X15)),hAPP(X19,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X18,X19,X22,X3,X15)),X15) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_432_433,plain,
! [X22,X19,X18,X15,X3] :
( c_in(X22,c_FuncSet_OPi(X18,X19,X3,X15),tc_fun(X3,X15))
| ~ c_in(hAPP(X22,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X18,X19,X22,X3,X15)),hAPP(X19,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X18,X19,X22,X3,X15)),X15) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_433_434,plain,
! [X22,X19,X18,X15,X3] :
( c_in(X22,c_FuncSet_OPi(X18,c_COMBK(X19,tc_fun(X15,tc_bool),X3),X3,X15),tc_fun(X3,X15))
| ~ c_in(hAPP(X22,c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X18,X19,X22,X3,X15)),X19,X15) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_434_435,plain,
! [X25,X17,X21,X19,X18,X26,X15,X3] :
( c_lessequals(c_Relation_Orel__comp(X17,X25,X3,X15,X26),c_Product__Type_OSigma(X18,c_COMBK(X21,tc_fun(X26,tc_bool),X3),X3,X26),tc_fun(tc_prod(X3,X26),tc_bool))
| ~ c_lessequals(X25,c_Product__Type_OSigma(X19,c_COMBK(X21,tc_fun(X26,tc_bool),X15),X15,X26),tc_fun(tc_prod(X15,X26),tc_bool))
| ~ c_lessequals(X17,c_Product__Type_OSigma(X18,c_COMBK(X19,tc_fun(X15,tc_bool),X3),X3,X15),tc_fun(tc_prod(X3,X15),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_435_436,plain,
! [X17,X6,X18,X15,X3] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X18,X6,X17,X15,X3),X6,X15,X3),X17,tc_prod(X15,X3))
| ~ c_in(X6,c_Relation_OImage(X17,X18,X15,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_436_437,plain,
! [X17,X6,X18,X15,X3] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X18,X6,X17,X15,X3),X6,X15,X3),X17,tc_prod(X15,X3))
| ~ c_in(X6,c_Relation_OImage(X17,X18,X15,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_437_438,plain,
! [X35,X25,X36,X17,X26,X15,X3] :
( c_lessequals(c_Relation_Orel__comp(X36,X35,X3,X15,X26),c_Relation_Orel__comp(X17,X25,X3,X15,X26),tc_fun(tc_prod(X3,X26),tc_bool))
| ~ c_lessequals(X35,X25,tc_fun(tc_prod(X15,X26),tc_bool))
| ~ c_lessequals(X36,X17,tc_fun(tc_prod(X3,X15),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_438_439,plain,
! [X25,X17,X3] :
( c_lessequals(c_Transitive__Closure_Ortrancl(X17,X3),X25,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Ortrancl(X17,X3),X25,tc_fun(tc_prod(X3,X3),tc_bool)),X17,X3,X3,X3),X25,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(c_Relation_OId(X3),X25,tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_439_440,plain,
! [X25,X17,X3] :
( c_lessequals(c_Transitive__Closure_Otrancl(X17,X3),X25,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Otrancl(X17,X3),X25,tc_fun(tc_prod(X3,X3),tc_bool)),X17,X3,X3,X3),X25,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(X17,X25,tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_440_441,plain,
! [X25,X17,X23,X6,X7,X26,X15,X3] :
( c_in(c_Pair(X7,X23,X3,X26),c_Relation_Orel__comp(X17,X25,X3,X15,X26),tc_prod(X3,X26))
| ~ c_in(c_Pair(X6,X23,X15,X26),X25,tc_prod(X15,X26))
| ~ c_in(c_Pair(X7,X6,X3,X15),X17,tc_prod(X3,X15)) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_441_442,plain,
! [X12,X10,X17,X27,X22,X15,X3] :
( c_Recdef_Ocut(X22,X17,X10,X3,X15) != c_Recdef_Ocut(X27,X17,X10,X3,X15)
| hAPP(X22,X12) = hAPP(X27,X12)
| ~ c_in(c_Pair(X12,X10,X3,X3),X17,tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_442_443,plain,
! [X11,X24,X3] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X24,X11,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_lessequals(c_Relation_Orel__comp(X24,X11,X3,X3,X3),X24,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Wellfounded_Owf(X11,X3)
| ~ c_Wellfounded_Owf(X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_443_444,plain,
! [X24,X3] :
( c_Wellfounded_Owf(X24,X3)
| ~ c_Wellfounded_Owf(c_Relation_Orel__comp(X24,X24,X3,X3,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_444_445,plain,
! [X38,X21,X19,X18,X15,X3] :
( c_lessequals(c_Product__Type_OSigma(X18,X19,X3,X15),c_Product__Type_OSigma(X21,X38,X3,X15),tc_fun(tc_prod(X3,X15),tc_bool))
| c_in(c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(X18,X19,X38,X3,X15),X18,X3)
| ~ c_lessequals(X18,X21,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_445_446,plain,
! [X12,X10,X6,X7,X8] :
( c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X8,X7,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X7,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X12
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X6 ),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_446_447,plain,
! [X12,X10,X6,X7,X8] :
( c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X8,X7,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X12
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X6 ),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_447_448,axiom,
! [X22,X19,X18,X15,X3] :
( c_in(X22,c_FuncSet_OPi(X18,c_COMBK(X19,tc_fun(X15,tc_bool),X3),X3,X15),tc_fun(X3,X15))
| c_in(c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X18,X19,X22,X3,X15),X18,X3) ),
c_0_23 ).
fof(c_0_448_449,plain,
! [X10,X17,X22,X7,X15,X3] :
( hAPP(c_Recdef_Ocut(X22,X17,X7,X3,X15),X10) = hAPP(X22,X10)
| ~ c_in(c_Pair(X10,X7,X3,X3),X17,tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_449_450,plain,
! [X10,X22,X7,X24,X15,X3] :
( hAPP(c_Recdef_Ocut(X22,X24,X7,X3,X15),X10) = hAPP(X22,X10)
| ~ c_in(c_Pair(X10,X7,X3,X3),X24,tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_450_451,plain,
! [X17,X6,X18,X15,X3] :
( c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X18,X6,X17,X15,X3),X18,X15)
| ~ c_in(X6,c_Relation_OImage(X17,X18,X15,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_451_452,plain,
! [X17,X6,X18,X15,X3] :
( c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X18,X6,X17,X15,X3),X18,X15)
| ~ c_in(X6,c_Relation_OImage(X17,X18,X15,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_452_453,plain,
! [X20,X10,X17,X3] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X17,X10,X20,X3),X20,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3))
| c_in(c_Pair(X10,X20,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(c_Pair(X10,X20,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_453_454,plain,
! [X17,X18,X3] :
( c_Relation_Orefl__on(X18,X17,X3)
| ~ c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1(X18,X17,X3),c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1(X18,X17,X3),X3,X3),X17,tc_prod(X3,X3))
| ~ c_lessequals(X17,c_Product__Type_OSigma(X18,c_COMBK(X18,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_454_455,plain,
! [X17,X18,X3] :
( c_Relation_Orefl__on(X18,X17,X3)
| ~ c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1(X18,X17,X3),c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1(X18,X17,X3),X3,X3),X17,tc_prod(X3,X3))
| ~ c_lessequals(X17,c_Product__Type_OSigma(X18,c_COMBK(X18,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_455_456,plain,
! [X20,X10,X17,X3] :
( c_in(c_Pair(X10,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X17,X10,X20,X3),X3,X3),X17,tc_prod(X3,X3))
| c_in(c_Pair(X10,X20,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(c_Pair(X10,X20,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_456_457,axiom,
! [X22,X19,X18,X15,X3] :
( c_in(X22,c_FuncSet_OPi(X18,X19,X3,X15),tc_fun(X3,X15))
| c_in(c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X18,X19,X22,X3,X15),X18,X3) ),
c_0_32 ).
fof(c_0_457_458,axiom,
! [X22,X19,X18,X15,X3] :
( c_in(X22,c_FuncSet_OPi(X18,X19,X3,X15),tc_fun(X3,X15))
| c_in(c_FuncSet_Osko__FuncSet__XPi__I__1__1(X18,X19,X22,X3,X15),X18,X3) ),
c_0_33 ).
fof(c_0_458_459,plain,
! [X10,X21,X19,X18,X15,X3] :
( c_lessequals(X18,X19,tc_fun(X15,tc_bool))
| ~ c_lessequals(c_Product__Type_OSigma(X18,c_COMBK(X21,tc_fun(X3,tc_bool),X15),X15,X3),c_Product__Type_OSigma(X19,c_COMBK(X21,tc_fun(X3,tc_bool),X15),X15,X3),tc_fun(tc_prod(X15,X3),tc_bool))
| ~ c_in(X10,X21,X3) ),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_459_460,plain,
! [X17,X18,X3] :
( c_lessequals(X17,c_Relation_Orel__comp(c_Relation_Oconverse(X17,X3,X3),X17,X3,X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Relation_Orefl__on(X18,X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_460_461,plain,
! [X17,X3] :
( c_lessequals(c_Relation_Orel__comp(c_Relation_Oconverse(X17,X3,X3),X17,X3,X3,X3),X17,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Relation_Otrans(X17,X3)
| ~ c_Relation_Osym(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_461_462,plain,
! [X12,X10,X17,X3] :
( ~ c_in(c_Pair(X10,X12,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3))
| ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X12,X10,X3,X3),X17,tc_prod(X3,X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_37]) ).
fof(c_0_462_463,plain,
! [X12,X10,X6,X7,X8] :
( c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X8,X7,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X7
| ~ c_in(c_Pair(X10,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X12
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X6 ),
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_463_464,plain,
! [X12,X10,X6,X7,X8] :
( c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X8,X7,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X6,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X12 = X7
| X10 = X12
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X6 ),
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_464_465,plain,
! [X12,X10,X6,X7,X8] :
( c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X8,X7,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X12 = X6
| ~ c_in(c_Pair(X7,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X12
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X6 ),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_465_466,plain,
! [X12,X10,X6,X7,X8] :
( c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X8,X7,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X6
| X10 = X12
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X6 ),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_466_467,plain,
! [X12,X10,X6,X8] :
( ~ c_in(c_Pair(X6,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X12
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X10 = X6
| c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X8,X10,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_467_468,plain,
! [X16,X10,X7,X8] :
( ~ c_in(c_Pair(X16,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X16 = X10
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X10
| c_in(c_Pair(X16,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X8,X7,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X16,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_468_469,plain,
! [X16,X10,X7,X8] :
( ~ c_in(c_Pair(X16,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X7,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X16 = X10
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X10
| c_in(c_Pair(X16,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X8,X7,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_469_470,plain,
! [X12,X10,X6,X8] :
( ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X12
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X10 = X6
| c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X8,X10,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_470_471,plain,
! [X17,X3] :
( c_lessequals(c_Relation_Orel__comp(X17,X17,X3,X3,X3),X17,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Relation_Otrans(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_471_472,plain,
! [X12,X10,X24,X3] :
( c_in(c_Pair(X10,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X24,X10,X12,X3),X3,X3),c_Transitive__Closure_Ortrancl(X24,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X10,X12,X3,X3),c_Transitive__Closure_Otrancl(X24,X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_47]) ).
fof(c_0_472_473,plain,
! [X12,X10,X24,X3] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X24,X10,X12,X3),X12,X3,X3),c_Transitive__Closure_Ortrancl(X24,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X10,X12,X3,X3),c_Transitive__Closure_Otrancl(X24,X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_473_474,plain,
! [X12,X10,X24,X3] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X24,X10,X12,X3),X12,X3,X3),X24,tc_prod(X3,X3))
| ~ c_in(c_Pair(X10,X12,X3,X3),c_Transitive__Closure_Otrancl(X24,X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_474_475,plain,
! [X12,X10,X24,X3] :
( c_in(c_Pair(X10,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X24,X10,X12,X3),X3,X3),X24,tc_prod(X3,X3))
| ~ c_in(c_Pair(X10,X12,X3,X3),c_Transitive__Closure_Otrancl(X24,X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_475_476,plain,
! [X17,X23,X6,X7,X3] :
( c_in(c_Pair(X7,X23,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X6,X23,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X7,X6,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_476_477,plain,
! [X17,X23,X6,X7,X3] :
( c_in(c_Pair(X7,X23,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X6,X23,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X7,X6,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_52]) ).
fof(c_0_477_478,plain,
! [X20,X12,X10,X17,X3] :
( c_in(c_Pair(X10,X20,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X12,X20,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X10,X12,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_478_479,plain,
! [X17,X23,X6,X7,X3] :
( c_in(c_Pair(X7,X23,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X6,X23,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X7,X6,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_479_480,plain,
! [X17,X6,X7,X18,X3] :
( c_in(X7,X18,X3)
| X7 = X6
| ~ c_lessequals(X17,c_Product__Type_OSigma(X18,c_COMBK(X18,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_in(c_Pair(X7,X6,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_480_481,plain,
! [X17,X23,X6,X7,X3] :
( c_in(c_Pair(X7,X23,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X6,X23,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(c_Pair(X7,X6,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_481_482,plain,
! [X17,X23,X6,X7,X3] :
( c_in(c_Pair(X7,X23,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X6,X23,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X7,X6,X3,X3),X17,tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_57]) ).
fof(c_0_482_483,plain,
! [X17,X23,X6,X7,X3] :
( c_in(c_Pair(X7,X23,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X6,X23,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(c_Pair(X7,X6,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_483_484,plain,
! [X17,X23,X6,X7,X3] :
( c_in(c_Pair(X7,X23,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X6,X23,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X7,X6,X3,X3),X17,tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_59]) ).
fof(c_0_484_485,plain,
! [X17,X23,X6,X7,X3] :
( c_in(c_Pair(X7,X23,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X6,X23,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X7,X6,X3,X3),X17,tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_485_486,plain,
! [X17,X23,X6,X7,X3] :
( c_in(c_Pair(X7,X23,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X6,X23,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(c_Pair(X7,X6,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_486_487,plain,
! [X24,X3] :
( c_Wellfounded_Owf(c_Relation_Orel__comp(X24,X24,X3,X3,X3),X3)
| ~ c_Wellfounded_Owf(X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_487_488,plain,
! [X17,X18,X3] :
( c_lessequals(c_Transitive__Closure_Otrancl(X17,X3),c_Product__Type_OSigma(X18,c_COMBK(X18,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(X17,c_Product__Type_OSigma(X18,c_COMBK(X18,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_488_489,plain,
! [X23,X6,X7,X24,X3] :
( c_in(c_Pair(X7,X23,X3,X3),c_Transitive__Closure_Otrancl(X24,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X6,X23,X3,X3),X24,tc_prod(X3,X3))
| ~ c_in(c_Pair(X7,X6,X3,X3),X24,tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_489_490,plain,
! [X17,X23,X6,X7,X3] :
( c_in(c_Pair(X7,X23,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(c_Pair(X6,X23,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(c_Pair(X7,X6,X3,X3),X17,tc_prod(X3,X3))
| ~ c_Relation_Otrans(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_65]) ).
fof(c_0_490_491,plain,
! [X20,X12,X10,X17,X3] :
( c_in(c_Pair(X10,X20,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(c_Pair(X12,X20,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(c_Pair(X10,X12,X3,X3),X17,tc_prod(X3,X3))
| ~ c_Relation_Otrans(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_491_492,plain,
! [X12,X10,X17,X22,X15,X3] :
( c_in(c_Pair(hAPP(X22,X10),hAPP(X22,X12),X15,X15),X17,tc_prod(X15,X15))
| ~ c_in(c_Pair(X10,X12,X3,X3),c_Relation_Oinv__image(X17,X22,X15,X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_492_493,axiom,
! [X17,X3] :
( c_Relation_Orel__comp(c_Relation_Oconverse(X17,X3,X3),X17,X3,X3,X3) != X17
| c_Equiv__Relations_Oequiv(c_Relation_ODomain(X17,X3,X3),X17,X3) ),
c_0_68 ).
fof(c_0_493_494,plain,
! [X12,X10,X17,X22,X15,X3] :
( c_in(c_Pair(X10,X12,X3,X3),c_Relation_Oinv__image(X17,X22,X15,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(hAPP(X22,X10),hAPP(X22,X12),X15,X15),X17,tc_prod(X15,X15)) ),
inference(fof_simplification,[status(thm)],[c_0_69]) ).
fof(c_0_494_495,plain,
! [X17,X21,X19,X18,X15,X3] :
( c_lessequals(c_Relation_OImage(X17,X21,X3,X15),X19,tc_fun(X15,tc_bool))
| ~ c_lessequals(X17,c_Product__Type_OSigma(X18,c_COMBK(X19,tc_fun(X15,tc_bool),X3),X3,X15),tc_fun(tc_prod(X3,X15),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_70]) ).
fof(c_0_495_496,plain,
! [X17,X19,X18,X3] :
( c_Wellfounded_Owf(X17,X3)
| c_in(c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1(X18,X19,X17,X3),X19,X3)
| ~ c_lessequals(X17,c_Product__Type_OSigma(X18,c_COMBK(X19,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_71]) ).
fof(c_0_496_497,plain,
! [X17,X19,X18,X3] :
( c_Wellfounded_Owf(X17,X3)
| c_in(c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1(X18,X19,X17,X3),X18,X3)
| ~ c_lessequals(X17,c_Product__Type_OSigma(X18,c_COMBK(X19,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_497_498,plain,
! [X12,X10,X17,X3] :
( c_in(c_Pair(X10,X12,X3,X3),c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X17,X3),X3,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X10,X12,X3,X3),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X17,X3,X3),X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_73]) ).
fof(c_0_498_499,plain,
! [X12,X10,X17,X3] :
( c_in(c_Pair(X10,X12,X3,X3),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X17,X3,X3),X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X10,X12,X3,X3),c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X17,X3),X3,X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_74]) ).
fof(c_0_499_500,plain,
! [X22,X19,X18,X15,X3] :
( c_lessequals(c_Set_Oimage(X22,X18,X3,X15),X19,tc_fun(X15,tc_bool))
| ~ c_in(X22,c_FuncSet_OPi(X18,c_COMBK(X19,tc_fun(X15,tc_bool),X3),X3,X15),tc_fun(X3,X15)) ),
inference(fof_simplification,[status(thm)],[c_0_75]) ).
fof(c_0_500_501,plain,
! [X12,X10,X8] :
( ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X12,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X12
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_76]) ).
fof(c_0_501_502,plain,
! [X6,X7,X8] :
( ~ c_in(c_Pair(X6,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X7,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_77]) ).
fof(c_0_502_503,plain,
! [X10,X21,X19,X18,X15,X3] :
( c_lessequals(c_Product__Type_OSigma(X18,c_COMBK(X21,tc_fun(X3,tc_bool),X15),X15,X3),c_Product__Type_OSigma(X19,c_COMBK(X21,tc_fun(X3,tc_bool),X15),X15,X3),tc_fun(tc_prod(X15,X3),tc_bool))
| ~ c_lessequals(X18,X19,tc_fun(X15,tc_bool))
| ~ c_in(X10,X21,X3) ),
inference(fof_simplification,[status(thm)],[c_0_78]) ).
fof(c_0_503_504,plain,
! [X12,X10,X17,X3] :
( c_in(c_Pair(X12,X10,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X10,X12,X3,X3),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X17,X3,X3),X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_79]) ).
fof(c_0_504_505,plain,
! [X12,X10,X17,X3] :
( c_Wellfounded_Owf(X17,X3)
| ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X12,X10,X3,X3),X17,tc_prod(X3,X3)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_80]) ).
fof(c_0_505_506,plain,
! [X10,X17,X7,X3] :
( ~ c_in(c_Pair(X10,X7,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(c_Pair(X7,X10,X3,X3),X17,tc_prod(X3,X3))
| ~ c_Wellfounded_Owf(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_506_507,plain,
! [X17,X7,X15,X3] :
( c_in(c_Pair(X7,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X7,X17,X3,X15),X3,X15),X17,tc_prod(X3,X15))
| ~ c_in(X7,c_Relation_ODomain(X17,X3,X15),X3) ),
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_507_508,plain,
! [X17,X7,X15,X3] :
( c_in(c_Pair(X7,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X7,X17,X3,X15),X3,X15),X17,tc_prod(X3,X15))
| ~ c_in(X7,c_Relation_ODomain(X17,X3,X15),X3) ),
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_508_509,plain,
! [X17,X7,X15,X3] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X7,X17,X3,X15),X7,X15,X3),X17,tc_prod(X15,X3))
| ~ c_in(X7,c_Relation_ORange(X17,X15,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_509_510,plain,
! [X17,X6,X15,X3] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X6,X17,X3,X15),X6,X15,X3),X17,tc_prod(X15,X3))
| ~ c_in(X6,c_Relation_ORange(X17,X15,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_510_511,plain,
! [X12,X10,X6,X7,X8] :
( c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X12 = X6
| X10 = X6
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X8,X7,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X6 ),
inference(fof_simplification,[status(thm)],[c_0_86]) ).
fof(c_0_511_512,plain,
! [X16,X10,X7,X8] :
( X16 = X10
| ~ c_in(c_Pair(X16,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X8,X7,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X10
| c_in(c_Pair(X16,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X16 = X7 ),
inference(fof_simplification,[status(thm)],[c_0_87]) ).
fof(c_0_512_513,plain,
! [X12,X10,X6,X7,X8] :
( c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X7
| X12 = X7
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X8,X7,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X6 ),
inference(fof_simplification,[status(thm)],[c_0_88]) ).
fof(c_0_513_514,plain,
! [X12,X10,X6,X8] :
( X12 = X10
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X8,X10,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X10 = X6
| c_in(c_Pair(X6,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X12 = X6 ),
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_514_515,plain,
! [X12,X10,X7,X8] :
( ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X8,X7,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X10
| c_in(c_Pair(X7,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_515_516,plain,
! [X16,X10,X6,X8] :
( ~ c_in(c_Pair(X16,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X8,X10,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X10 = X6
| c_in(c_Pair(X16,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_516_517,plain,
! [X17,X2,X18,X3] :
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_in(X2,c_Equiv__Relations_Oquotient(X18,X17,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X17,c_Product__Type_OSigma(X18,c_COMBK(X18,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Finite__Set_Ofinite(X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_517_518,plain,
! [X12,X10,X17,X3] :
( c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X12,X10,X3,X3),X17,tc_prod(X3,X3)),X3)
| c_in(c_Pair(X10,X12,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3))
| ~ c_Wellfounded_Owf(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_518_519,plain,
! [X6,X7,X19,X18,X15,X3] :
( c_in(X6,hAPP(X19,X7),X15)
| ~ c_in(c_Pair(X7,X6,X3,X15),c_Product__Type_OSigma(X18,X19,X3,X15),tc_prod(X3,X15)) ),
inference(fof_simplification,[status(thm)],[c_0_94]) ).
fof(c_0_519_520,plain,
! [X12,X10,X17,X3] :
( c_in(c_Pair(X10,X12,X3,X3),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X17,X3,X3),X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X12,X10,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_95]) ).
fof(c_0_520_521,plain,
! [X12,X10,X17,X1,X2,X18,X3] :
( X2 = X1
| ~ c_in(c_Pair(X10,X12,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(X12,X1,X3)
| ~ c_in(X10,X2,X3)
| ~ c_in(X1,c_Equiv__Relations_Oquotient(X18,X17,X3),tc_fun(X3,tc_bool))
| ~ c_in(X2,c_Equiv__Relations_Oquotient(X18,X17,X3),tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X18,X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_96]) ).
fof(c_0_521_522,plain,
! [X12,X10,X6,X7,X8] :
( c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X8,X7,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X12 = X6
| X10 = X6
| X10 = X12
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X6 ),
inference(fof_simplification,[status(thm)],[c_0_97]) ).
fof(c_0_522_523,plain,
! [X12,X10,X6,X7,X8] :
( c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X8,X7,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X7
| X12 = X7
| X10 = X12
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X6 ),
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_523_524,plain,
! [X16,X10,X7,X8] :
( ~ c_in(c_Pair(X16,X7,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X16 = X10
| X16 = X10
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X10
| c_in(c_Pair(X16,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X8,X7,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[c_0_99]) ).
fof(c_0_524_525,plain,
! [X12,X10,X6,X8] :
( X10 = X6
| X10 = X12
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X10 = X6
| c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X8,X10,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[c_0_100]) ).
fof(c_0_525_526,plain,
! [X12,X10,X6,X8] :
( ~ c_in(c_Pair(X6,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X12 = X10
| X10 = X12
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X10 = X6
| c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X8,X10,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[c_0_101]) ).
fof(c_0_526_527,plain,
! [X16,X10,X7,X8] :
( X10 = X7
| X16 = X10
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X10
| c_in(c_Pair(X16,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X8,X7,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X16,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[c_0_102]) ).
fof(c_0_527_528,plain,
! [X16,X10,X8] :
( ~ c_in(c_Pair(X16,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X16 = X10
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X16 = X10
| c_in(c_Pair(X16,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X8,X16,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_528_529,plain,
! [X12,X10,X7,X8] :
( ~ c_in(c_Pair(X7,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X12
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X10
| c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X8,X7,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_529_530,plain,
! [X16,X10,X8] :
( ~ c_in(c_Pair(X10,X16,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X16
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X10 = X16
| c_in(c_Pair(X10,X16,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X8,X10,X16),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_530_531,plain,
! [X16,X10,X6,X8] :
( ~ c_in(c_Pair(X16,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X16 = X10
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X10 = X6
| c_in(c_Pair(X16,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X8,X10,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_531_532,plain,
! [X6,X7,X19,X18,X15,X3] :
( c_in(X7,X18,X3)
| ~ c_in(c_Pair(X7,X6,X3,X15),c_Product__Type_OSigma(X18,X19,X3,X15),tc_prod(X3,X15)) ),
inference(fof_simplification,[status(thm)],[c_0_107]) ).
fof(c_0_532_533,plain,
! [X17,X18,X3] :
( c_Relation_Orefl__on(X18,X17,X3)
| c_in(c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1(X18,X17,X3),X18,X3)
| ~ c_lessequals(X17,c_Product__Type_OSigma(X18,c_COMBK(X18,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_108]) ).
fof(c_0_533_534,plain,
! [X17,X18,X3] :
( c_Relation_Orefl__on(X18,X17,X3)
| c_in(c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1(X18,X17,X3),X18,X3)
| ~ c_lessequals(X17,c_Product__Type_OSigma(X18,c_COMBK(X18,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_109]) ).
fof(c_0_534_535,plain,
! [X17,X6,X7,X15,X3] :
( c_in(c_Pair(X6,X7,X15,X3),X17,tc_prod(X15,X3))
| ~ c_in(c_Pair(X7,X6,X3,X15),c_Relation_Oconverse(X17,X15,X3),tc_prod(X3,X15)) ),
inference(fof_simplification,[status(thm)],[c_0_110]) ).
fof(c_0_535_536,plain,
! [X10,X17,X3] :
( ~ c_in(c_Pair(X10,X10,X3,X3),X17,tc_prod(X3,X3))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X17,X3),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X17,X3),X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_536_537,plain,
! [X17,X6,X7,X15,X3] :
( c_in(c_Pair(X6,X7,X15,X3),c_Relation_Oconverse(X17,X3,X15),tc_prod(X15,X3))
| ~ c_in(c_Pair(X7,X6,X3,X15),X17,tc_prod(X3,X15)) ),
inference(fof_simplification,[status(thm)],[c_0_112]) ).
fof(c_0_537_538,plain,
! [X17,X6,X7,X15,X3] :
( c_in(c_Pair(X7,X6,X3,X15),c_Relation_Oconverse(X17,X15,X3),tc_prod(X3,X15))
| ~ c_in(c_Pair(X6,X7,X15,X3),X17,tc_prod(X15,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_113]) ).
fof(c_0_538_539,plain,
! [X10,X22,X19,X18,X15,X3] :
( c_in(hAPP(X22,X10),X19,X15)
| ~ c_in(X10,X18,X3)
| ~ c_in(X22,c_FuncSet_OPi(X18,c_COMBK(X19,tc_fun(X15,tc_bool),X3),X3,X15),tc_fun(X3,X15)) ),
inference(fof_simplification,[status(thm)],[c_0_114]) ).
fof(c_0_539_540,plain,
! [X6,X7,X24,X3] :
( c_in(c_Pair(X7,X6,X3,X3),c_Transitive__Closure_Otrancl(X24,X3),tc_prod(X3,X3))
| X7 = X6
| ~ c_in(c_Pair(X7,X6,X3,X3),c_Transitive__Closure_Ortrancl(X24,X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_115]) ).
fof(c_0_540_541,plain,
! [X12,X10,X24,X3] :
( c_in(c_Pair(X10,X12,X3,X3),c_Transitive__Closure_Otrancl(X24,X3),tc_prod(X3,X3))
| X10 = X12
| ~ c_in(c_Pair(X10,X12,X3,X3),c_Transitive__Closure_Ortrancl(X24,X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_116]) ).
fof(c_0_541_542,plain,
! [X12,X10,X24,X3] :
( c_in(c_Pair(X10,X12,X3,X3),c_Transitive__Closure_Ortrancl(X24,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X10,X12,X3,X3),c_Transitive__Closure_Otrancl(X24,X3),tc_prod(X3,X3))
| X10 = X12 ),
inference(fof_simplification,[status(thm)],[c_0_117]) ).
fof(c_0_542_543,plain,
! [X17,X6,X7,X3] :
( c_in(c_Pair(X7,X6,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X7,X6,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_118]) ).
fof(c_0_543_544,plain,
! [X17,X6,X7,X18,X15,X3] :
( c_in(X6,c_Relation_OImage(X17,X18,X3,X15),X15)
| ~ c_in(c_Pair(X7,X6,X3,X15),X17,tc_prod(X3,X15))
| ~ c_in(X7,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_119]) ).
fof(c_0_544_545,plain,
! [X10,X17,X6,X18,X15,X3] :
( c_in(X6,c_Relation_OImage(X17,X18,X15,X3),X3)
| ~ c_in(c_Pair(X10,X6,X15,X3),X17,tc_prod(X15,X3))
| ~ c_in(X10,X18,X15) ),
inference(fof_simplification,[status(thm)],[c_0_120]) ).
fof(c_0_545_546,plain,
! [X17,X6,X7,X3] :
( c_in(c_Pair(X7,X6,X3,X3),c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X7,X6,X3,X3),X17,tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_121]) ).
fof(c_0_546_547,plain,
! [X12,X10,X17,X3] :
( c_in(c_Pair(X12,X10,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(c_Pair(X10,X12,X3,X3),X17,tc_prod(X3,X3))
| ~ c_Relation_Osym(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_122]) ).
fof(c_0_547_548,plain,
! [X17,X6,X7,X3] :
( c_in(c_Pair(X6,X7,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(c_Pair(X7,X6,X3,X3),X17,tc_prod(X3,X3))
| ~ c_Relation_Osym(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_123]) ).
fof(c_0_548_549,plain,
! [X20,X12,X10,X8] :
( c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X12 = X20
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X8,X20),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[c_0_124]) ).
fof(c_0_549_550,plain,
! [X20,X12,X10,X8] :
( c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X20
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X8,X20),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[c_0_125]) ).
fof(c_0_550_551,plain,
! [X20,X12,X10,X8] :
( c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X8,X20),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X12
| X10 = X20 ),
inference(fof_simplification,[status(thm)],[c_0_126]) ).
fof(c_0_551_552,plain,
! [X20,X12,X10,X8] :
( c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X8,X20),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X12 = X20
| X10 = X20 ),
inference(fof_simplification,[status(thm)],[c_0_127]) ).
fof(c_0_552_553,plain,
! [X20,X12,X10,X8] :
( c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X8,X20),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X12
| X12 = X20 ),
inference(fof_simplification,[status(thm)],[c_0_128]) ).
fof(c_0_553_554,plain,
! [X20,X12,X10,X8] :
( c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X8,X20),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X20
| X12 = X20 ),
inference(fof_simplification,[status(thm)],[c_0_129]) ).
fof(c_0_554_555,plain,
! [X12,X16,X17,X31,X3] :
( ~ c_in(X12,X31,X3)
| ~ c_in(c_Pair(X12,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X31,X17,X3),X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(X16,X31,X3)
| ~ c_Wellfounded_Owf(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_130]) ).
fof(c_0_555_556,plain,
! [X12,X10,X24,X31,X3] :
( ~ c_in(X12,X31,X3)
| ~ c_in(c_Pair(X12,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X31,X24,X3),X3,X3),X24,tc_prod(X3,X3))
| ~ c_in(X10,X31,X3)
| ~ c_Wellfounded_Owf(X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_131]) ).
fof(c_0_556_557,plain,
! [X12,X17,X7,X29,X3] :
( hBOOL(hAPP(X29,X7))
| hBOOL(hAPP(X29,X12))
| ~ c_in(c_Pair(X12,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X29,X17,X3),X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(X7,c_Wellfounded_Oacc(X17,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_132]) ).
fof(c_0_557_558,plain,
! [X12,X17,X7,X29,X3] :
( hBOOL(hAPP(X29,X7))
| hBOOL(hAPP(X29,X12))
| ~ c_in(c_Pair(X12,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X29,X17,X3),X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(X7,c_Wellfounded_Oacc(X17,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_133]) ).
fof(c_0_558_559,plain,
! [X12,X16,X10,X17,X18,X3] :
( ~ c_in(X12,X10,X3)
| ~ c_in(X16,X10,X3)
| ~ c_in(X10,c_Equiv__Relations_Oquotient(X18,X17,X3),tc_fun(X3,tc_bool))
| ~ c_in(X10,c_Equiv__Relations_Oquotient(X18,X17,X3),tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X18,X17,X3)
| c_in(c_Pair(X16,X12,X3,X3),X17,tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_134]) ).
fof(c_0_559_560,plain,
! [X16,X10,X17,X18,X3] :
( c_in(c_Pair(X16,X10,X3,X3),X17,tc_prod(X3,X3))
| c_in(c_Pair(X10,X16,X3,X3),X17,tc_prod(X3,X3))
| X10 = X16
| ~ c_in(X16,X18,X3)
| ~ c_in(X10,X18,X3)
| ~ c_Relation_Ototal__on(X18,X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_135]) ).
fof(c_0_560_561,plain,
! [X17,X18,X3] :
( c_Relation_Orel__comp(c_Relation_Oconverse(X17,X3,X3),X17,X3,X3,X3) = X17
| ~ c_Equiv__Relations_Oequiv(X18,X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_136]) ).
fof(c_0_561_562,plain,
! [X36,X17,X37,X18,X15,X3] :
( c_lessequals(c_Relation_OImage(X36,X37,X3,X15),c_Relation_OImage(X17,X18,X3,X15),tc_fun(X15,tc_bool))
| ~ c_lessequals(X37,X18,tc_fun(X3,tc_bool))
| ~ c_lessequals(X36,X17,tc_fun(tc_prod(X3,X15),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_137]) ).
fof(c_0_562_563,plain,
! [X10,X21,X19,X18,X15,X3] :
( c_Product__Type_OSigma(X18,c_COMBK(X21,tc_fun(X3,tc_bool),X15),X15,X3) != c_Product__Type_OSigma(X19,c_COMBK(X21,tc_fun(X3,tc_bool),X15),X15,X3)
| ~ c_in(X10,X21,X3)
| X18 = X19 ),
inference(fof_simplification,[status(thm)],[c_0_138]) ).
fof(c_0_563_564,plain,
! [X12,X10,X8] :
( c_in(c_Pair(X12,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X10 = X12
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_139]) ).
fof(c_0_564_565,plain,
! [X6,X7,X19,X18,X15,X3] :
( c_in(c_Pair(X7,X6,X3,X15),c_Product__Type_OSigma(X18,X19,X3,X15),tc_prod(X3,X15))
| ~ c_in(X6,hAPP(X19,X7),X15)
| ~ c_in(X7,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_140]) ).
fof(c_0_565_566,plain,
! [X6,X7,X19,X18,X15,X3] :
( c_in(c_Pair(X7,X6,X3,X15),c_Product__Type_OSigma(X18,X19,X3,X15),tc_prod(X3,X15))
| ~ c_in(X6,hAPP(X19,X7),X15)
| ~ c_in(X7,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_141]) ).
fof(c_0_566_567,plain,
! [X10,X6,X7,X8] :
( ~ c_in(c_Pair(X10,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X8,X7,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X6 ),
inference(fof_simplification,[status(thm)],[c_0_142]) ).
fof(c_0_567_568,plain,
! [X10,X6,X7,X8] :
( ~ c_in(c_Pair(X10,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X8,X7,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X6 ),
inference(fof_simplification,[status(thm)],[c_0_143]) ).
fof(c_0_568_569,plain,
! [X30,X10,X17,X29] :
( hBOOL(hAPP(X29,X10))
| c_in(X30,c_Wellfounded_Oacc(X17,t_a),t_a)
| ~ c_in(c_Pair(X30,v_sko__Wellfounded__Xacc__Xinduct__1(X29,X17),t_a,t_a),X17,tc_prod(t_a,t_a))
| ~ c_in(X10,c_Wellfounded_Oacc(X17,t_a),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_144]) ).
fof(c_0_569_570,plain,
! [X30,X10,X17,X29] :
( hBOOL(hAPP(X29,X10))
| c_in(X30,c_Wellfounded_Oacc(X17,t_a),t_a)
| ~ c_in(c_Pair(X30,v_sko__Wellfounded__Xacc__Xinducts__1(X29,X17),t_a,t_a),X17,tc_prod(t_a,t_a))
| ~ c_in(X10,c_Wellfounded_Oacc(X17,t_a),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_145]) ).
fof(c_0_570_571,plain,
! [X22,X19,X18,X15,X3] :
( c_lessequals(c_Set_Oimage(X22,X18,X3,X15),c_Set_Oimage(X22,X19,X3,X15),tc_fun(X15,tc_bool))
| ~ c_lessequals(X18,X19,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_146]) ).
fof(c_0_571_572,plain,
! [X10,X22,X18,X15,X3] :
( ~ c_lessequals(X10,X18,tc_fun(X15,tc_bool))
| c_lessequals(c_Set_Oimage(X22,X10,X15,X3),c_Set_Oimage(X22,X18,X15,X3),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_147]) ).
fof(c_0_572_573,plain,
! [X17,X6,X7,X3] :
( c_in(X6,c_Wellfounded_Oacc(X17,X3),X3)
| ~ c_in(c_Pair(X6,X7,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(X7,c_Wellfounded_Oacc(X17,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_148]) ).
fof(c_0_573_574,plain,
! [X17,X6,X7,X3] :
( c_in(X6,c_Wellfounded_Oacc(X17,X3),X3)
| ~ c_in(X7,c_Wellfounded_Oacc(X17,X3),X3)
| ~ c_in(c_Pair(X6,X7,X3,X3),c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_149]) ).
fof(c_0_574_575,plain,
! [X12,X10,X17,X29] :
( hBOOL(hAPP(X29,X10))
| hBOOL(hAPP(X29,X12))
| ~ c_in(c_Pair(X12,v_sko__Wellfounded__Xacc__Xinducts__1(X29,X17),t_a,t_a),X17,tc_prod(t_a,t_a))
| ~ c_in(X10,c_Wellfounded_Oacc(X17,t_a),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_150]) ).
fof(c_0_575_576,plain,
! [X12,X10,X17,X29] :
( hBOOL(hAPP(X29,X10))
| hBOOL(hAPP(X29,X12))
| ~ c_in(c_Pair(X12,v_sko__Wellfounded__Xacc__Xinduct__1(X29,X17),t_a,t_a),X17,tc_prod(t_a,t_a))
| ~ c_in(X10,c_Wellfounded_Oacc(X17,t_a),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_151]) ).
fof(c_0_576_577,plain,
! [X17,X6,X7,X3] :
( c_in(X7,c_Wellfounded_Oacc(X17,X3),X3)
| ~ c_in(c_Pair(X7,X6,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(X6,c_Wellfounded_Oacc(X17,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_152]) ).
fof(c_0_577_578,plain,
! [X12,X17,X7,X3] :
( c_in(X12,c_Wellfounded_Oacc(X17,X3),X3)
| ~ c_in(c_Pair(X12,X7,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(X7,c_Wellfounded_Oacc(X17,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_153]) ).
fof(c_0_578_579,plain,
! [X12,X10,X24,X3] :
( X10 = X12
| ~ c_in(c_Pair(X10,X12,X3,X3),c_Transitive__Closure_Ortrancl(X24,X3),tc_prod(X3,X3))
| c_in(X10,c_Relation_ODomain(X24,X3,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_154]) ).
fof(c_0_579_580,plain,
! [X10,X22,X19,X18,X15,X3] :
( c_in(hAPP(X22,X10),hAPP(X19,X10),X15)
| ~ c_in(X10,X18,X3)
| ~ c_in(X22,c_FuncSet_OPi(X18,X19,X3,X15),tc_fun(X3,X15)) ),
inference(fof_simplification,[status(thm)],[c_0_155]) ).
fof(c_0_580_581,plain,
! [X10,X22,X19,X18,X15,X3] :
( ~ c_in(X10,X18,X3)
| c_in(hAPP(X22,X10),hAPP(X19,X10),X15)
| ~ c_in(X22,c_FuncSet_OPi(X18,X19,X3,X15),tc_fun(X3,X15)) ),
inference(fof_simplification,[status(thm)],[c_0_156]) ).
fof(c_0_581_582,plain,
! [X17,X3] :
( c_Nitpick_Orefl_H(X17,X3)
| ~ c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X17,X3),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X17,X3),X3,X3),X17,tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_157]) ).
fof(c_0_582_583,plain,
! [X10,X22,X19,X18,X15,X3] :
( c_in(hAPP(X22,X10),X19,X3)
| ~ c_in(X10,X18,X15)
| ~ c_lessequals(c_Set_Oimage(X22,X18,X15,X3),X19,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_158]) ).
fof(c_0_583_584,plain,
! [X10,X17,X7,X15,X3] :
( c_in(X7,c_Relation_ORange(X17,X15,X3),X3)
| ~ c_in(c_Pair(X10,X7,X15,X3),X17,tc_prod(X15,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_159]) ).
fof(c_0_584_585,plain,
! [X17,X6,X7,X15,X3] :
( c_in(X6,c_Relation_ORange(X17,X3,X15),X15)
| ~ c_in(c_Pair(X7,X6,X3,X15),X17,tc_prod(X3,X15)) ),
inference(fof_simplification,[status(thm)],[c_0_160]) ).
fof(c_0_585_586,plain,
! [X10,X17,X7,X15,X3] :
( c_in(X7,c_Relation_ODomain(X17,X3,X15),X3)
| ~ c_in(c_Pair(X7,X10,X3,X15),X17,tc_prod(X3,X15)) ),
inference(fof_simplification,[status(thm)],[c_0_161]) ).
fof(c_0_586_587,plain,
! [X17,X6,X7,X15,X3] :
( c_in(X7,c_Relation_ODomain(X17,X3,X15),X3)
| ~ c_in(c_Pair(X7,X6,X3,X15),X17,tc_prod(X3,X15)) ),
inference(fof_simplification,[status(thm)],[c_0_162]) ).
fof(c_0_587_588,plain,
! [X9] :
( v_thesis____
| ~ c_in(X9,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X9,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[c_0_163]) ).
fof(c_0_588_589,plain,
! [X12,X10,X17,X18,X3] :
( c_in(X12,X18,X3)
| ~ c_in(c_Pair(X10,X12,X3,X3),X17,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X18,X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_164]) ).
fof(c_0_589_590,plain,
! [X12,X10,X17,X18,X3] :
( c_in(X10,X18,X3)
| ~ c_in(c_Pair(X10,X12,X3,X3),X17,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X18,X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_165]) ).
fof(c_0_590_591,plain,
! [X12,X10,X17,X18,X3] :
( c_in(X12,X18,X3)
| ~ c_in(c_Pair(X10,X12,X3,X3),X17,tc_prod(X3,X3))
| ~ c_Relation_Orefl__on(X18,X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_166]) ).
fof(c_0_591_592,plain,
! [X12,X10,X17,X18,X3] :
( c_in(X10,X18,X3)
| ~ c_in(c_Pair(X10,X12,X3,X3),X17,tc_prod(X3,X3))
| ~ c_Relation_Orefl__on(X18,X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_167]) ).
fof(c_0_592_593,plain,
! [X17,X18,X3] :
( c_lessequals(X17,c_Product__Type_OSigma(X18,c_COMBK(X18,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Equiv__Relations_Oequiv(X18,X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_168]) ).
fof(c_0_593_594,plain,
! [X17,X18,X3] :
( c_lessequals(X17,c_Product__Type_OSigma(X18,c_COMBK(X18,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Relation_Orefl__on(X18,X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_169]) ).
fof(c_0_594_595,plain,
! [X12,X10,X18,X3] :
( c_in(X10,X18,X3)
| ~ c_in(c_Pair(X10,X12,X3,X3),c_Relation_OId__on(X18,X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_170]) ).
fof(c_0_595_596,plain,
! [X12,X10,X18,X3] :
( X10 = X12
| ~ c_in(c_Pair(X10,X12,X3,X3),c_Relation_OId__on(X18,X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_171]) ).
fof(c_0_596_597,plain,
! [X22,X19,X18,X15,X3] :
( c_Finite__Set_Ofinite(X19,X15)
| ~ c_lessequals(X19,c_Set_Oimage(X22,X18,X3,X15),tc_fun(X15,tc_bool))
| ~ c_Finite__Set_Ofinite(X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_172]) ).
fof(c_0_597_598,plain,
! [X17,X7,X3] :
( ~ c_in(c_Pair(X7,X7,X3,X3),X17,tc_prod(X3,X3))
| ~ c_Wellfounded_Owf(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_173]) ).
fof(c_0_598_599,plain,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3),c_Lattices_Olower__semilattice__class_Oinf(X10,X20,X3),X3),c_Lattices_Olower__semilattice__class_Oinf(X10,c_Lattices_Oupper__semilattice__class_Osup(X12,X20,X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_174]) ).
fof(c_0_599_600,plain,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Olower__semilattice__class_Oinf(X12,X20,X3),X3),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),c_Lattices_Oupper__semilattice__class_Osup(X10,X20,X3),X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_175]) ).
fof(c_0_600_601,plain,
! [X6,X7,X3] :
( X7 = X6
| ~ c_in(c_Pair(X7,X6,X3,X3),c_Relation_OId(X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_176]) ).
fof(c_0_601_602,plain,
! [X10,X22,X18,X15,X3] :
( c_Set_Oinsert(hAPP(X22,X10),c_Set_Oimage(X22,X18,X3,X15),X15) = c_Set_Oimage(X22,X18,X3,X15)
| ~ c_in(X10,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_177]) ).
fof(c_0_602_603,axiom,
! [X10,X17,X3] :
( c_in(X10,c_Wellfounded_Oacc(X17,X3),X3)
| c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X17,X10,X3),X10,X3,X3),X17,tc_prod(X3,X3)) ),
c_0_178 ).
fof(c_0_603_604,axiom,
! [X10,X24,X3] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X24,X10,X3),X10,X3,X3),X24,tc_prod(X3,X3))
| c_in(X10,c_Wellfounded_Oacc(X24,X3),X3) ),
c_0_179 ).
fof(c_0_604_605,plain,
! [X16,X10,X8] :
( X16 = X10
| X10 = X16
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X10 = X16
| c_in(c_Pair(X10,X16,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X8,X10,X16),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[c_0_180]) ).
fof(c_0_605_606,plain,
! [X16,X10,X8] :
( X16 = X10
| X16 = X10
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X16 = X10
| c_in(c_Pair(X16,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X8,X16,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[c_0_181]) ).
fof(c_0_606_607,plain,
! [X17,X2,X18,X3] :
( c_in(c_List_Osko__Equiv__Relations__XquotientE__1__1(X18,X2,X17,X3),X18,X3)
| ~ c_in(X2,c_Equiv__Relations_Oquotient(X18,X17,X3),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_182]) ).
fof(c_0_607_608,axiom,
! [X21,X19,X18,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)),X21,tc_fun(X3,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X18,c_Lattices_Oupper__semilattice__class_Osup(X19,X21,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| c_lessequals(X21,X18,tc_fun(X3,tc_bool)) ),
c_0_183 ).
fof(c_0_608_609,plain,
! [X10,X11,X24,X3] :
( c_in(X10,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X24,X11,tc_fun(tc_prod(X3,X3),tc_bool)),X3),tc_prod(X3,X3))
| ~ c_in(X10,c_Transitive__Closure_Ortrancl(X11,X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_184]) ).
fof(c_0_609_610,plain,
! [X10,X11,X24,X3] :
( c_in(X10,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X24,X11,tc_fun(tc_prod(X3,X3),tc_bool)),X3),tc_prod(X3,X3))
| ~ c_in(X10,c_Transitive__Closure_Ortrancl(X24,X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_185]) ).
fof(c_0_610_611,axiom,
! [X13,X6,X14,X7,X15,X3] :
( c_Pair(X7,X6,X3,X15) != c_Pair(X14,X13,X3,X15)
| X6 = X13 ),
c_0_186 ).
fof(c_0_611_612,axiom,
! [X13,X6,X14,X7,X15,X3] :
( c_Pair(X7,X6,X3,X15) != c_Pair(X14,X13,X3,X15)
| X7 = X14 ),
c_0_187 ).
fof(c_0_612_613,axiom,
! [X10,X24,X3] :
( c_in(X10,c_Relation_ODomain(X24,X3,X3),X3)
| c_in(c_Pair(X10,X10,X3,X3),c_Transitive__Closure_Ortrancl(X24,X3),tc_prod(X3,X3)) ),
c_0_188 ).
fof(c_0_613_614,plain,
! [X10,X17,X18,X3] :
( c_in(c_Pair(X10,X10,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(X10,X18,X3)
| ~ c_Relation_Orefl__on(X18,X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_189]) ).
fof(c_0_614_615,plain,
! [X17,X7,X18,X3] :
( c_in(c_Pair(X7,X7,X3,X3),X17,tc_prod(X3,X3))
| ~ c_in(X7,X18,X3)
| ~ c_Relation_Orefl__on(X18,X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_190]) ).
fof(c_0_615_616,plain,
! [X10,X18,X3] :
( c_in(c_Pair(X10,X10,X3,X3),c_Relation_OId__on(X18,X3),tc_prod(X3,X3))
| ~ c_in(X10,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_191]) ).
fof(c_0_616_617,plain,
! [X10,X22,X18,X43,X3] :
( ~ c_in(X10,X18,X43)
| c_in(hAPP(X22,X10),c_Set_Oimage(X22,X18,X43,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_192]) ).
fof(c_0_617_618,plain,
! [X10,X22,X18,X15,X3] :
( ~ c_in(X10,X18,X15)
| c_in(hAPP(X22,X10),c_Set_Oimage(X22,X18,X15,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_193]) ).
fof(c_0_618_619,plain,
! [X10,X22,X18,X15,X3] :
( c_in(hAPP(X22,X10),c_Set_Oimage(X22,X18,X15,X3),X3)
| ~ c_in(X10,X18,X15) ),
inference(fof_simplification,[status(thm)],[c_0_194]) ).
fof(c_0_619_620,plain,
! [X10,X22,X18,X15,X3] :
( c_in(hAPP(X22,X10),c_Set_Oimage(X22,X18,X3,X15),X15)
| ~ c_in(X10,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_195]) ).
fof(c_0_620,plain,
! [X25,X17,X19,X18,X3] :
( c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(X18,X19,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X17,X25,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Relation_Orefl__on(X19,X25,X3)
| ~ c_Relation_Orefl__on(X18,X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_196]) ).
fof(c_0_621,plain,
! [X25,X17,X19,X18,X3] :
( c_Relation_Orefl__on(c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X17,X25,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Relation_Orefl__on(X19,X25,X3)
| ~ c_Relation_Orefl__on(X18,X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_197]) ).
fof(c_0_622,plain,
! [X23,X18,X3] :
( X23 = c_Pair(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X18,X23,X3),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X18,X23,X3),X3,X3)
| ~ c_in(X23,c_Relation_OId__on(X18,X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_198]) ).
fof(c_0_623,plain,
! [X38,X21,X19,X18,X3] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X18,X19,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X21,X38,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X19,X38,tc_fun(X3,tc_bool))
| ~ c_lessequals(X18,X21,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_199]) ).
fof(c_0_624,plain,
! [X38,X21,X19,X18,X3] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X21,X38,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X19,X38,tc_fun(X3,tc_bool))
| ~ c_lessequals(X18,X21,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_200]) ).
fof(c_0_625,plain,
! [X10,X17,X3] :
( c_in(c_Pair(X10,X10,X3,X3),X17,tc_prod(X3,X3))
| ~ c_Nitpick_Orefl_H(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_201]) ).
fof(c_0_626,axiom,
! [X12,X10,X8] :
( X10 = X12
| X12 = X10
| c_in(c_Pair(X10,X12,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X8,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_202 ).
fof(c_0_627,axiom,
! [X16,X10,X8] :
( X16 = X10
| X16 = X10
| c_in(c_Pair(X16,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X8,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_203 ).
fof(c_0_628,axiom,
! [X6,X7] :
( c_in(c_Pair(X7,X6,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X7,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X7 = X6 ),
c_0_204 ).
fof(c_0_629,plain,
! [X10,X19,X18,X3] :
( hBOOL(hAPP(X19,X10))
| hBOOL(hAPP(X18,X10))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X18,X19,tc_fun(X3,tc_bool)),X10)) ),
inference(fof_simplification,[status(thm)],[c_0_205]) ).
fof(c_0_630,plain,
! [X21,X19,X18,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)),X21,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X18,c_Lattices_Oupper__semilattice__class_Osup(X19,X21,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X21,X18,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_206]) ).
fof(c_0_631,plain,
! [X10,X19,X18,X3] :
( hBOOL(hAPP(X19,X10))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)),X10)) ),
inference(fof_simplification,[status(thm)],[c_0_207]) ).
fof(c_0_632,plain,
! [X10,X19,X18,X3] :
( hBOOL(hAPP(X18,X10))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)),X10)) ),
inference(fof_simplification,[status(thm)],[c_0_208]) ).
fof(c_0_633,plain,
! [X17,X7,X29,X3] :
( hBOOL(hAPP(X29,X7))
| ~ hBOOL(hAPP(X29,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X29,X17,X3)))
| ~ c_in(X7,c_Wellfounded_Oacc(X17,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_209]) ).
fof(c_0_634,plain,
! [X17,X7,X29,X3] :
( hBOOL(hAPP(X29,X7))
| ~ hBOOL(hAPP(X29,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X29,X17,X3)))
| ~ c_in(X7,c_Wellfounded_Oacc(X17,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_210]) ).
fof(c_0_635,plain,
! [X17,X22,X15,X3] :
( c_Relation_Otrans(c_Relation_Oinv__image(X17,X22,X3,X15),X15)
| ~ c_Relation_Otrans(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_211]) ).
fof(c_0_636,plain,
! [X40,X41,X15,X3] :
( c_Finite__Set_Ofinite(c_Set_Oimage(X40,X41,X3,X15),X15)
| ~ c_Finite__Set_Ofinite(X41,X3) ),
inference(fof_simplification,[status(thm)],[c_0_212]) ).
fof(c_0_637,plain,
! [X17,X22,X15,X3] :
( c_Wellfounded_Owf(c_Relation_Oinv__image(X17,X22,X3,X15),X15)
| ~ c_Wellfounded_Owf(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_213]) ).
fof(c_0_638,plain,
! [X17,X22,X15,X3] :
( c_Relation_Osym(c_Relation_Oinv__image(X17,X22,X3,X15),X15)
| ~ c_Relation_Osym(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_214]) ).
fof(c_0_639,plain,
! [X25,X17,X15,X3] :
( c_lessequals(c_Relation_ODomain(X17,X3,X15),c_Relation_ODomain(X25,X3,X15),tc_fun(X3,tc_bool))
| ~ c_lessequals(X17,X25,tc_fun(tc_prod(X3,X15),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_215]) ).
fof(c_0_640,plain,
! [X25,X17,X28,X3] :
( c_in(X28,c_Transitive__Closure_Otrancl(X25,X3),tc_prod(X3,X3))
| ~ c_lessequals(X17,X25,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_in(X28,c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_216]) ).
fof(c_0_641,plain,
! [X7,X21,X19,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X7,X19,X3),X21,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X7,c_Lattices_Olower__semilattice__class_Oinf(X19,X21,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X7,X21,X3) ),
inference(fof_simplification,[status(thm)],[c_0_217]) ).
fof(c_0_642,plain,
! [X7,X19,X18,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(X18,c_Set_Oinsert(X7,X19,X3),tc_fun(X3,tc_bool)) = c_Set_Oinsert(X7,c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X7,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_218]) ).
fof(c_0_643,plain,
! [X11,X24,X3] :
( c_Transitive__Closure_Ortrancl(X11,X3) = c_Transitive__Closure_Ortrancl(X24,X3)
| ~ c_lessequals(X11,c_Transitive__Closure_Ortrancl(X24,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(X24,X11,tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_219]) ).
fof(c_0_644,plain,
! [X21,X19,X18,X3] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X18,X19,tc_fun(X3,tc_bool)),X21,tc_fun(X3,tc_bool))
| ~ c_lessequals(X19,X21,tc_fun(X3,tc_bool))
| ~ c_lessequals(X18,X21,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_220]) ).
fof(c_0_645,plain,
! [X21,X19,X18,X3] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X18,X19,tc_fun(X3,tc_bool)),X21,tc_fun(X3,tc_bool))
| ~ c_lessequals(X19,X21,tc_fun(X3,tc_bool))
| ~ c_lessequals(X18,X21,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_221]) ).
fof(c_0_646,plain,
! [X21,X19,X18,X3] :
( c_lessequals(X21,c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X21,X19,tc_fun(X3,tc_bool))
| ~ c_lessequals(X21,X18,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_222]) ).
fof(c_0_647,plain,
! [X21,X19,X18,X3] :
( c_lessequals(X21,c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X21,X19,tc_fun(X3,tc_bool))
| ~ c_lessequals(X21,X18,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_223]) ).
fof(c_0_648,plain,
! [X8] :
( c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Relation_Oconverse(X8,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_224]) ).
fof(c_0_649,plain,
! [X21,X19,X18,X3] :
( c_lessequals(X21,X19,tc_fun(X3,tc_bool))
| ~ c_lessequals(X21,c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_225]) ).
fof(c_0_650,plain,
! [X21,X19,X18,X3] :
( c_lessequals(X21,X18,tc_fun(X3,tc_bool))
| ~ c_lessequals(X21,c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_226]) ).
fof(c_0_651,plain,
! [X21,X19,X18,X3] :
( c_lessequals(X18,X21,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X18,X19,tc_fun(X3,tc_bool)),X21,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_227]) ).
fof(c_0_652,plain,
! [X21,X19,X18,X3] :
( c_lessequals(X19,X21,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X18,X19,tc_fun(X3,tc_bool)),X21,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_228]) ).
fof(c_0_653,plain,
! [X28,X3] :
( X28 = c_Pair(c_ATP__Linkup_Osko__Relation__XIdE__1__1(X28,X3),c_ATP__Linkup_Osko__Relation__XIdE__1__1(X28,X3),X3,X3)
| ~ c_in(X28,c_Relation_OId(X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_229]) ).
fof(c_0_654,plain,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Odistrib__lattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X12,X20,X3),X10,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X12,X10,X3),c_Lattices_Olower__semilattice__class_Oinf(X20,X10,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_230]) ).
fof(c_0_655,plain,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Odistrib__lattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X10,c_Lattices_Oupper__semilattice__class_Osup(X12,X20,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3),c_Lattices_Olower__semilattice__class_Oinf(X10,X20,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_231]) ).
fof(c_0_656,plain,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Odistrib__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X12,X20,X3),X10,X3) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X12,X10,X3),c_Lattices_Oupper__semilattice__class_Osup(X20,X10,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_232]) ).
fof(c_0_657,plain,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Odistrib__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Olower__semilattice__class_Oinf(X12,X20,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),c_Lattices_Oupper__semilattice__class_Osup(X10,X20,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_233]) ).
fof(c_0_658,plain,
! [X23,X19,X18,X3] :
( c_in(X23,X19,X3)
| c_in(X23,X18,X3)
| ~ c_in(X23,c_Lattices_Oupper__semilattice__class_Osup(X18,X19,tc_fun(X3,tc_bool)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_234]) ).
fof(c_0_659,plain,
! [X10,X19,X18,X3] :
( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)),X10))
| ~ hBOOL(hAPP(X19,X10))
| ~ hBOOL(hAPP(X18,X10)) ),
inference(fof_simplification,[status(thm)],[c_0_235]) ).
fof(c_0_660,plain,
! [X25,X17,X3] :
( c_lessequals(c_Transitive__Closure_Ortrancl(X17,X3),c_Transitive__Closure_Ortrancl(X25,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(X17,c_Transitive__Closure_Ortrancl(X25,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_236]) ).
fof(c_0_661,plain,
! [X10,X19,X18,X3] :
( c_lessequals(X18,X19,tc_fun(X3,tc_bool))
| c_in(X10,X18,X3)
| ~ c_lessequals(X18,c_Set_Oinsert(X10,X19,X3),tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_237]) ).
fof(c_0_662,plain,
! [X10,X19,X18,X3] :
( c_lessequals(X18,X19,tc_fun(X3,tc_bool))
| ~ c_lessequals(X18,c_Set_Oinsert(X10,X19,X3),tc_fun(X3,tc_bool))
| c_in(X10,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_238]) ).
fof(c_0_663,plain,
! [X12,X10,X18,X3] :
( hBOOL(hAPP(X18,X10))
| X12 = X10
| ~ hBOOL(hAPP(c_Set_Oinsert(X12,X18,X3),X10)) ),
inference(fof_simplification,[status(thm)],[c_0_239]) ).
fof(c_0_664,plain,
! [X7,X38,X21,X3] :
( c_lessequals(c_Set_Oinsert(X7,X21,X3),c_Set_Oinsert(X7,X38,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X21,X38,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_240]) ).
fof(c_0_665,plain,
! [X12,X10,X8] :
( c_in(c_Arrow__Order__Mirabelle_Obelow(X8,X10,X12),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X10 = X12 ),
inference(fof_simplification,[status(thm)],[c_0_241]) ).
fof(c_0_666,plain,
! [X12,X10,X8] :
( c_in(c_Arrow__Order__Mirabelle_Oabove(X8,X10,X12),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X10 = X12 ),
inference(fof_simplification,[status(thm)],[c_0_242]) ).
fof(c_0_667,plain,
! [X8] :
( c_in(c_Relation_Oconverse(X8,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_243]) ).
fof(c_0_668,plain,
! [X10,X19,X18,X3] :
( c_lessequals(c_Set_Oinsert(X10,X18,X3),X19,tc_fun(X3,tc_bool))
| ~ c_lessequals(X18,X19,tc_fun(X3,tc_bool))
| ~ c_in(X10,X19,X3) ),
inference(fof_simplification,[status(thm)],[c_0_244]) ).
fof(c_0_669,plain,
! [X25,X17,X3] :
( c_lessequals(c_Transitive__Closure_Ortrancl(X17,X3),c_Transitive__Closure_Ortrancl(X25,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(X17,X25,tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_245]) ).
fof(c_0_670,plain,
! [X10,X19,X18,X3] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X18,X19,tc_fun(X3,tc_bool)),X10))
| ~ hBOOL(hAPP(X19,X10)) ),
inference(fof_simplification,[status(thm)],[c_0_246]) ).
fof(c_0_671,plain,
! [X10,X19,X18,X3] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X18,X19,tc_fun(X3,tc_bool)),X10))
| ~ hBOOL(hAPP(X18,X10)) ),
inference(fof_simplification,[status(thm)],[c_0_247]) ).
fof(c_0_672,plain,
! [X21,X18,X3] :
( c_in(c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X18,X21,X3),X21,tc_fun(X3,tc_bool))
| ~ c_in(X18,c_Complete__Lattice_OSup__class_OSup(X21,tc_fun(X3,tc_bool)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_248]) ).
fof(c_0_673,plain,
! [X23,X19,X18,X3] :
( c_in(X23,X19,X3)
| ~ c_in(X23,c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_249]) ).
fof(c_0_674,plain,
! [X23,X19,X18,X3] :
( c_in(X23,X18,X3)
| ~ c_in(X23,c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_250]) ).
fof(c_0_675,plain,
! [X21,X18,X3] :
( c_in(X18,c_Complete__Lattice_OInf__class_OInf(X21,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X18,c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X18,X21,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_251]) ).
fof(c_0_676,plain,
! [X23,X19,X18,X3] :
( c_in(X23,c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X23,X19,X3)
| ~ c_in(X23,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_252]) ).
fof(c_0_677,plain,
! [X23,X19,X18,X3] :
( c_in(X23,c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X23,X19,X3)
| ~ c_in(X23,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_253]) ).
fof(c_0_678,plain,
! [X2,X21,X18,X3] :
( c_in(X18,X2,X3)
| ~ c_in(X2,X21,tc_fun(X3,tc_bool))
| ~ c_in(X18,c_Complete__Lattice_OInf__class_OInf(X21,tc_fun(X3,tc_bool)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_254]) ).
fof(c_0_679,plain,
! [X10,X17,X3] :
( c_in(X10,c_Wellfounded_Oacc(X17,X3),X3)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X17,X10,X3),c_Wellfounded_Oacc(X17,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_255]) ).
fof(c_0_680,plain,
! [X10,X24,X3] :
( ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X24,X10,X3),c_Wellfounded_Oacc(X24,X3),X3)
| c_in(X10,c_Wellfounded_Oacc(X24,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_256]) ).
fof(c_0_681,plain,
! [X10,X19,X18,X3] :
( c_lessequals(X18,X19,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X10,X18,X3),X19,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_257]) ).
fof(c_0_682,plain,
! [X17,X3] :
( c_Wellfounded_Owf(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X17,X3),X3,X3),X3)
| ~ c_Wellfounded_Owf(c_Relation_Oconverse(X17,X3,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_258]) ).
fof(c_0_683,plain,
! [X10,X19,X18,X3] :
( c_lessequals(X18,c_Set_Oinsert(X10,X19,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X18,X19,tc_fun(X3,tc_bool))
| c_in(X10,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_259]) ).
fof(c_0_684,plain,
! [X10,X19,X18,X3] :
( c_lessequals(X18,c_Set_Oinsert(X10,X19,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X18,X19,tc_fun(X3,tc_bool))
| c_in(X10,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_260]) ).
fof(c_0_685,plain,
! [X21,X18,X3] :
( c_in(X18,c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X18,X21,X3),X3)
| ~ c_in(X18,c_Complete__Lattice_OSup__class_OSup(X21,tc_fun(X3,tc_bool)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_261]) ).
fof(c_0_686,plain,
! [X17,X7,X29,X3] :
( hBOOL(hAPP(X29,X7))
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X29,X17,X3),c_Wellfounded_Oacc(X17,X3),X3)
| ~ c_in(X7,c_Wellfounded_Oacc(X17,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_262]) ).
fof(c_0_687,plain,
! [X17,X7,X29,X3] :
( hBOOL(hAPP(X29,X7))
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X29,X17,X3),c_Wellfounded_Oacc(X17,X3),X3)
| ~ c_in(X7,c_Wellfounded_Oacc(X17,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_263]) ).
fof(c_0_688,plain,
! [X10,X19,X18,X3] :
( c_in(X10,X19,X3)
| ~ c_lessequals(c_Set_Oinsert(X10,X18,X3),X19,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_264]) ).
fof(c_0_689,plain,
! [X10,X6,X7,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X7,X6,X3),X10,X3)
| ~ c_lessequals(X6,X10,X3)
| ~ c_lessequals(X7,X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_265]) ).
fof(c_0_690,plain,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X12,X20,X3),X10,X3)
| ~ c_lessequals(X20,X10,X3)
| ~ c_lessequals(X12,X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_266]) ).
fof(c_0_691,plain,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X20,X3)
| ~ c_lessequals(X12,X20,X3)
| ~ c_lessequals(X10,X20,X3) ),
inference(fof_simplification,[status(thm)],[c_0_267]) ).
fof(c_0_692,plain,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X10,c_Lattices_Olower__semilattice__class_Oinf(X12,X20,X3),X3)
| ~ c_lessequals(X10,X20,X3)
| ~ c_lessequals(X10,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_268]) ).
fof(c_0_693,plain,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X10,c_Lattices_Olower__semilattice__class_Oinf(X12,X20,X3),X3)
| ~ c_lessequals(X10,X20,X3)
| ~ c_lessequals(X10,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_269]) ).
fof(c_0_694,plain,
! [X10,X6,X7,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X10,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,X3),X3)
| ~ c_lessequals(X10,X6,X3)
| ~ c_lessequals(X10,X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_270]) ).
fof(c_0_695,plain,
! [X2,X21,X18,X3] :
( c_in(X18,c_Complete__Lattice_OSup__class_OSup(X21,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X18,X2,X3)
| ~ c_in(X2,X21,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_271]) ).
fof(c_0_696,plain,
! [X25,X17,X3] :
( c_lessequals(c_Relation_OField(X17,X3),c_Relation_OField(X25,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X17,X25,tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_272]) ).
fof(c_0_697,plain,
! [X33,X34,X3] :
( c_lessequals(c_Wellfounded_Oacc(X33,X3),c_Wellfounded_Oacc(X34,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X34,X33,tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_273]) ).
fof(c_0_698,plain,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X20,X3) = c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Oupper__semilattice__class_Osup(X12,X20,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_274]) ).
fof(c_0_699,plain,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Oupper__semilattice__class_Osup(X12,X20,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X12,c_Lattices_Oupper__semilattice__class_Osup(X10,X20,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_275]) ).
fof(c_0_700,plain,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Oupper__semilattice__class_Osup(X12,X20,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X12,c_Lattices_Oupper__semilattice__class_Osup(X10,X20,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_276]) ).
fof(c_0_701,plain,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X20,X3) = c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Oupper__semilattice__class_Osup(X12,X20,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_277]) ).
fof(c_0_702,plain,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3),X20,X3) = c_Lattices_Olower__semilattice__class_Oinf(X10,c_Lattices_Olower__semilattice__class_Oinf(X12,X20,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_278]) ).
fof(c_0_703,plain,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X10,c_Lattices_Olower__semilattice__class_Oinf(X12,X20,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X12,c_Lattices_Olower__semilattice__class_Oinf(X10,X20,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_279]) ).
fof(c_0_704,plain,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X10,c_Lattices_Olower__semilattice__class_Oinf(X12,X20,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X12,c_Lattices_Olower__semilattice__class_Oinf(X10,X20,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_280]) ).
fof(c_0_705,plain,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3),X20,X3) = c_Lattices_Olower__semilattice__class_Oinf(X10,c_Lattices_Olower__semilattice__class_Oinf(X12,X20,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_281]) ).
fof(c_0_706,plain,
! [X23,X18,X3] :
( c_in(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X18,X23,X3),X18,X3)
| ~ c_in(X23,c_Relation_OId__on(X18,X3),tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_282]) ).
fof(c_0_707,plain,
! [X10,X8] :
( c_in(c_Arrow__Order__Mirabelle_Omktop(X8,X10),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_283]) ).
fof(c_0_708,plain,
! [X10,X8] :
( c_in(c_Arrow__Order__Mirabelle_Omkbot(X8,X10),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_284]) ).
fof(c_0_709,plain,
! [X21,X19,X18,X3] :
( c_lessequals(X18,X21,tc_fun(X3,tc_bool))
| ~ c_lessequals(X19,X21,tc_fun(X3,tc_bool))
| ~ c_lessequals(X18,X19,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_285]) ).
fof(c_0_710,axiom,
! [X7,X19,X18,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(X18,c_Set_Oinsert(X7,X19,X3),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool))
| c_in(X7,X18,X3) ),
c_0_286 ).
fof(c_0_711,axiom,
! [X7,X21,X19,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X7,X19,X3),X21,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X19,X21,tc_fun(X3,tc_bool))
| c_in(X7,X21,X3) ),
c_0_287 ).
fof(c_0_712,plain,
! [X25,X17,X3] :
( c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X17,X25,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Relation_Osym(X25,X3)
| ~ c_Relation_Osym(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_288]) ).
fof(c_0_713,plain,
! [X25,X17,X3] :
( c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X17,X25,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Relation_Osym(X25,X3)
| ~ c_Relation_Osym(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_289]) ).
fof(c_0_714,plain,
! [X25,X17,X3] :
( c_Relation_Otrans(c_Lattices_Olower__semilattice__class_Oinf(X17,X25,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Relation_Otrans(X25,X3)
| ~ c_Relation_Otrans(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_290]) ).
fof(c_0_715,plain,
! [X10,X6,X7,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X10,X7,X3)
| ~ c_lessequals(X10,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_291]) ).
fof(c_0_716,plain,
! [X10,X6,X7,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X10,X6,X3)
| ~ c_lessequals(X10,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_292]) ).
fof(c_0_717,plain,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X10,X12,X3)
| ~ c_lessequals(X10,c_Lattices_Olower__semilattice__class_Oinf(X12,X20,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_293]) ).
fof(c_0_718,plain,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(X10,X20,X3)
| ~ c_lessequals(X10,c_Lattices_Olower__semilattice__class_Oinf(X12,X20,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_294]) ).
fof(c_0_719,plain,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X12,X20,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X20,X3) ),
inference(fof_simplification,[status(thm)],[c_0_295]) ).
fof(c_0_720,plain,
! [X20,X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X10,X20,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X20,X3) ),
inference(fof_simplification,[status(thm)],[c_0_296]) ).
fof(c_0_721,plain,
! [X10,X6,X7,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X6,X10,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X7,X6,X3),X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_297]) ).
fof(c_0_722,plain,
! [X10,X6,X7,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X7,X10,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X7,X6,X3),X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_298]) ).
fof(c_0_723,plain,
! [X6,X7,X18,X3] :
( c_in(X7,X18,X3)
| X7 = X6
| ~ c_in(X7,c_Set_Oinsert(X6,X18,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_299]) ).
fof(c_0_724,axiom,
! [X21,X18,X3] :
( c_in(X18,c_Complete__Lattice_OInf__class_OInf(X21,tc_fun(X3,tc_bool)),X3)
| c_in(c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X18,X21,X3),X21,tc_fun(X3,tc_bool)) ),
c_0_300 ).
fof(c_0_725,plain,
! [X17,X18,X3] :
( c_Relation_Orefl__on(X18,X17,X3)
| ~ c_Relation_Orefl__on(X18,c_Relation_Oconverse(X17,X3,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_301]) ).
fof(c_0_726,plain,
! [X17,X18,X3] :
( c_Relation_Ototal__on(X18,X17,X3)
| ~ c_Relation_Ototal__on(X18,c_Relation_Oconverse(X17,X3,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_302]) ).
fof(c_0_727,plain,
! [X6,X19,X18,X3] :
( c_lessequals(X18,c_Set_Oinsert(X6,X19,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X18,X19,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_303]) ).
fof(c_0_728,plain,
! [X17,X3] :
( c_Relation_Otrans(c_Lattices_Oupper__semilattice__class_Osup(X17,c_Relation_OId(X3),tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Relation_Otrans(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_304]) ).
fof(c_0_729,plain,
! [X23,X19,X18,X3] :
( c_in(X23,c_Lattices_Oupper__semilattice__class_Osup(X18,X19,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X23,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_305]) ).
fof(c_0_730,plain,
! [X23,X19,X18,X3] :
( c_in(X23,c_Lattices_Oupper__semilattice__class_Osup(X18,X19,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X23,X19,X3) ),
inference(fof_simplification,[status(thm)],[c_0_306]) ).
fof(c_0_731,plain,
! [X36,X17,X3] :
( c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X17,X36,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Wellfounded_Owf(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_307]) ).
fof(c_0_732,plain,
! [X36,X17,X3] :
( c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X36,X17,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Wellfounded_Owf(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_308]) ).
fof(c_0_733,plain,
! [X12,X10,X18,X3] :
( hBOOL(hAPP(c_Set_Oinsert(X12,X18,X3),X10))
| ~ hBOOL(hAPP(X18,X10)) ),
inference(fof_simplification,[status(thm)],[c_0_309]) ).
fof(c_0_734,axiom,
! [X10,X19,X18,X3] :
( c_Set_Oinsert(X10,X18,X3) != c_Set_Oinsert(X10,X19,X3)
| c_in(X10,X19,X3)
| c_in(X10,X18,X3)
| X18 = X19 ),
c_0_310 ).
fof(c_0_735,plain,
! [X10,X17,X29] :
( hBOOL(hAPP(X29,X10))
| ~ hBOOL(hAPP(X29,v_sko__Wellfounded__Xacc__Xinduct__1(X29,X17)))
| ~ c_in(X10,c_Wellfounded_Oacc(X17,t_a),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_311]) ).
fof(c_0_736,plain,
! [X10,X17,X29] :
( hBOOL(hAPP(X29,X10))
| ~ hBOOL(hAPP(X29,v_sko__Wellfounded__Xacc__Xinducts__1(X29,X17)))
| ~ c_in(X10,c_Wellfounded_Oacc(X17,t_a),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_312]) ).
fof(c_0_737,plain,
! [X42,X41,X3] :
( c_Finite__Set_Ofinite(X41,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X41,X42,tc_fun(X3,tc_bool)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_313]) ).
fof(c_0_738,plain,
! [X42,X41,X3] :
( c_Finite__Set_Ofinite(X42,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X41,X42,tc_fun(X3,tc_bool)),X3) ),
inference(fof_simplification,[status(thm)],[c_0_314]) ).
fof(c_0_739,plain,
! [X19,X18,X3] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X18,tc_fun(X3,tc_bool)),X19,tc_fun(X3,tc_bool))
| ~ c_in(X19,X18,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_315]) ).
fof(c_0_740,plain,
! [X19,X18,X3] :
( c_lessequals(X19,c_Complete__Lattice_OSup__class_OSup(X18,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_in(X19,X18,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_316]) ).
fof(c_0_741,plain,
! [X10,X24,X31,X3] :
( c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X31,X24,X3),X31,X3)
| ~ c_in(X10,X31,X3)
| ~ c_Wellfounded_Owf(X24,X3) ),
inference(fof_simplification,[status(thm)],[c_0_317]) ).
fof(c_0_742,plain,
! [X16,X17,X31,X3] :
( c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X31,X17,X3),X31,X3)
| ~ c_in(X16,X31,X3)
| ~ c_Wellfounded_Owf(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_318]) ).
fof(c_0_743,plain,
! [X32,X19,X18,X3] :
( c_in(X32,X19,X3)
| ~ c_in(X32,X18,X3)
| ~ c_lessequals(X18,X19,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_319]) ).
fof(c_0_744,plain,
! [X10,X19,X18,X3] :
( c_in(X10,X19,X3)
| ~ c_lessequals(X18,X19,tc_fun(X3,tc_bool))
| ~ c_in(X10,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_320]) ).
fof(c_0_745,plain,
! [X23,X19,X18,X3] :
( c_in(X23,X19,X3)
| ~ c_in(X23,X18,X3)
| ~ c_lessequals(X18,X19,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_321]) ).
fof(c_0_746,plain,
! [X10,X19,X18,X3] :
( c_in(X10,X19,X3)
| ~ c_in(X10,X18,X3)
| ~ c_lessequals(X18,X19,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_322]) ).
fof(c_0_747,plain,
! [X10,X6,X7,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,X3),X10,X3)
| ~ c_lessequals(X7,X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_323]) ).
fof(c_0_748,plain,
! [X10,X6,X7,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,X3),X10,X3)
| ~ c_lessequals(X6,X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_324]) ).
fof(c_0_749,plain,
! [X10,X6,X7,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X10,c_Lattices_Oupper__semilattice__class_Osup(X7,X6,X3),X3)
| ~ c_lessequals(X10,X6,X3) ),
inference(fof_simplification,[status(thm)],[c_0_325]) ).
fof(c_0_750,plain,
! [X10,X6,X7,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X10,c_Lattices_Oupper__semilattice__class_Osup(X7,X6,X3),X3)
| ~ c_lessequals(X10,X7,X3) ),
inference(fof_simplification,[status(thm)],[c_0_326]) ).
fof(c_0_751,plain,
! [X6,X7,X18,X3] :
( c_in(X7,c_Set_Oinsert(X6,X18,X3),X3)
| ~ c_in(X7,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_327]) ).
fof(c_0_752,plain,
! [X6,X7,X19,X3] :
( c_in(X7,c_Set_Oinsert(X6,X19,X3),X3)
| ~ c_in(X7,X19,X3) ),
inference(fof_simplification,[status(thm)],[c_0_328]) ).
fof(c_0_753,plain,
! [X17,X18,X3] :
( c_Relation_Orefl__on(X18,c_Relation_Oconverse(X17,X3,X3),X3)
| ~ c_Relation_Orefl__on(X18,X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_329]) ).
fof(c_0_754,plain,
! [X17,X18,X3] :
( c_Relation_Ototal__on(X18,c_Relation_Oconverse(X17,X3,X3),X3)
| ~ c_Relation_Ototal__on(X18,X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_330]) ).
fof(c_0_755,plain,
! [X19,X18,X3] :
( X18 = X19
| ~ c_lessequals(X19,X18,tc_fun(X3,tc_bool))
| ~ c_lessequals(X18,X19,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_331]) ).
fof(c_0_756,plain,
! [X19,X18,X3] :
( X18 = X19
| ~ c_lessequals(X19,X18,tc_fun(X3,tc_bool))
| ~ c_lessequals(X18,X19,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_332]) ).
fof(c_0_757,plain,
! [X17,X28,X3] :
( c_Wellfounded_Owf(X28,X3)
| ~ c_lessequals(X28,X17,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Wellfounded_Owf(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_333]) ).
fof(c_0_758,plain,
! [X10,X27,X22,X15,X3] :
( ~ class_HOL_Oord(X15)
| c_lessequals(hAPP(X22,X10),hAPP(X27,X10),X15)
| ~ c_lessequals(X22,X27,tc_fun(X3,X15)) ),
inference(fof_simplification,[status(thm)],[c_0_334]) ).
fof(c_0_759,plain,
! [X20,X12,X10,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X10,X20,X3)
| ~ c_lessequals(X12,X20,X3)
| ~ c_lessequals(X10,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_335]) ).
fof(c_0_760,plain,
! [X20,X12,X10,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X20,X10,X3)
| ~ c_lessequals(X20,X12,X3)
| ~ c_lessequals(X12,X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_336]) ).
fof(c_0_761,plain,
! [X17,X28,X3] :
( c_in(X28,c_Transitive__Closure_Ortrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(X28,X17,tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_337]) ).
fof(c_0_762,plain,
! [X17,X28,X3] :
( c_in(X28,c_Transitive__Closure_Otrancl(X17,X3),tc_prod(X3,X3))
| ~ c_in(X28,X17,tc_prod(X3,X3)) ),
inference(fof_simplification,[status(thm)],[c_0_338]) ).
fof(c_0_763,plain,
! [X10,X39,X3] :
( c_Finite__Set_Ofinite(c_Complete__Lattice_OInf__class_OInf(X39,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X10,X3)
| ~ c_in(X10,X39,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_339]) ).
fof(c_0_764,plain,
! [X17,X18,X3] :
( c_Complete__Lattice_OSup__class_OSup(c_Equiv__Relations_Oquotient(X18,X17,X3),tc_fun(X3,tc_bool)) = X18
| ~ c_Equiv__Relations_Oequiv(X18,X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_340]) ).
fof(c_0_765,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_341]) ).
fof(c_0_766,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_342]) ).
fof(c_0_767,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X10,c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_343]) ).
fof(c_0_768,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X10,c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_344]) ).
fof(c_0_769,plain,
! [X42,X41,X3] :
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X41,X42,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X42,X3)
| ~ c_Finite__Set_Ofinite(X41,X3) ),
inference(fof_simplification,[status(thm)],[c_0_345]) ).
fof(c_0_770,plain,
! [X42,X41,X3] :
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X41,X42,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X42,X3)
| ~ c_Finite__Set_Ofinite(X41,X3) ),
inference(fof_simplification,[status(thm)],[c_0_346]) ).
fof(c_0_771,plain,
! [X7,X18,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X7,X18,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X7,c_Complete__Lattice_OInf__class_OInf(X18,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_347]) ).
fof(c_0_772,plain,
! [X7,X18,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X7,X18,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X7,c_Complete__Lattice_OSup__class_OSup(X18,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_348]) ).
fof(c_0_773,plain,
! [X17,X3] :
( c_Relation_Otrans(X17,X3)
| ~ c_Relation_Otrans(c_Relation_Oconverse(X17,X3,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_349]) ).
fof(c_0_774,plain,
! [X7,X18,X3] :
( c_Finite__Set_Ofinite(X18,X3)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X7,X18,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_350]) ).
fof(c_0_775,plain,
! [X17,X3] :
( c_Relation_Osym(X17,X3)
| ~ c_Relation_Osym(c_Relation_Oconverse(X17,X3,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_351]) ).
fof(c_0_776,axiom,
! [X19,X18,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X18,X19,tc_fun(X3,tc_bool)) != X19
| c_lessequals(X18,X19,tc_fun(X3,tc_bool)) ),
c_0_352 ).
fof(c_0_777,plain,
! [X19,X18,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)) = X18
| ~ c_lessequals(X18,X19,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_353]) ).
fof(c_0_778,plain,
! [X19,X18,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(X18,X19,tc_fun(X3,tc_bool)) = X19
| ~ c_lessequals(X19,X18,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_354]) ).
fof(c_0_779,plain,
! [X19,X18,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X18,X19,tc_fun(X3,tc_bool)) = X19
| ~ c_lessequals(X18,X19,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_355]) ).
fof(c_0_780,plain,
! [X19,X18,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X18,X19,tc_fun(X3,tc_bool)) = X18
| ~ c_lessequals(X19,X18,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_356]) ).
fof(c_0_781,plain,
! [X10,X31,X29,X3] :
( hBOOL(hAPP(X31,X10))
| ~ c_lessequals(X29,X31,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X29,X10)) ),
inference(fof_simplification,[status(thm)],[c_0_357]) ).
fof(c_0_782,plain,
! [X10,X31,X29,X3] :
( hBOOL(hAPP(X31,X10))
| ~ hBOOL(hAPP(X29,X10))
| ~ c_lessequals(X29,X31,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_358]) ).
fof(c_0_783,plain,
! [X42,X41,X3] :
( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X41,X42,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X42,X3) ),
inference(fof_simplification,[status(thm)],[c_0_359]) ).
fof(c_0_784,plain,
! [X42,X41,X3] :
( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X41,X42,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X41,X3) ),
inference(fof_simplification,[status(thm)],[c_0_360]) ).
fof(c_0_785,plain,
! [X17,X3] :
( c_Wellfounded_Owf(X17,X3)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X17,X3),c_Wellfounded_Oacc(X17,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_361]) ).
fof(c_0_786,plain,
! [X17,X3] :
( c_Wellfounded_Owf(X17,X3)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X17,X3),c_Wellfounded_Oacc(X17,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_362]) ).
fof(c_0_787,plain,
! [X12,X10,X3] :
( ~ class_Orderings_Oorder(X3)
| X10 = X12
| ~ c_lessequals(X10,X12,X3)
| ~ c_lessequals(X12,X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_363]) ).
fof(c_0_788,plain,
! [X12,X10,X3] :
( ~ class_Orderings_Oorder(X3)
| X10 = X12
| ~ c_lessequals(X12,X10,X3)
| ~ c_lessequals(X10,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_364]) ).
fof(c_0_789,plain,
! [X12,X10,X3] :
( ~ class_Orderings_Oorder(X3)
| X10 = X12
| ~ c_lessequals(X12,X10,X3)
| ~ c_lessequals(X10,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_365]) ).
fof(c_0_790,plain,
! [X10,X18,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X18,X3),X10,X3)
| ~ c_in(X10,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_366]) ).
fof(c_0_791,plain,
! [X10,X18,X3] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_lessequals(X10,c_Complete__Lattice_OSup__class_OSup(X18,X3),X3)
| ~ c_in(X10,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_367]) ).
fof(c_0_792,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3),X3) = X10 ),
inference(fof_simplification,[status(thm)],[c_0_368]) ).
fof(c_0_793,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X10,c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X3) = X10 ),
inference(fof_simplification,[status(thm)],[c_0_369]) ).
fof(c_0_794,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X10,c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_370]) ).
fof(c_0_795,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X12,c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_371]) ).
fof(c_0_796,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(X12,c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_372]) ).
fof(c_0_797,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(X10,c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3),X3) ),
inference(fof_simplification,[status(thm)],[c_0_373]) ).
fof(c_0_798,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3),X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_374]) ).
fof(c_0_799,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_375]) ).
fof(c_0_800,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3),X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_376]) ).
fof(c_0_801,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3),X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_377]) ).
fof(c_0_802,plain,
! [X19,X18,X3] :
( c_Finite__Set_Ofinite(X18,X3)
| ~ c_Finite__Set_Ofinite(X19,X3)
| ~ c_lessequals(X18,X19,tc_fun(X3,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_378]) ).
fof(c_0_803,plain,
! [X19,X18,X3] :
( c_Finite__Set_Ofinite(X18,X3)
| ~ c_lessequals(X18,X19,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X19,X3) ),
inference(fof_simplification,[status(thm)],[c_0_379]) ).
fof(c_0_804,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3) != X10
| c_lessequals(X10,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_380]) ).
fof(c_0_805,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3) != X12
| c_lessequals(X10,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_381]) ).
fof(c_0_806,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3) = X10
| ~ c_lessequals(X10,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_382]) ).
fof(c_0_807,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3) = X12
| ~ c_lessequals(X12,X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_383]) ).
fof(c_0_808,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3) = X10
| ~ c_lessequals(X12,X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_384]) ).
fof(c_0_809,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3) = X12
| ~ c_lessequals(X10,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_385]) ).
fof(c_0_810,axiom,
! [X6,X7] :
( c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X7,X6),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X7 = X6 ),
c_0_386 ).
fof(c_0_811,plain,
! [X17,X3] :
( c_Relation_Otrans(c_Relation_Oconverse(X17,X3,X3),X3)
| ~ c_Relation_Otrans(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_387]) ).
fof(c_0_812,plain,
! [X7,X18,X3] :
( c_Finite__Set_Ofinite(c_Set_Oinsert(X7,X18,X3),X3)
| ~ c_Finite__Set_Ofinite(X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_388]) ).
fof(c_0_813,plain,
! [X17,X3] :
( c_Relation_Osym(c_Relation_Oconverse(X17,X3,X3),X3)
| ~ c_Relation_Osym(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_389]) ).
fof(c_0_814,plain,
! [X7,X18,X3] :
( c_Set_Oinsert(X7,X18,X3) = X18
| ~ c_in(X7,X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_390]) ).
fof(c_0_815,plain,
! [X17,X18,X3] :
( c_Relation_Orefl__on(X18,X17,X3)
| ~ c_Equiv__Relations_Oequiv(X18,X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_391]) ).
fof(c_0_816,plain,
! [X12,X10,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X12,X10,X3)
| c_lessequals(X10,X12,X3) ),
inference(fof_simplification,[status(thm)],[c_0_392]) ).
fof(c_0_817,plain,
! [X10,X11,X3] :
( hBOOL(hAPP(X11,X10))
| ~ c_in(X10,X11,X3) ),
inference(fof_simplification,[status(thm)],[c_0_393]) ).
fof(c_0_818,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3) = c_Lattices_Olower__semilattice__class_Oinf(X12,X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_394]) ).
fof(c_0_819,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X10,X12,X3) = c_Lattices_Olower__semilattice__class_Oinf(X12,X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_395]) ).
fof(c_0_820,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3) = c_Lattices_Oupper__semilattice__class_Osup(X12,X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_396]) ).
fof(c_0_821,plain,
! [X12,X10,X3] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,X12,X3) = c_Lattices_Oupper__semilattice__class_Osup(X12,X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_397]) ).
fof(c_0_822,plain,
! [X10,X17,X3] :
( c_in(X10,c_Wellfounded_Oacc(X17,X3),X3)
| ~ c_Wellfounded_Owf(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_398]) ).
fof(c_0_823,plain,
! [X10,X11,X3] :
( c_in(X10,X11,X3)
| ~ hBOOL(hAPP(X11,X10)) ),
inference(fof_simplification,[status(thm)],[c_0_399]) ).
fof(c_0_824,axiom,
! [X17,X3] :
( c_Relation_Oconverse(X17,X3,X3) != X17
| c_Relation_Osym(X17,X3) ),
c_0_400 ).
fof(c_0_825,plain,
! [X17,X18,X3] :
( c_Relation_Otrans(X17,X3)
| ~ c_Equiv__Relations_Oequiv(X18,X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_401]) ).
fof(c_0_826,plain,
! [X17,X18,X3] :
( c_Relation_Osym(X17,X3)
| ~ c_Equiv__Relations_Oequiv(X18,X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_402]) ).
fof(c_0_827,plain,
! [X1,X2,X3] :
( X2 = X1
| ~ c_fequal(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[c_0_403]) ).
fof(c_0_828,plain,
! [X17,X3] :
( c_Relation_Oconverse(X17,X3,X3) = X17
| ~ c_Relation_Osym(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_404]) ).
fof(c_0_829,plain,
! [X17,X3] :
( c_Relation_Osym(c_Transitive__Closure_Ortrancl(X17,X3),X3)
| ~ c_Relation_Osym(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_405]) ).
fof(c_0_830,plain,
! [X17,X3] :
( c_Relation_Osym(c_Transitive__Closure_Otrancl(X17,X3),X3)
| ~ c_Relation_Osym(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_406]) ).
fof(c_0_831,plain,
! [X17,X3] :
( c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X17,X3),X3)
| ~ c_Wellfounded_Owf(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_407]) ).
fof(c_0_832,plain,
! [X10,X3] :
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X10,X10,X3) = X10 ),
inference(fof_simplification,[status(thm)],[c_0_408]) ).
fof(c_0_833,plain,
! [X10,X3] :
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X10,X10,X3) = X10 ),
inference(fof_simplification,[status(thm)],[c_0_409]) ).
fof(c_0_834,plain,
! [X10,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X10,X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_410]) ).
fof(c_0_835,plain,
! [X10,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X10,X10,X3) ),
inference(fof_simplification,[status(thm)],[c_0_411]) ).
fof(c_0_836,plain,
! [X4,X5] :
( class_Finite__Set_Ofinite_Ofinite(tc_prod(X4,X5))
| ~ class_Finite__Set_Ofinite_Ofinite(X5)
| ~ class_Finite__Set_Ofinite_Ofinite(X4) ),
inference(fof_simplification,[status(thm)],[c_0_412]) ).
fof(c_0_837,plain,
! [X4,X5] :
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X4,X5))
| ~ class_Finite__Set_Ofinite_Ofinite(X5)
| ~ class_Finite__Set_Ofinite_Ofinite(X4) ),
inference(fof_simplification,[status(thm)],[c_0_413]) ).
fof(c_0_838,plain,
! [X17,X3] :
( c_Transitive__Closure_Otrancl(X17,X3) = X17
| ~ c_Relation_Otrans(X17,X3) ),
inference(fof_simplification,[status(thm)],[c_0_414]) ).
fof(c_0_839,plain,
! [X4,X5] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X4,X5))
| ~ class_Complete__Lattice_Ocomplete__lattice(X5) ),
inference(fof_simplification,[status(thm)],[c_0_415]) ).
fof(c_0_840,plain,
! [X4,X5] :
( class_Lattices_Oupper__semilattice(tc_fun(X4,X5))
| ~ class_Lattices_Olattice(X5) ),
inference(fof_simplification,[status(thm)],[c_0_416]) ).
fof(c_0_841,plain,
! [X4,X5] :
( class_Lattices_Olower__semilattice(tc_fun(X4,X5))
| ~ class_Lattices_Olattice(X5) ),
inference(fof_simplification,[status(thm)],[c_0_417]) ).
fof(c_0_842,plain,
! [X4,X5] :
( class_Lattices_Odistrib__lattice(tc_fun(X4,X5))
| ~ class_Lattices_Odistrib__lattice(X5) ),
inference(fof_simplification,[status(thm)],[c_0_418]) ).
fof(c_0_843,plain,
! [X4,X5] :
( class_Orderings_Opreorder(tc_fun(X4,X5))
| ~ class_Orderings_Opreorder(X5) ),
inference(fof_simplification,[status(thm)],[c_0_419]) ).
fof(c_0_844,plain,
! [X4,X5] :
( class_Lattices_Olattice(tc_fun(X4,X5))
| ~ class_Lattices_Olattice(X5) ),
inference(fof_simplification,[status(thm)],[c_0_420]) ).
fof(c_0_845,plain,
! [X4,X5] :
( class_Orderings_Oorder(tc_fun(X4,X5))
| ~ class_Orderings_Oorder(X5) ),
inference(fof_simplification,[status(thm)],[c_0_421]) ).
fof(c_0_846,plain,
! [X4,X5] :
( class_HOL_Oord(tc_fun(X4,X5))
| ~ class_HOL_Oord(X5) ),
inference(fof_simplification,[status(thm)],[c_0_422]) ).
fof(c_0_847,plain,
! [X18,X3] :
( ~ class_Finite__Set_Ofinite_Ofinite(X3)
| c_Finite__Set_Ofinite(X18,X3) ),
inference(fof_simplification,[status(thm)],[c_0_423]) ).
fof(c_0_848,plain,
! [X27,X28,X29,X30,X31,X32,X33] :
( c_in(c_Pair(X30,c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X30,X29,X28,X27,X33,X32,X31),X33,X31),X28,tc_prod(X33,X31))
| ~ c_in(c_Pair(X30,X29,X33,X32),c_Relation_Orel__comp(X28,X27,X33,X31,X32),tc_prod(X33,X32)) ),
inference(variable_rename,[status(thm)],[c_0_424]) ).
fof(c_0_849,plain,
! [X27,X28,X29,X30,X31,X32,X33] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X30,X29,X28,X27,X33,X32,X31),X29,X31,X32),X27,tc_prod(X31,X32))
| ~ c_in(c_Pair(X30,X29,X33,X32),c_Relation_Orel__comp(X28,X27,X33,X31,X32),tc_prod(X33,X32)) ),
inference(variable_rename,[status(thm)],[c_0_425]) ).
fof(c_0_850,plain,
! [X28,X29,X30,X31,X32,X33] :
( hAPP(X31,c_List_Osko__Recdef__Xcuts__eq__1__1(X31,X30,X29,X28,X33,X32)) != hAPP(X30,c_List_Osko__Recdef__Xcuts__eq__1__1(X31,X30,X29,X28,X33,X32))
| c_Recdef_Ocut(X31,X29,X28,X33,X32) = c_Recdef_Ocut(X30,X29,X28,X33,X32) ),
inference(variable_rename,[status(thm)],[c_0_426]) ).
fof(c_0_851,plain,
! [X25,X26,X27] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X26,X25,tc_fun(tc_prod(X27,X27),tc_bool)),X27)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X26,X26,X27,X27,X27),c_Relation_Orel__comp(X25,X26,X27,X27,X27),tc_fun(tc_prod(X27,X27),tc_bool)),X25,tc_fun(tc_prod(X27,X27),tc_bool)),X27) ),
inference(variable_rename,[status(thm)],[c_0_427]) ).
fof(c_0_852,plain,
! [X28,X29,X30,X31,X32,X33] :
( c_Recdef_Ocut(X31,X29,X28,X33,X32) = c_Recdef_Ocut(X30,X29,X28,X33,X32)
| c_in(c_Pair(c_List_Osko__Recdef__Xcuts__eq__1__1(X31,X30,X29,X28,X33,X32),X28,X33,X33),X29,tc_prod(X33,X33)) ),
inference(variable_rename,[status(thm)],[c_0_428]) ).
fof(c_0_853,plain,
! [X25,X26,X27] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X26,X26,X27,X27,X27),c_Relation_Orel__comp(X25,X26,X27,X27,X27),tc_fun(tc_prod(X27,X27),tc_bool)),X25,tc_fun(tc_prod(X27,X27),tc_bool)),X27)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X26,X25,tc_fun(tc_prod(X27,X27),tc_bool)),X27) ),
inference(variable_rename,[status(thm)],[c_0_429]) ).
fof(c_0_854,plain,
! [X39,X40,X41,X42,X43,X44] :
( c_lessequals(c_Product__Type_OSigma(X42,X41,X44,X43),c_Product__Type_OSigma(X40,X39,X44,X43),tc_fun(tc_prod(X44,X43),tc_bool))
| ~ c_lessequals(hAPP(X41,c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(X42,X41,X39,X44,X43)),hAPP(X39,c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(X42,X41,X39,X44,X43)),tc_fun(X43,tc_bool))
| ~ c_lessequals(X42,X40,tc_fun(X44,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_430]) ).
fof(c_0_855,plain,
! [X23,X24,X25,X26,X27] :
( c_in(X23,c_FuncSet_OPi(X25,X24,X27,X26),tc_fun(X27,X26))
| ~ c_in(hAPP(X23,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X25,X24,X23,X27,X26)),hAPP(X24,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X25,X24,X23,X27,X26)),X26) ),
inference(variable_rename,[status(thm)],[c_0_431]) ).
fof(c_0_856,plain,
! [X23,X24,X25,X26,X27] :
( c_in(X23,c_FuncSet_OPi(X25,X24,X27,X26),tc_fun(X27,X26))
| ~ c_in(hAPP(X23,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X25,X24,X23,X27,X26)),hAPP(X24,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X25,X24,X23,X27,X26)),X26) ),
inference(variable_rename,[status(thm)],[c_0_432]) ).
fof(c_0_857,plain,
! [X23,X24,X25,X26,X27] :
( c_in(X23,c_FuncSet_OPi(X25,c_COMBK(X24,tc_fun(X26,tc_bool),X27),X27,X26),tc_fun(X27,X26))
| ~ c_in(hAPP(X23,c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X25,X24,X23,X27,X26)),X24,X26) ),
inference(variable_rename,[status(thm)],[c_0_433]) ).
fof(c_0_858,plain,
! [X27,X28,X29,X30,X31,X32,X33,X34] :
( c_lessequals(c_Relation_Orel__comp(X28,X27,X34,X33,X32),c_Product__Type_OSigma(X31,c_COMBK(X29,tc_fun(X32,tc_bool),X34),X34,X32),tc_fun(tc_prod(X34,X32),tc_bool))
| ~ c_lessequals(X27,c_Product__Type_OSigma(X30,c_COMBK(X29,tc_fun(X32,tc_bool),X33),X33,X32),tc_fun(tc_prod(X33,X32),tc_bool))
| ~ c_lessequals(X28,c_Product__Type_OSigma(X31,c_COMBK(X30,tc_fun(X33,tc_bool),X34),X34,X33),tc_fun(tc_prod(X34,X33),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_434]) ).
fof(c_0_859,plain,
! [X19,X20,X21,X22,X23] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X21,X20,X19,X22,X23),X20,X22,X23),X19,tc_prod(X22,X23))
| ~ c_in(X20,c_Relation_OImage(X19,X21,X22,X23),X23) ),
inference(variable_rename,[status(thm)],[c_0_435]) ).
fof(c_0_860,plain,
! [X19,X20,X21,X22,X23] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X21,X20,X19,X22,X23),X20,X22,X23),X19,tc_prod(X22,X23))
| ~ c_in(X20,c_Relation_OImage(X19,X21,X22,X23),X23) ),
inference(variable_rename,[status(thm)],[c_0_436]) ).
fof(c_0_861,plain,
! [X37,X38,X39,X40,X41,X42,X43] :
( c_lessequals(c_Relation_Orel__comp(X39,X37,X43,X42,X41),c_Relation_Orel__comp(X40,X38,X43,X42,X41),tc_fun(tc_prod(X43,X41),tc_bool))
| ~ c_lessequals(X37,X38,tc_fun(tc_prod(X42,X41),tc_bool))
| ~ c_lessequals(X39,X40,tc_fun(tc_prod(X43,X42),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_437]) ).
fof(c_0_862,plain,
! [X26,X27,X28] :
( c_lessequals(c_Transitive__Closure_Ortrancl(X27,X28),X26,tc_fun(tc_prod(X28,X28),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Ortrancl(X27,X28),X26,tc_fun(tc_prod(X28,X28),tc_bool)),X27,X28,X28,X28),X26,tc_fun(tc_prod(X28,X28),tc_bool))
| ~ c_lessequals(c_Relation_OId(X28),X26,tc_fun(tc_prod(X28,X28),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_438]) ).
fof(c_0_863,plain,
! [X26,X27,X28] :
( c_lessequals(c_Transitive__Closure_Otrancl(X27,X28),X26,tc_fun(tc_prod(X28,X28),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Otrancl(X27,X28),X26,tc_fun(tc_prod(X28,X28),tc_bool)),X27,X28,X28,X28),X26,tc_fun(tc_prod(X28,X28),tc_bool))
| ~ c_lessequals(X27,X26,tc_fun(tc_prod(X28,X28),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_439]) ).
fof(c_0_864,plain,
! [X27,X28,X29,X30,X31,X32,X33,X34] :
( c_in(c_Pair(X31,X29,X34,X32),c_Relation_Orel__comp(X28,X27,X34,X33,X32),tc_prod(X34,X32))
| ~ c_in(c_Pair(X30,X29,X33,X32),X27,tc_prod(X33,X32))
| ~ c_in(c_Pair(X31,X30,X34,X33),X28,tc_prod(X34,X33)) ),
inference(variable_rename,[status(thm)],[c_0_440]) ).
fof(c_0_865,plain,
! [X28,X29,X30,X31,X32,X33,X34] :
( c_Recdef_Ocut(X32,X30,X29,X34,X33) != c_Recdef_Ocut(X31,X30,X29,X34,X33)
| hAPP(X32,X28) = hAPP(X31,X28)
| ~ c_in(c_Pair(X28,X29,X34,X34),X30,tc_prod(X34,X34)) ),
inference(variable_rename,[status(thm)],[c_0_441]) ).
fof(c_0_866,plain,
! [X25,X26,X27] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X26,X25,tc_fun(tc_prod(X27,X27),tc_bool)),X27)
| ~ c_lessequals(c_Relation_Orel__comp(X26,X25,X27,X27,X27),X26,tc_fun(tc_prod(X27,X27),tc_bool))
| ~ c_Wellfounded_Owf(X25,X27)
| ~ c_Wellfounded_Owf(X26,X27) ),
inference(variable_rename,[status(thm)],[c_0_442]) ).
fof(c_0_867,plain,
! [X25,X26] :
( c_Wellfounded_Owf(X25,X26)
| ~ c_Wellfounded_Owf(c_Relation_Orel__comp(X25,X25,X26,X26,X26),X26) ),
inference(variable_rename,[status(thm)],[c_0_443]) ).
fof(c_0_868,plain,
! [X39,X40,X41,X42,X43,X44] :
( c_lessequals(c_Product__Type_OSigma(X42,X41,X44,X43),c_Product__Type_OSigma(X40,X39,X44,X43),tc_fun(tc_prod(X44,X43),tc_bool))
| c_in(c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(X42,X41,X39,X44,X43),X42,X44)
| ~ c_lessequals(X42,X40,tc_fun(X44,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_444]) ).
fof(c_0_869,plain,
! [X13,X14,X15,X16,X17] :
( c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X17,X16,X15),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X17,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X14,X16,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X17,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X16,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X17,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X14 = X13
| ~ c_in(X17,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X16 = X15 ),
inference(variable_rename,[status(thm)],[c_0_445]) ).
fof(c_0_870,plain,
! [X13,X14,X15,X16,X17] :
( c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X17,X16,X15),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X17,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X15,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X17,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X14,X15,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X17,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X14 = X13
| ~ c_in(X17,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X16 = X15 ),
inference(variable_rename,[status(thm)],[c_0_446]) ).
fof(c_0_871,plain,
! [X23,X24,X25,X26,X27] :
( c_in(X23,c_FuncSet_OPi(X25,c_COMBK(X24,tc_fun(X26,tc_bool),X27),X27,X26),tc_fun(X27,X26))
| c_in(c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X25,X24,X23,X27,X26),X25,X27) ),
inference(variable_rename,[status(thm)],[c_0_447]) ).
fof(c_0_872,plain,
! [X23,X24,X25,X26,X27,X28] :
( hAPP(c_Recdef_Ocut(X25,X24,X26,X28,X27),X23) = hAPP(X25,X23)
| ~ c_in(c_Pair(X23,X26,X28,X28),X24,tc_prod(X28,X28)) ),
inference(variable_rename,[status(thm)],[c_0_448]) ).
fof(c_0_873,plain,
! [X25,X26,X27,X28,X29,X30] :
( hAPP(c_Recdef_Ocut(X26,X28,X27,X30,X29),X25) = hAPP(X26,X25)
| ~ c_in(c_Pair(X25,X27,X30,X30),X28,tc_prod(X30,X30)) ),
inference(variable_rename,[status(thm)],[c_0_449]) ).
fof(c_0_874,plain,
! [X19,X20,X21,X22,X23] :
( c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X21,X20,X19,X22,X23),X21,X22)
| ~ c_in(X20,c_Relation_OImage(X19,X21,X22,X23),X23) ),
inference(variable_rename,[status(thm)],[c_0_450]) ).
fof(c_0_875,plain,
! [X19,X20,X21,X22,X23] :
( c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X21,X20,X19,X22,X23),X21,X22)
| ~ c_in(X20,c_Relation_OImage(X19,X21,X22,X23),X23) ),
inference(variable_rename,[status(thm)],[c_0_451]) ).
fof(c_0_876,plain,
! [X21,X22,X23,X24] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X23,X22,X21,X24),X21,X24,X24),c_Transitive__Closure_Otrancl(X23,X24),tc_prod(X24,X24))
| c_in(c_Pair(X22,X21,X24,X24),X23,tc_prod(X24,X24))
| ~ c_in(c_Pair(X22,X21,X24,X24),c_Transitive__Closure_Otrancl(X23,X24),tc_prod(X24,X24)) ),
inference(variable_rename,[status(thm)],[c_0_452]) ).
fof(c_0_877,plain,
! [X19,X20,X21] :
( c_Relation_Orefl__on(X20,X19,X21)
| ~ c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1(X20,X19,X21),c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1(X20,X19,X21),X21,X21),X19,tc_prod(X21,X21))
| ~ c_lessequals(X19,c_Product__Type_OSigma(X20,c_COMBK(X20,tc_fun(X21,tc_bool),X21),X21,X21),tc_fun(tc_prod(X21,X21),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_453]) ).
fof(c_0_878,plain,
! [X19,X20,X21] :
( c_Relation_Orefl__on(X20,X19,X21)
| ~ c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1(X20,X19,X21),c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1(X20,X19,X21),X21,X21),X19,tc_prod(X21,X21))
| ~ c_lessequals(X19,c_Product__Type_OSigma(X20,c_COMBK(X20,tc_fun(X21,tc_bool),X21),X21,X21),tc_fun(tc_prod(X21,X21),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_454]) ).
fof(c_0_879,plain,
! [X21,X22,X23,X24] :
( c_in(c_Pair(X22,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X23,X22,X21,X24),X24,X24),X23,tc_prod(X24,X24))
| c_in(c_Pair(X22,X21,X24,X24),X23,tc_prod(X24,X24))
| ~ c_in(c_Pair(X22,X21,X24,X24),c_Transitive__Closure_Otrancl(X23,X24),tc_prod(X24,X24)) ),
inference(variable_rename,[status(thm)],[c_0_455]) ).
fof(c_0_880,plain,
! [X23,X24,X25,X26,X27] :
( c_in(X23,c_FuncSet_OPi(X25,X24,X27,X26),tc_fun(X27,X26))
| c_in(c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X25,X24,X23,X27,X26),X25,X27) ),
inference(variable_rename,[status(thm)],[c_0_456]) ).
fof(c_0_881,plain,
! [X23,X24,X25,X26,X27] :
( c_in(X23,c_FuncSet_OPi(X25,X24,X27,X26),tc_fun(X27,X26))
| c_in(c_FuncSet_Osko__FuncSet__XPi__I__1__1(X25,X24,X23,X27,X26),X25,X27) ),
inference(variable_rename,[status(thm)],[c_0_457]) ).
fof(c_0_882,plain,
! [X22,X23,X24,X25,X26,X27] :
( c_lessequals(X25,X24,tc_fun(X26,tc_bool))
| ~ c_lessequals(c_Product__Type_OSigma(X25,c_COMBK(X23,tc_fun(X27,tc_bool),X26),X26,X27),c_Product__Type_OSigma(X24,c_COMBK(X23,tc_fun(X27,tc_bool),X26),X26,X27),tc_fun(tc_prod(X26,X27),tc_bool))
| ~ c_in(X22,X23,X27) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_458])])]) ).
fof(c_0_883,plain,
! [X19,X20,X21] :
( c_lessequals(X19,c_Relation_Orel__comp(c_Relation_Oconverse(X19,X21,X21),X19,X21,X21,X21),tc_fun(tc_prod(X21,X21),tc_bool))
| ~ c_Relation_Orefl__on(X20,X19,X21) ),
inference(variable_rename,[status(thm)],[c_0_459]) ).
fof(c_0_884,plain,
! [X18,X19] :
( c_lessequals(c_Relation_Orel__comp(c_Relation_Oconverse(X18,X19,X19),X18,X19,X19,X19),X18,tc_fun(tc_prod(X19,X19),tc_bool))
| ~ c_Relation_Otrans(X18,X19)
| ~ c_Relation_Osym(X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_460]) ).
fof(c_0_885,plain,
! [X18,X19,X20,X21] :
( ~ c_in(c_Pair(X19,X18,X21,X21),c_Transitive__Closure_Ortrancl(X20,X21),tc_prod(X21,X21))
| ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X18,X19,X21,X21),X20,tc_prod(X21,X21)),X21) ),
inference(variable_rename,[status(thm)],[c_0_461]) ).
fof(c_0_886,plain,
! [X13,X14,X15,X16,X17] :
( c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X17,X16,X15),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X17,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X14 = X16
| ~ c_in(c_Pair(X14,X15,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X17,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X14 = X13
| ~ c_in(X17,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X16 = X15 ),
inference(variable_rename,[status(thm)],[c_0_462]) ).
fof(c_0_887,plain,
! [X13,X14,X15,X16,X17] :
( c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X17,X16,X15),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X17,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X15,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X17,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X13 = X16
| X14 = X13
| ~ c_in(X17,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X16 = X15 ),
inference(variable_rename,[status(thm)],[c_0_463]) ).
fof(c_0_888,plain,
! [X13,X14,X15,X16,X17] :
( c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X17,X16,X15),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X17,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X13 = X15
| ~ c_in(c_Pair(X16,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X17,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X14 = X13
| ~ c_in(X17,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X16 = X15 ),
inference(variable_rename,[status(thm)],[c_0_464]) ).
fof(c_0_889,plain,
! [X13,X14,X15,X16,X17] :
( c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X17,X16,X15),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X17,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X14,X16,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X17,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X14 = X15
| X14 = X13
| ~ c_in(X17,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X16 = X15 ),
inference(variable_rename,[status(thm)],[c_0_465]) ).
fof(c_0_890,plain,
! [X13,X14,X15,X16] :
( ~ c_in(c_Pair(X15,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X16,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X14,X15,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X16,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X14 = X13
| ~ c_in(X16,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X14 = X15
| c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X16,X14,X15),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(variable_rename,[status(thm)],[c_0_466]) ).
fof(c_0_891,plain,
! [X17,X18,X19,X20] :
( ~ c_in(c_Pair(X17,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X20,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X17 = X18
| ~ c_in(X20,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X19 = X18
| c_in(c_Pair(X17,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X20,X19,X18),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X17,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X20,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(variable_rename,[status(thm)],[c_0_467]) ).
fof(c_0_892,plain,
! [X17,X18,X19,X20] :
( ~ c_in(c_Pair(X17,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X20,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X19,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X20,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X17 = X18
| ~ c_in(X20,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X19 = X18
| c_in(c_Pair(X17,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X20,X19,X18),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(variable_rename,[status(thm)],[c_0_468]) ).
fof(c_0_893,plain,
! [X13,X14,X15,X16] :
( ~ c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X16,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X14 = X13
| ~ c_in(X16,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X14 = X15
| c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X16,X14,X15),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X16,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(variable_rename,[status(thm)],[c_0_469]) ).
fof(c_0_894,plain,
! [X18,X19] :
( c_lessequals(c_Relation_Orel__comp(X18,X18,X19,X19,X19),X18,tc_fun(tc_prod(X19,X19),tc_bool))
| ~ c_Relation_Otrans(X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_470]) ).
fof(c_0_895,plain,
! [X25,X26,X27,X28] :
( c_in(c_Pair(X26,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X27,X26,X25,X28),X28,X28),c_Transitive__Closure_Ortrancl(X27,X28),tc_prod(X28,X28))
| ~ c_in(c_Pair(X26,X25,X28,X28),c_Transitive__Closure_Otrancl(X27,X28),tc_prod(X28,X28)) ),
inference(variable_rename,[status(thm)],[c_0_471]) ).
fof(c_0_896,plain,
! [X25,X26,X27,X28] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X27,X26,X25,X28),X25,X28,X28),c_Transitive__Closure_Ortrancl(X27,X28),tc_prod(X28,X28))
| ~ c_in(c_Pair(X26,X25,X28,X28),c_Transitive__Closure_Otrancl(X27,X28),tc_prod(X28,X28)) ),
inference(variable_rename,[status(thm)],[c_0_472]) ).
fof(c_0_897,plain,
! [X25,X26,X27,X28] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X27,X26,X25,X28),X25,X28,X28),X27,tc_prod(X28,X28))
| ~ c_in(c_Pair(X26,X25,X28,X28),c_Transitive__Closure_Otrancl(X27,X28),tc_prod(X28,X28)) ),
inference(variable_rename,[status(thm)],[c_0_473]) ).
fof(c_0_898,plain,
! [X25,X26,X27,X28] :
( c_in(c_Pair(X26,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X27,X26,X25,X28),X28,X28),X27,tc_prod(X28,X28))
| ~ c_in(c_Pair(X26,X25,X28,X28),c_Transitive__Closure_Otrancl(X27,X28),tc_prod(X28,X28)) ),
inference(variable_rename,[status(thm)],[c_0_474]) ).
fof(c_0_899,plain,
! [X24,X25,X26,X27,X28] :
( c_in(c_Pair(X27,X25,X28,X28),c_Transitive__Closure_Ortrancl(X24,X28),tc_prod(X28,X28))
| ~ c_in(c_Pair(X26,X25,X28,X28),c_Transitive__Closure_Ortrancl(X24,X28),tc_prod(X28,X28))
| ~ c_in(c_Pair(X27,X26,X28,X28),c_Transitive__Closure_Ortrancl(X24,X28),tc_prod(X28,X28)) ),
inference(variable_rename,[status(thm)],[c_0_475]) ).
fof(c_0_900,plain,
! [X24,X25,X26,X27,X28] :
( c_in(c_Pair(X27,X25,X28,X28),c_Transitive__Closure_Otrancl(X24,X28),tc_prod(X28,X28))
| ~ c_in(c_Pair(X26,X25,X28,X28),c_Transitive__Closure_Ortrancl(X24,X28),tc_prod(X28,X28))
| ~ c_in(c_Pair(X27,X26,X28,X28),c_Transitive__Closure_Otrancl(X24,X28),tc_prod(X28,X28)) ),
inference(variable_rename,[status(thm)],[c_0_476]) ).
fof(c_0_901,plain,
! [X21,X22,X23,X24,X25] :
( c_in(c_Pair(X23,X21,X25,X25),c_Transitive__Closure_Otrancl(X24,X25),tc_prod(X25,X25))
| ~ c_in(c_Pair(X22,X21,X25,X25),c_Transitive__Closure_Otrancl(X24,X25),tc_prod(X25,X25))
| ~ c_in(c_Pair(X23,X22,X25,X25),c_Transitive__Closure_Ortrancl(X24,X25),tc_prod(X25,X25)) ),
inference(variable_rename,[status(thm)],[c_0_477]) ).
fof(c_0_902,plain,
! [X24,X25,X26,X27,X28] :
( c_in(c_Pair(X27,X25,X28,X28),c_Transitive__Closure_Otrancl(X24,X28),tc_prod(X28,X28))
| ~ c_in(c_Pair(X26,X25,X28,X28),c_Transitive__Closure_Otrancl(X24,X28),tc_prod(X28,X28))
| ~ c_in(c_Pair(X27,X26,X28,X28),c_Transitive__Closure_Otrancl(X24,X28),tc_prod(X28,X28)) ),
inference(variable_rename,[status(thm)],[c_0_478]) ).
fof(c_0_903,plain,
! [X19,X20,X21,X22,X23] :
( c_in(X21,X22,X23)
| X21 = X20
| ~ c_lessequals(X19,c_Product__Type_OSigma(X22,c_COMBK(X22,tc_fun(X23,tc_bool),X23),X23,X23),tc_fun(tc_prod(X23,X23),tc_bool))
| ~ c_in(c_Pair(X21,X20,X23,X23),c_Transitive__Closure_Ortrancl(X19,X23),tc_prod(X23,X23)) ),
inference(variable_rename,[status(thm)],[c_0_479]) ).
fof(c_0_904,plain,
! [X24,X25,X26,X27,X28] :
( c_in(c_Pair(X27,X25,X28,X28),c_Transitive__Closure_Otrancl(X24,X28),tc_prod(X28,X28))
| ~ c_in(c_Pair(X26,X25,X28,X28),X24,tc_prod(X28,X28))
| ~ c_in(c_Pair(X27,X26,X28,X28),c_Transitive__Closure_Ortrancl(X24,X28),tc_prod(X28,X28)) ),
inference(variable_rename,[status(thm)],[c_0_480]) ).
fof(c_0_905,plain,
! [X24,X25,X26,X27,X28] :
( c_in(c_Pair(X27,X25,X28,X28),c_Transitive__Closure_Otrancl(X24,X28),tc_prod(X28,X28))
| ~ c_in(c_Pair(X26,X25,X28,X28),c_Transitive__Closure_Ortrancl(X24,X28),tc_prod(X28,X28))
| ~ c_in(c_Pair(X27,X26,X28,X28),X24,tc_prod(X28,X28)) ),
inference(variable_rename,[status(thm)],[c_0_481]) ).
fof(c_0_906,plain,
! [X24,X25,X26,X27,X28] :
( c_in(c_Pair(X27,X25,X28,X28),c_Transitive__Closure_Ortrancl(X24,X28),tc_prod(X28,X28))
| ~ c_in(c_Pair(X26,X25,X28,X28),X24,tc_prod(X28,X28))
| ~ c_in(c_Pair(X27,X26,X28,X28),c_Transitive__Closure_Ortrancl(X24,X28),tc_prod(X28,X28)) ),
inference(variable_rename,[status(thm)],[c_0_482]) ).
fof(c_0_907,plain,
! [X24,X25,X26,X27,X28] :
( c_in(c_Pair(X27,X25,X28,X28),c_Transitive__Closure_Ortrancl(X24,X28),tc_prod(X28,X28))
| ~ c_in(c_Pair(X26,X25,X28,X28),c_Transitive__Closure_Ortrancl(X24,X28),tc_prod(X28,X28))
| ~ c_in(c_Pair(X27,X26,X28,X28),X24,tc_prod(X28,X28)) ),
inference(variable_rename,[status(thm)],[c_0_483]) ).
fof(c_0_908,plain,
! [X24,X25,X26,X27,X28] :
( c_in(c_Pair(X27,X25,X28,X28),c_Transitive__Closure_Otrancl(X24,X28),tc_prod(X28,X28))
| ~ c_in(c_Pair(X26,X25,X28,X28),c_Transitive__Closure_Otrancl(X24,X28),tc_prod(X28,X28))
| ~ c_in(c_Pair(X27,X26,X28,X28),X24,tc_prod(X28,X28)) ),
inference(variable_rename,[status(thm)],[c_0_484]) ).
fof(c_0_909,plain,
! [X24,X25,X26,X27,X28] :
( c_in(c_Pair(X27,X25,X28,X28),c_Transitive__Closure_Otrancl(X24,X28),tc_prod(X28,X28))
| ~ c_in(c_Pair(X26,X25,X28,X28),X24,tc_prod(X28,X28))
| ~ c_in(c_Pair(X27,X26,X28,X28),c_Transitive__Closure_Otrancl(X24,X28),tc_prod(X28,X28)) ),
inference(variable_rename,[status(thm)],[c_0_485]) ).
fof(c_0_910,plain,
! [X25,X26] :
( c_Wellfounded_Owf(c_Relation_Orel__comp(X25,X25,X26,X26,X26),X26)
| ~ c_Wellfounded_Owf(X25,X26) ),
inference(variable_rename,[status(thm)],[c_0_486]) ).
fof(c_0_911,plain,
! [X19,X20,X21] :
( c_lessequals(c_Transitive__Closure_Otrancl(X19,X21),c_Product__Type_OSigma(X20,c_COMBK(X20,tc_fun(X21,tc_bool),X21),X21,X21),tc_fun(tc_prod(X21,X21),tc_bool))
| ~ c_lessequals(X19,c_Product__Type_OSigma(X20,c_COMBK(X20,tc_fun(X21,tc_bool),X21),X21,X21),tc_fun(tc_prod(X21,X21),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_487]) ).
fof(c_0_912,plain,
! [X25,X26,X27,X28,X29] :
( c_in(c_Pair(X27,X25,X29,X29),c_Transitive__Closure_Otrancl(X28,X29),tc_prod(X29,X29))
| ~ c_in(c_Pair(X26,X25,X29,X29),X28,tc_prod(X29,X29))
| ~ c_in(c_Pair(X27,X26,X29,X29),X28,tc_prod(X29,X29)) ),
inference(variable_rename,[status(thm)],[c_0_488]) ).
fof(c_0_913,plain,
! [X24,X25,X26,X27,X28] :
( c_in(c_Pair(X27,X25,X28,X28),X24,tc_prod(X28,X28))
| ~ c_in(c_Pair(X26,X25,X28,X28),X24,tc_prod(X28,X28))
| ~ c_in(c_Pair(X27,X26,X28,X28),X24,tc_prod(X28,X28))
| ~ c_Relation_Otrans(X24,X28) ),
inference(variable_rename,[status(thm)],[c_0_489]) ).
fof(c_0_914,plain,
! [X21,X22,X23,X24,X25] :
( c_in(c_Pair(X23,X21,X25,X25),X24,tc_prod(X25,X25))
| ~ c_in(c_Pair(X22,X21,X25,X25),X24,tc_prod(X25,X25))
| ~ c_in(c_Pair(X23,X22,X25,X25),X24,tc_prod(X25,X25))
| ~ c_Relation_Otrans(X24,X25) ),
inference(variable_rename,[status(thm)],[c_0_490]) ).
fof(c_0_915,plain,
! [X23,X24,X25,X26,X27,X28] :
( c_in(c_Pair(hAPP(X26,X24),hAPP(X26,X23),X27,X27),X25,tc_prod(X27,X27))
| ~ c_in(c_Pair(X24,X23,X28,X28),c_Relation_Oinv__image(X25,X26,X27,X28),tc_prod(X28,X28)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_491])])]) ).
fof(c_0_916,plain,
! [X18,X19] :
( c_Relation_Orel__comp(c_Relation_Oconverse(X18,X19,X19),X18,X19,X19,X19) != X18
| c_Equiv__Relations_Oequiv(c_Relation_ODomain(X18,X19,X19),X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_492]) ).
fof(c_0_917,plain,
! [X23,X24,X25,X26,X27,X28] :
( c_in(c_Pair(X24,X23,X28,X28),c_Relation_Oinv__image(X25,X26,X27,X28),tc_prod(X28,X28))
| ~ c_in(c_Pair(hAPP(X26,X24),hAPP(X26,X23),X27,X27),X25,tc_prod(X27,X27)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_493])])]) ).
fof(c_0_918,plain,
! [X22,X23,X24,X25,X26,X27] :
( c_lessequals(c_Relation_OImage(X22,X23,X27,X26),X24,tc_fun(X26,tc_bool))
| ~ c_lessequals(X22,c_Product__Type_OSigma(X25,c_COMBK(X24,tc_fun(X26,tc_bool),X27),X27,X26),tc_fun(tc_prod(X27,X26),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_494]) ).
fof(c_0_919,plain,
! [X20,X21,X22,X23] :
( c_Wellfounded_Owf(X20,X23)
| c_in(c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1(X22,X21,X20,X23),X21,X23)
| ~ c_lessequals(X20,c_Product__Type_OSigma(X22,c_COMBK(X21,tc_fun(X23,tc_bool),X23),X23,X23),tc_fun(tc_prod(X23,X23),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_495]) ).
fof(c_0_920,plain,
! [X20,X21,X22,X23] :
( c_Wellfounded_Owf(X20,X23)
| c_in(c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1(X22,X21,X20,X23),X22,X23)
| ~ c_lessequals(X20,c_Product__Type_OSigma(X22,c_COMBK(X21,tc_fun(X23,tc_bool),X23),X23,X23),tc_fun(tc_prod(X23,X23),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_496]) ).
fof(c_0_921,plain,
! [X18,X19,X20,X21] :
( c_in(c_Pair(X19,X18,X21,X21),c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X20,X21),X21,X21),tc_prod(X21,X21))
| ~ c_in(c_Pair(X19,X18,X21,X21),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X20,X21,X21),X21),tc_prod(X21,X21)) ),
inference(variable_rename,[status(thm)],[c_0_497]) ).
fof(c_0_922,plain,
! [X18,X19,X20,X21] :
( c_in(c_Pair(X19,X18,X21,X21),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X20,X21,X21),X21),tc_prod(X21,X21))
| ~ c_in(c_Pair(X19,X18,X21,X21),c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X20,X21),X21,X21),tc_prod(X21,X21)) ),
inference(variable_rename,[status(thm)],[c_0_498]) ).
fof(c_0_923,plain,
! [X23,X24,X25,X26,X27] :
( c_lessequals(c_Set_Oimage(X23,X25,X27,X26),X24,tc_fun(X26,tc_bool))
| ~ c_in(X23,c_FuncSet_OPi(X25,c_COMBK(X24,tc_fun(X26,tc_bool),X27),X27,X26),tc_fun(X27,X26)) ),
inference(variable_rename,[status(thm)],[c_0_499]) ).
fof(c_0_924,plain,
! [X13,X14,X15] :
( ~ c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X15,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X13,X14,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X15,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X14 = X13
| ~ c_in(X15,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_500]) ).
fof(c_0_925,plain,
! [X9,X10,X11] :
( ~ c_in(c_Pair(X9,X10,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X11,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X10,X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X11,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X11,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_501]) ).
fof(c_0_926,plain,
! [X22,X23,X24,X25,X26,X27] :
( c_lessequals(c_Product__Type_OSigma(X25,c_COMBK(X23,tc_fun(X27,tc_bool),X26),X26,X27),c_Product__Type_OSigma(X24,c_COMBK(X23,tc_fun(X27,tc_bool),X26),X26,X27),tc_fun(tc_prod(X26,X27),tc_bool))
| ~ c_lessequals(X25,X24,tc_fun(X26,tc_bool))
| ~ c_in(X22,X23,X27) ),
inference(variable_rename,[status(thm)],[c_0_502]) ).
fof(c_0_927,plain,
! [X18,X19,X20,X21] :
( c_in(c_Pair(X18,X19,X21,X21),c_Transitive__Closure_Ortrancl(X20,X21),tc_prod(X21,X21))
| ~ c_in(c_Pair(X19,X18,X21,X21),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X20,X21,X21),X21),tc_prod(X21,X21)) ),
inference(variable_rename,[status(thm)],[c_0_503]) ).
fof(c_0_928,plain,
! [X18,X19,X20,X21] :
( c_Wellfounded_Owf(X20,X21)
| ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X18,X19,X21,X21),X20,tc_prod(X21,X21)),X21) ),
inference(variable_rename,[status(thm)],[c_0_504]) ).
fof(c_0_929,plain,
! [X18,X19,X20,X21] :
( ~ c_in(c_Pair(X18,X20,X21,X21),X19,tc_prod(X21,X21))
| ~ c_in(c_Pair(X20,X18,X21,X21),X19,tc_prod(X21,X21))
| ~ c_Wellfounded_Owf(X19,X21) ),
inference(variable_rename,[status(thm)],[c_0_505]) ).
fof(c_0_930,plain,
! [X18,X19,X20,X21] :
( c_in(c_Pair(X19,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X19,X18,X21,X20),X21,X20),X18,tc_prod(X21,X20))
| ~ c_in(X19,c_Relation_ODomain(X18,X21,X20),X21) ),
inference(variable_rename,[status(thm)],[c_0_506]) ).
fof(c_0_931,plain,
! [X18,X19,X20,X21] :
( c_in(c_Pair(X19,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X19,X18,X21,X20),X21,X20),X18,tc_prod(X21,X20))
| ~ c_in(X19,c_Relation_ODomain(X18,X21,X20),X21) ),
inference(variable_rename,[status(thm)],[c_0_507]) ).
fof(c_0_932,plain,
! [X18,X19,X20,X21] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X19,X18,X21,X20),X19,X20,X21),X18,tc_prod(X20,X21))
| ~ c_in(X19,c_Relation_ORange(X18,X20,X21),X21) ),
inference(variable_rename,[status(thm)],[c_0_508]) ).
fof(c_0_933,plain,
! [X18,X19,X20,X21] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X19,X18,X21,X20),X19,X20,X21),X18,tc_prod(X20,X21))
| ~ c_in(X19,c_Relation_ORange(X18,X20,X21),X21) ),
inference(variable_rename,[status(thm)],[c_0_509]) ).
fof(c_0_934,plain,
! [X13,X14,X15,X16,X17] :
( c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X17,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X13 = X15
| X14 = X15
| ~ c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X17,X16,X15),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X17,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X16 = X15 ),
inference(variable_rename,[status(thm)],[c_0_510]) ).
fof(c_0_935,plain,
! [X17,X18,X19,X20] :
( X17 = X18
| ~ c_in(c_Pair(X17,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X20,X19,X18),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X20,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X19 = X18
| c_in(c_Pair(X17,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X20,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X17 = X19 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_511])])]) ).
fof(c_0_936,plain,
! [X13,X14,X15,X16,X17] :
( c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X17,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X14 = X16
| X13 = X16
| ~ c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X17,X16,X15),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X17,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X16 = X15 ),
inference(variable_rename,[status(thm)],[c_0_512]) ).
fof(c_0_937,plain,
! [X13,X14,X15,X16] :
( X13 = X14
| ~ c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X16,X14,X15),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X16,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X14 = X15
| c_in(c_Pair(X15,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X16,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X13 = X15 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_513])])]) ).
fof(c_0_938,plain,
! [X13,X14,X15,X16] :
( ~ c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X16,X15,X14),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X16,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X15 = X14
| c_in(c_Pair(X15,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X16,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(variable_rename,[status(thm)],[c_0_514]) ).
fof(c_0_939,plain,
! [X17,X18,X19,X20] :
( ~ c_in(c_Pair(X17,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X20,X18,X19),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X20,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X18 = X19
| c_in(c_Pair(X17,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X20,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(variable_rename,[status(thm)],[c_0_515]) ).
fof(c_0_940,plain,
! [X19,X20,X21,X22] :
( c_Finite__Set_Ofinite(X20,X22)
| ~ c_in(X20,c_Equiv__Relations_Oquotient(X21,X19,X22),tc_fun(X22,tc_bool))
| ~ c_lessequals(X19,c_Product__Type_OSigma(X21,c_COMBK(X21,tc_fun(X22,tc_bool),X22),X22,X22),tc_fun(tc_prod(X22,X22),tc_bool))
| ~ c_Finite__Set_Ofinite(X21,X22) ),
inference(variable_rename,[status(thm)],[c_0_516]) ).
fof(c_0_941,plain,
! [X18,X19,X20,X21] :
( c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X18,X19,X21,X21),X20,tc_prod(X21,X21)),X21)
| c_in(c_Pair(X19,X18,X21,X21),c_Transitive__Closure_Ortrancl(X20,X21),tc_prod(X21,X21))
| ~ c_Wellfounded_Owf(X20,X21) ),
inference(variable_rename,[status(thm)],[c_0_517]) ).
fof(c_0_942,plain,
! [X20,X21,X22,X23,X24,X25] :
( c_in(X20,hAPP(X22,X21),X24)
| ~ c_in(c_Pair(X21,X20,X25,X24),c_Product__Type_OSigma(X23,X22,X25,X24),tc_prod(X25,X24)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_518])])]) ).
fof(c_0_943,plain,
! [X18,X19,X20,X21] :
( c_in(c_Pair(X19,X18,X21,X21),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X20,X21,X21),X21),tc_prod(X21,X21))
| ~ c_in(c_Pair(X18,X19,X21,X21),c_Transitive__Closure_Ortrancl(X20,X21),tc_prod(X21,X21)) ),
inference(variable_rename,[status(thm)],[c_0_519]) ).
fof(c_0_944,plain,
! [X19,X20,X21,X22,X23,X24,X25] :
( X23 = X22
| ~ c_in(c_Pair(X20,X19,X25,X25),X21,tc_prod(X25,X25))
| ~ c_in(X19,X22,X25)
| ~ c_in(X20,X23,X25)
| ~ c_in(X22,c_Equiv__Relations_Oquotient(X24,X21,X25),tc_fun(X25,tc_bool))
| ~ c_in(X23,c_Equiv__Relations_Oquotient(X24,X21,X25),tc_fun(X25,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X24,X21,X25) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_520])])]) ).
fof(c_0_945,plain,
! [X13,X14,X15,X16,X17] :
( c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X17,X16,X15),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X17,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X13 = X15
| X14 = X15
| X14 = X13
| ~ c_in(X17,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X16 = X15 ),
inference(variable_rename,[status(thm)],[c_0_521]) ).
fof(c_0_946,plain,
! [X13,X14,X15,X16,X17] :
( c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X17,X16,X15),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X17,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X14 = X16
| X13 = X16
| X14 = X13
| ~ c_in(X17,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X16 = X15 ),
inference(variable_rename,[status(thm)],[c_0_522]) ).
fof(c_0_947,plain,
! [X17,X18,X19,X20] :
( ~ c_in(c_Pair(X17,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X20,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X17 = X18
| X17 = X18
| ~ c_in(X20,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X19 = X18
| c_in(c_Pair(X17,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X20,X19,X18),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(variable_rename,[status(thm)],[c_0_523]) ).
fof(c_0_948,plain,
! [X13,X14,X15,X16] :
( X14 = X15
| X14 = X13
| ~ c_in(X16,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X14 = X15
| c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X16,X14,X15),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X16,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_524])])]) ).
fof(c_0_949,plain,
! [X13,X14,X15,X16] :
( ~ c_in(c_Pair(X15,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X16,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X13 = X14
| X14 = X13
| ~ c_in(X16,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X14 = X15
| c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X16,X14,X15),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(variable_rename,[status(thm)],[c_0_525]) ).
fof(c_0_950,plain,
! [X17,X18,X19,X20] :
( X18 = X19
| X17 = X18
| ~ c_in(X20,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X19 = X18
| c_in(c_Pair(X17,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X20,X19,X18),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X17,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X20,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_526])])]) ).
fof(c_0_951,plain,
! [X17,X18,X19] :
( ~ c_in(c_Pair(X17,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X19,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X17 = X18
| ~ c_in(X19,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X17 = X18
| c_in(c_Pair(X17,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X19,X17,X18),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(variable_rename,[status(thm)],[c_0_527]) ).
fof(c_0_952,plain,
! [X13,X14,X15,X16] :
( ~ c_in(c_Pair(X15,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X16,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X14 = X13
| ~ c_in(X16,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X15 = X14
| c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X16,X15,X14),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(variable_rename,[status(thm)],[c_0_528]) ).
fof(c_0_953,plain,
! [X17,X18,X19] :
( ~ c_in(c_Pair(X18,X17,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X19,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X18 = X17
| ~ c_in(X19,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X18 = X17
| c_in(c_Pair(X18,X17,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X19,X18,X17),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(variable_rename,[status(thm)],[c_0_529]) ).
fof(c_0_954,plain,
! [X17,X18,X19,X20] :
( ~ c_in(c_Pair(X17,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X20,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X17 = X18
| ~ c_in(X20,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X18 = X19
| c_in(c_Pair(X17,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X20,X18,X19),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(variable_rename,[status(thm)],[c_0_530]) ).
fof(c_0_955,plain,
! [X20,X21,X22,X23,X24,X25] :
( c_in(X21,X23,X25)
| ~ c_in(c_Pair(X21,X20,X25,X24),c_Product__Type_OSigma(X23,X22,X25,X24),tc_prod(X25,X24)) ),
inference(variable_rename,[status(thm)],[c_0_531]) ).
fof(c_0_956,plain,
! [X19,X20,X21] :
( c_Relation_Orefl__on(X20,X19,X21)
| c_in(c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1(X20,X19,X21),X20,X21)
| ~ c_lessequals(X19,c_Product__Type_OSigma(X20,c_COMBK(X20,tc_fun(X21,tc_bool),X21),X21,X21),tc_fun(tc_prod(X21,X21),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_532]) ).
fof(c_0_957,plain,
! [X19,X20,X21] :
( c_Relation_Orefl__on(X20,X19,X21)
| c_in(c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1(X20,X19,X21),X20,X21)
| ~ c_lessequals(X19,c_Product__Type_OSigma(X20,c_COMBK(X20,tc_fun(X21,tc_bool),X21),X21,X21),tc_fun(tc_prod(X21,X21),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_533]) ).
fof(c_0_958,plain,
! [X18,X19,X20,X21,X22] :
( c_in(c_Pair(X19,X20,X21,X22),X18,tc_prod(X21,X22))
| ~ c_in(c_Pair(X20,X19,X22,X21),c_Relation_Oconverse(X18,X21,X22),tc_prod(X22,X21)) ),
inference(variable_rename,[status(thm)],[c_0_534]) ).
fof(c_0_959,plain,
! [X18,X19,X20] :
( ~ c_in(c_Pair(X18,X18,X20,X20),X19,tc_prod(X20,X20))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X19,X20),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X19,X20),X20,X20),c_Transitive__Closure_Otrancl(X19,X20),tc_prod(X20,X20)) ),
inference(variable_rename,[status(thm)],[c_0_535]) ).
fof(c_0_960,plain,
! [X18,X19,X20,X21,X22] :
( c_in(c_Pair(X19,X20,X21,X22),c_Relation_Oconverse(X18,X22,X21),tc_prod(X21,X22))
| ~ c_in(c_Pair(X20,X19,X22,X21),X18,tc_prod(X22,X21)) ),
inference(variable_rename,[status(thm)],[c_0_536]) ).
fof(c_0_961,plain,
! [X18,X19,X20,X21,X22] :
( c_in(c_Pair(X20,X19,X22,X21),c_Relation_Oconverse(X18,X21,X22),tc_prod(X22,X21))
| ~ c_in(c_Pair(X19,X20,X21,X22),X18,tc_prod(X21,X22)) ),
inference(variable_rename,[status(thm)],[c_0_537]) ).
fof(c_0_962,plain,
! [X23,X24,X25,X26,X27,X28] :
( c_in(hAPP(X24,X23),X25,X27)
| ~ c_in(X23,X26,X28)
| ~ c_in(X24,c_FuncSet_OPi(X26,c_COMBK(X25,tc_fun(X27,tc_bool),X28),X28,X27),tc_fun(X28,X27)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_538])])]) ).
fof(c_0_963,plain,
! [X25,X26,X27,X28] :
( c_in(c_Pair(X26,X25,X28,X28),c_Transitive__Closure_Otrancl(X27,X28),tc_prod(X28,X28))
| X26 = X25
| ~ c_in(c_Pair(X26,X25,X28,X28),c_Transitive__Closure_Ortrancl(X27,X28),tc_prod(X28,X28)) ),
inference(variable_rename,[status(thm)],[c_0_539]) ).
fof(c_0_964,plain,
! [X25,X26,X27,X28] :
( c_in(c_Pair(X26,X25,X28,X28),c_Transitive__Closure_Otrancl(X27,X28),tc_prod(X28,X28))
| X26 = X25
| ~ c_in(c_Pair(X26,X25,X28,X28),c_Transitive__Closure_Ortrancl(X27,X28),tc_prod(X28,X28)) ),
inference(variable_rename,[status(thm)],[c_0_540]) ).
fof(c_0_965,plain,
! [X25,X26,X27,X28] :
( c_in(c_Pair(X26,X25,X28,X28),c_Transitive__Closure_Ortrancl(X27,X28),tc_prod(X28,X28))
| ~ c_in(c_Pair(X26,X25,X28,X28),c_Transitive__Closure_Otrancl(X27,X28),tc_prod(X28,X28))
| X26 = X25 ),
inference(variable_rename,[status(thm)],[c_0_541]) ).
fof(c_0_966,plain,
! [X18,X19,X20,X21] :
( c_in(c_Pair(X20,X19,X21,X21),c_Transitive__Closure_Ortrancl(X18,X21),tc_prod(X21,X21))
| ~ c_in(c_Pair(X20,X19,X21,X21),c_Transitive__Closure_Otrancl(X18,X21),tc_prod(X21,X21)) ),
inference(variable_rename,[status(thm)],[c_0_542]) ).
fof(c_0_967,plain,
! [X19,X20,X21,X22,X23,X24] :
( c_in(X20,c_Relation_OImage(X19,X22,X24,X23),X23)
| ~ c_in(c_Pair(X21,X20,X24,X23),X19,tc_prod(X24,X23))
| ~ c_in(X21,X22,X24) ),
inference(variable_rename,[status(thm)],[c_0_543]) ).
fof(c_0_968,plain,
! [X19,X20,X21,X22,X23,X24] :
( c_in(X21,c_Relation_OImage(X20,X22,X23,X24),X24)
| ~ c_in(c_Pair(X19,X21,X23,X24),X20,tc_prod(X23,X24))
| ~ c_in(X19,X22,X23) ),
inference(variable_rename,[status(thm)],[c_0_544]) ).
fof(c_0_969,plain,
! [X18,X19,X20,X21] :
( c_in(c_Pair(X20,X19,X21,X21),c_Transitive__Closure_Otrancl(X18,X21),tc_prod(X21,X21))
| ~ c_in(c_Pair(X20,X19,X21,X21),X18,tc_prod(X21,X21)) ),
inference(variable_rename,[status(thm)],[c_0_545]) ).
fof(c_0_970,plain,
! [X18,X19,X20,X21] :
( c_in(c_Pair(X18,X19,X21,X21),X20,tc_prod(X21,X21))
| ~ c_in(c_Pair(X19,X18,X21,X21),X20,tc_prod(X21,X21))
| ~ c_Relation_Osym(X20,X21) ),
inference(variable_rename,[status(thm)],[c_0_546]) ).
fof(c_0_971,plain,
! [X18,X19,X20,X21] :
( c_in(c_Pair(X19,X20,X21,X21),X18,tc_prod(X21,X21))
| ~ c_in(c_Pair(X20,X19,X21,X21),X18,tc_prod(X21,X21))
| ~ c_Relation_Osym(X18,X21) ),
inference(variable_rename,[status(thm)],[c_0_547]) ).
fof(c_0_972,plain,
! [X21,X22,X23,X24] :
( c_in(c_Pair(X23,X22,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X24,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X22 = X21
| ~ c_in(c_Pair(X23,X22,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X24,X21),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(variable_rename,[status(thm)],[c_0_548]) ).
fof(c_0_973,plain,
! [X21,X22,X23,X24] :
( c_in(c_Pair(X23,X22,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X24,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X23 = X21
| ~ c_in(c_Pair(X23,X22,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X24,X21),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(variable_rename,[status(thm)],[c_0_549]) ).
fof(c_0_974,plain,
! [X21,X22,X23,X24] :
( c_in(c_Pair(X23,X22,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X24,X21),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X23,X22,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X24,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X23 = X22
| X23 = X21 ),
inference(variable_rename,[status(thm)],[c_0_550]) ).
fof(c_0_975,plain,
! [X21,X22,X23,X24] :
( c_in(c_Pair(X23,X22,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X24,X21),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X23,X22,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X24,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X22 = X21
| X23 = X21 ),
inference(variable_rename,[status(thm)],[c_0_551]) ).
fof(c_0_976,plain,
! [X21,X22,X23,X24] :
( c_in(c_Pair(X23,X22,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X24,X21),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X23,X22,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X24,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X23 = X22
| X22 = X21 ),
inference(variable_rename,[status(thm)],[c_0_552]) ).
fof(c_0_977,plain,
! [X21,X22,X23,X24] :
( c_in(c_Pair(X23,X22,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X24,X21),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X23,X22,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X24,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X23 = X21
| X22 = X21 ),
inference(variable_rename,[status(thm)],[c_0_553]) ).
fof(c_0_978,plain,
! [X32,X33,X34,X35,X36] :
( ~ c_in(X32,X35,X36)
| ~ c_in(c_Pair(X32,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X35,X34,X36),X36,X36),X34,tc_prod(X36,X36))
| ~ c_in(X33,X35,X36)
| ~ c_Wellfounded_Owf(X34,X36) ),
inference(variable_rename,[status(thm)],[c_0_554]) ).
fof(c_0_979,plain,
! [X32,X33,X34,X35,X36] :
( ~ c_in(X32,X35,X36)
| ~ c_in(c_Pair(X32,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X35,X34,X36),X36,X36),X34,tc_prod(X36,X36))
| ~ c_in(X33,X35,X36)
| ~ c_Wellfounded_Owf(X34,X36) ),
inference(variable_rename,[status(thm)],[c_0_555]) ).
fof(c_0_980,plain,
! [X30,X31,X32,X33,X34] :
( hBOOL(hAPP(X33,X32))
| hBOOL(hAPP(X33,X30))
| ~ c_in(c_Pair(X30,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X33,X31,X34),X34,X34),X31,tc_prod(X34,X34))
| ~ c_in(X32,c_Wellfounded_Oacc(X31,X34),X34) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_556])])]) ).
fof(c_0_981,plain,
! [X30,X31,X32,X33,X34] :
( hBOOL(hAPP(X33,X32))
| hBOOL(hAPP(X33,X30))
| ~ c_in(c_Pair(X30,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X33,X31,X34),X34,X34),X31,tc_prod(X34,X34))
| ~ c_in(X32,c_Wellfounded_Oacc(X31,X34),X34) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_557])])]) ).
fof(c_0_982,plain,
! [X19,X20,X21,X22,X23,X24] :
( ~ c_in(X19,X21,X24)
| ~ c_in(X20,X21,X24)
| ~ c_in(X21,c_Equiv__Relations_Oquotient(X23,X22,X24),tc_fun(X24,tc_bool))
| ~ c_in(X21,c_Equiv__Relations_Oquotient(X23,X22,X24),tc_fun(X24,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X23,X22,X24)
| c_in(c_Pair(X20,X19,X24,X24),X22,tc_prod(X24,X24)) ),
inference(variable_rename,[status(thm)],[c_0_558]) ).
fof(c_0_983,plain,
! [X19,X20,X21,X22,X23] :
( c_in(c_Pair(X19,X20,X23,X23),X21,tc_prod(X23,X23))
| c_in(c_Pair(X20,X19,X23,X23),X21,tc_prod(X23,X23))
| X20 = X19
| ~ c_in(X19,X22,X23)
| ~ c_in(X20,X22,X23)
| ~ c_Relation_Ototal__on(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_559]) ).
fof(c_0_984,plain,
! [X19,X20,X21] :
( c_Relation_Orel__comp(c_Relation_Oconverse(X19,X21,X21),X19,X21,X21,X21) = X19
| ~ c_Equiv__Relations_Oequiv(X20,X19,X21) ),
inference(variable_rename,[status(thm)],[c_0_560]) ).
fof(c_0_985,plain,
! [X38,X39,X40,X41,X42,X43] :
( c_lessequals(c_Relation_OImage(X38,X40,X43,X42),c_Relation_OImage(X39,X41,X43,X42),tc_fun(X42,tc_bool))
| ~ c_lessequals(X40,X41,tc_fun(X43,tc_bool))
| ~ c_lessequals(X38,X39,tc_fun(tc_prod(X43,X42),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_561]) ).
fof(c_0_986,plain,
! [X22,X23,X24,X25,X26,X27] :
( c_Product__Type_OSigma(X25,c_COMBK(X23,tc_fun(X27,tc_bool),X26),X26,X27) != c_Product__Type_OSigma(X24,c_COMBK(X23,tc_fun(X27,tc_bool),X26),X26,X27)
| ~ c_in(X22,X23,X27)
| X25 = X24 ),
inference(variable_rename,[status(thm)],[c_0_562]) ).
fof(c_0_987,plain,
! [X13,X14,X15] :
( c_in(c_Pair(X13,X14,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X15,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X15,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X14 = X13
| ~ c_in(X15,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_563]) ).
fof(c_0_988,plain,
! [X20,X21,X22,X23,X24,X25] :
( c_in(c_Pair(X21,X20,X25,X24),c_Product__Type_OSigma(X23,X22,X25,X24),tc_prod(X25,X24))
| ~ c_in(X20,hAPP(X22,X21),X24)
| ~ c_in(X21,X23,X25) ),
inference(variable_rename,[status(thm)],[c_0_564]) ).
fof(c_0_989,plain,
! [X20,X21,X22,X23,X24,X25] :
( c_in(c_Pair(X21,X20,X25,X24),c_Product__Type_OSigma(X23,X22,X25,X24),tc_prod(X25,X24))
| ~ c_in(X20,hAPP(X22,X21),X24)
| ~ c_in(X21,X23,X25) ),
inference(variable_rename,[status(thm)],[c_0_565]) ).
fof(c_0_990,plain,
! [X11,X12,X13,X14] :
( ~ c_in(c_Pair(X11,X11,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X14,X13,X12),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X14,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X13 = X12 ),
inference(variable_rename,[status(thm)],[c_0_566]) ).
fof(c_0_991,plain,
! [X11,X12,X13,X14] :
( ~ c_in(c_Pair(X11,X11,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X14,X13,X12),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X14,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X13 = X12 ),
inference(variable_rename,[status(thm)],[c_0_567]) ).
fof(c_0_992,plain,
! [X31,X32,X33,X34] :
( hBOOL(hAPP(X34,X32))
| c_in(X31,c_Wellfounded_Oacc(X33,t_a),t_a)
| ~ c_in(c_Pair(X31,v_sko__Wellfounded__Xacc__Xinduct__1(X34,X33),t_a,t_a),X33,tc_prod(t_a,t_a))
| ~ c_in(X32,c_Wellfounded_Oacc(X33,t_a),t_a) ),
inference(variable_rename,[status(thm)],[c_0_568]) ).
fof(c_0_993,plain,
! [X31,X32,X33,X34] :
( hBOOL(hAPP(X34,X32))
| c_in(X31,c_Wellfounded_Oacc(X33,t_a),t_a)
| ~ c_in(c_Pair(X31,v_sko__Wellfounded__Xacc__Xinducts__1(X34,X33),t_a,t_a),X33,tc_prod(t_a,t_a))
| ~ c_in(X32,c_Wellfounded_Oacc(X33,t_a),t_a) ),
inference(variable_rename,[status(thm)],[c_0_569]) ).
fof(c_0_994,plain,
! [X23,X24,X25,X26,X27] :
( c_lessequals(c_Set_Oimage(X23,X25,X27,X26),c_Set_Oimage(X23,X24,X27,X26),tc_fun(X26,tc_bool))
| ~ c_lessequals(X25,X24,tc_fun(X27,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_570]) ).
fof(c_0_995,plain,
! [X23,X24,X25,X26,X27] :
( ~ c_lessequals(X23,X25,tc_fun(X26,tc_bool))
| c_lessequals(c_Set_Oimage(X24,X23,X26,X27),c_Set_Oimage(X24,X25,X26,X27),tc_fun(X27,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_571])])]) ).
fof(c_0_996,plain,
! [X18,X19,X20,X21] :
( c_in(X19,c_Wellfounded_Oacc(X18,X21),X21)
| ~ c_in(c_Pair(X19,X20,X21,X21),c_Transitive__Closure_Ortrancl(X18,X21),tc_prod(X21,X21))
| ~ c_in(X20,c_Wellfounded_Oacc(X18,X21),X21) ),
inference(variable_rename,[status(thm)],[c_0_572]) ).
fof(c_0_997,plain,
! [X18,X19,X20,X21] :
( c_in(X19,c_Wellfounded_Oacc(X18,X21),X21)
| ~ c_in(X20,c_Wellfounded_Oacc(X18,X21),X21)
| ~ c_in(c_Pair(X19,X20,X21,X21),c_Transitive__Closure_Ortrancl(X18,X21),tc_prod(X21,X21)) ),
inference(variable_rename,[status(thm)],[c_0_573]) ).
fof(c_0_998,plain,
! [X30,X31,X32,X33] :
( hBOOL(hAPP(X33,X31))
| hBOOL(hAPP(X33,X30))
| ~ c_in(c_Pair(X30,v_sko__Wellfounded__Xacc__Xinducts__1(X33,X32),t_a,t_a),X32,tc_prod(t_a,t_a))
| ~ c_in(X31,c_Wellfounded_Oacc(X32,t_a),t_a) ),
inference(variable_rename,[status(thm)],[c_0_574]) ).
fof(c_0_999,plain,
! [X30,X31,X32,X33] :
( hBOOL(hAPP(X33,X31))
| hBOOL(hAPP(X33,X30))
| ~ c_in(c_Pair(X30,v_sko__Wellfounded__Xacc__Xinduct__1(X33,X32),t_a,t_a),X32,tc_prod(t_a,t_a))
| ~ c_in(X31,c_Wellfounded_Oacc(X32,t_a),t_a) ),
inference(variable_rename,[status(thm)],[c_0_575]) ).
fof(c_0_1000,plain,
! [X18,X19,X20,X21] :
( c_in(X20,c_Wellfounded_Oacc(X18,X21),X21)
| ~ c_in(c_Pair(X20,X19,X21,X21),X18,tc_prod(X21,X21))
| ~ c_in(X19,c_Wellfounded_Oacc(X18,X21),X21) ),
inference(variable_rename,[status(thm)],[c_0_576]) ).
fof(c_0_1001,plain,
! [X18,X19,X20,X21] :
( c_in(X18,c_Wellfounded_Oacc(X19,X21),X21)
| ~ c_in(c_Pair(X18,X20,X21,X21),X19,tc_prod(X21,X21))
| ~ c_in(X20,c_Wellfounded_Oacc(X19,X21),X21) ),
inference(variable_rename,[status(thm)],[c_0_577]) ).
fof(c_0_1002,plain,
! [X25,X26,X27,X28] :
( X26 = X25
| ~ c_in(c_Pair(X26,X25,X28,X28),c_Transitive__Closure_Ortrancl(X27,X28),tc_prod(X28,X28))
| c_in(X26,c_Relation_ODomain(X27,X28,X28),X28) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_578])])]) ).
fof(c_0_1003,plain,
! [X23,X24,X25,X26,X27,X28] :
( c_in(hAPP(X24,X23),hAPP(X25,X23),X27)
| ~ c_in(X23,X26,X28)
| ~ c_in(X24,c_FuncSet_OPi(X26,X25,X28,X27),tc_fun(X28,X27)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_579])])]) ).
fof(c_0_1004,plain,
! [X23,X24,X25,X26,X27,X28] :
( ~ c_in(X23,X26,X28)
| c_in(hAPP(X24,X23),hAPP(X25,X23),X27)
| ~ c_in(X24,c_FuncSet_OPi(X26,X25,X28,X27),tc_fun(X28,X27)) ),
inference(variable_rename,[status(thm)],[c_0_580]) ).
fof(c_0_1005,plain,
! [X18,X19] :
( c_Nitpick_Orefl_H(X18,X19)
| ~ c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X18,X19),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X18,X19),X19,X19),X18,tc_prod(X19,X19)) ),
inference(variable_rename,[status(thm)],[c_0_581]) ).
fof(c_0_1006,plain,
! [X23,X24,X25,X26,X27,X28] :
( c_in(hAPP(X24,X23),X25,X28)
| ~ c_in(X23,X26,X27)
| ~ c_lessequals(c_Set_Oimage(X24,X26,X27,X28),X25,tc_fun(X28,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_582]) ).
fof(c_0_1007,plain,
! [X18,X19,X20,X21,X22] :
( c_in(X20,c_Relation_ORange(X19,X21,X22),X22)
| ~ c_in(c_Pair(X18,X20,X21,X22),X19,tc_prod(X21,X22)) ),
inference(variable_rename,[status(thm)],[c_0_583]) ).
fof(c_0_1008,plain,
! [X18,X19,X20,X21,X22] :
( c_in(X19,c_Relation_ORange(X18,X22,X21),X21)
| ~ c_in(c_Pair(X20,X19,X22,X21),X18,tc_prod(X22,X21)) ),
inference(variable_rename,[status(thm)],[c_0_584]) ).
fof(c_0_1009,plain,
! [X18,X19,X20,X21,X22] :
( c_in(X20,c_Relation_ODomain(X19,X22,X21),X22)
| ~ c_in(c_Pair(X20,X18,X22,X21),X19,tc_prod(X22,X21)) ),
inference(variable_rename,[status(thm)],[c_0_585]) ).
fof(c_0_1010,plain,
! [X18,X19,X20,X21,X22] :
( c_in(X20,c_Relation_ODomain(X18,X22,X21),X22)
| ~ c_in(c_Pair(X20,X19,X22,X21),X18,tc_prod(X22,X21)) ),
inference(variable_rename,[status(thm)],[c_0_586]) ).
fof(c_0_1011,plain,
! [X10] :
( v_thesis____
| ~ c_in(X10,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X10,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_587])])]) ).
fof(c_0_1012,plain,
! [X19,X20,X21,X22,X23] :
( c_in(X19,X22,X23)
| ~ c_in(c_Pair(X20,X19,X23,X23),X21,tc_prod(X23,X23))
| ~ c_Equiv__Relations_Oequiv(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_588]) ).
fof(c_0_1013,plain,
! [X19,X20,X21,X22,X23] :
( c_in(X20,X22,X23)
| ~ c_in(c_Pair(X20,X19,X23,X23),X21,tc_prod(X23,X23))
| ~ c_Equiv__Relations_Oequiv(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_589]) ).
fof(c_0_1014,plain,
! [X19,X20,X21,X22,X23] :
( c_in(X19,X22,X23)
| ~ c_in(c_Pair(X20,X19,X23,X23),X21,tc_prod(X23,X23))
| ~ c_Relation_Orefl__on(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_590]) ).
fof(c_0_1015,plain,
! [X19,X20,X21,X22,X23] :
( c_in(X20,X22,X23)
| ~ c_in(c_Pair(X20,X19,X23,X23),X21,tc_prod(X23,X23))
| ~ c_Relation_Orefl__on(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_591]) ).
fof(c_0_1016,plain,
! [X19,X20,X21] :
( c_lessequals(X19,c_Product__Type_OSigma(X20,c_COMBK(X20,tc_fun(X21,tc_bool),X21),X21,X21),tc_fun(tc_prod(X21,X21),tc_bool))
| ~ c_Equiv__Relations_Oequiv(X20,X19,X21) ),
inference(variable_rename,[status(thm)],[c_0_592]) ).
fof(c_0_1017,plain,
! [X19,X20,X21] :
( c_lessequals(X19,c_Product__Type_OSigma(X20,c_COMBK(X20,tc_fun(X21,tc_bool),X21),X21,X21),tc_fun(tc_prod(X21,X21),tc_bool))
| ~ c_Relation_Orefl__on(X20,X19,X21) ),
inference(variable_rename,[status(thm)],[c_0_593]) ).
fof(c_0_1018,plain,
! [X19,X20,X21,X22] :
( c_in(X20,X21,X22)
| ~ c_in(c_Pair(X20,X19,X22,X22),c_Relation_OId__on(X21,X22),tc_prod(X22,X22)) ),
inference(variable_rename,[status(thm)],[c_0_594]) ).
fof(c_0_1019,plain,
! [X19,X20,X21,X22] :
( X20 = X19
| ~ c_in(c_Pair(X20,X19,X22,X22),c_Relation_OId__on(X21,X22),tc_prod(X22,X22)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_595])])]) ).
fof(c_0_1020,plain,
! [X23,X24,X25,X26,X27] :
( c_Finite__Set_Ofinite(X24,X26)
| ~ c_lessequals(X24,c_Set_Oimage(X23,X25,X27,X26),tc_fun(X26,tc_bool))
| ~ c_Finite__Set_Ofinite(X25,X27) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_596])])]) ).
fof(c_0_1021,plain,
! [X18,X19,X20] :
( ~ c_in(c_Pair(X19,X19,X20,X20),X18,tc_prod(X20,X20))
| ~ c_Wellfounded_Owf(X18,X20) ),
inference(variable_rename,[status(thm)],[c_0_597]) ).
fof(c_0_1022,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Olattice(X24)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X23,X22,X24),c_Lattices_Olower__semilattice__class_Oinf(X23,X21,X24),X24),c_Lattices_Olower__semilattice__class_Oinf(X23,c_Lattices_Oupper__semilattice__class_Osup(X22,X21,X24),X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_598]) ).
fof(c_0_1023,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Olattice(X24)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X23,c_Lattices_Olower__semilattice__class_Oinf(X22,X21,X24),X24),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X23,X22,X24),c_Lattices_Oupper__semilattice__class_Osup(X23,X21,X24),X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_599]) ).
fof(c_0_1024,plain,
! [X8,X9,X10] :
( X9 = X8
| ~ c_in(c_Pair(X9,X8,X10,X10),c_Relation_OId(X10),tc_prod(X10,X10)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_600])])]) ).
fof(c_0_1025,plain,
! [X23,X24,X25,X26,X27] :
( c_Set_Oinsert(hAPP(X24,X23),c_Set_Oimage(X24,X25,X27,X26),X26) = c_Set_Oimage(X24,X25,X27,X26)
| ~ c_in(X23,X25,X27) ),
inference(variable_rename,[status(thm)],[c_0_601]) ).
fof(c_0_1026,plain,
! [X18,X19,X20] :
( c_in(X18,c_Wellfounded_Oacc(X19,X20),X20)
| c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X19,X18,X20),X18,X20,X20),X19,tc_prod(X20,X20)) ),
inference(variable_rename,[status(thm)],[c_0_602]) ).
fof(c_0_1027,plain,
! [X25,X26,X27] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X26,X25,X27),X25,X27,X27),X26,tc_prod(X27,X27))
| c_in(X25,c_Wellfounded_Oacc(X26,X27),X27) ),
inference(variable_rename,[status(thm)],[c_0_603]) ).
fof(c_0_1028,plain,
! [X17,X18,X19] :
( X17 = X18
| X18 = X17
| ~ c_in(X19,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X18 = X17
| c_in(c_Pair(X18,X17,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X19,X18,X17),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_604])])]) ).
fof(c_0_1029,plain,
! [X17,X18,X19] :
( X17 = X18
| X17 = X18
| ~ c_in(X19,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X17 = X18
| c_in(c_Pair(X17,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X19,X17,X18),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_605])])]) ).
fof(c_0_1030,plain,
! [X19,X20,X21,X22] :
( c_in(c_List_Osko__Equiv__Relations__XquotientE__1__1(X21,X20,X19,X22),X21,X22)
| ~ c_in(X20,c_Equiv__Relations_Oquotient(X21,X19,X22),tc_fun(X22,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_606]) ).
fof(c_0_1031,plain,
! [X22,X23,X24,X25] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X24,X23,tc_fun(X25,tc_bool)),X22,tc_fun(X25,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X24,c_Lattices_Oupper__semilattice__class_Osup(X23,X22,tc_fun(X25,tc_bool)),tc_fun(X25,tc_bool))
| c_lessequals(X22,X24,tc_fun(X25,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_607]) ).
fof(c_0_1032,plain,
! [X25,X26,X27,X28] :
( c_in(X25,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X27,X26,tc_fun(tc_prod(X28,X28),tc_bool)),X28),tc_prod(X28,X28))
| ~ c_in(X25,c_Transitive__Closure_Ortrancl(X26,X28),tc_prod(X28,X28)) ),
inference(variable_rename,[status(thm)],[c_0_608]) ).
fof(c_0_1033,plain,
! [X25,X26,X27,X28] :
( c_in(X25,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X27,X26,tc_fun(tc_prod(X28,X28),tc_bool)),X28),tc_prod(X28,X28))
| ~ c_in(X25,c_Transitive__Closure_Ortrancl(X27,X28),tc_prod(X28,X28)) ),
inference(variable_rename,[status(thm)],[c_0_609]) ).
fof(c_0_1034,plain,
! [X16,X17,X18,X19,X20,X21] :
( c_Pair(X19,X17,X21,X20) != c_Pair(X18,X16,X21,X20)
| X17 = X16 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_610])])]) ).
fof(c_0_1035,plain,
! [X16,X17,X18,X19,X20,X21] :
( c_Pair(X19,X17,X21,X20) != c_Pair(X18,X16,X21,X20)
| X19 = X18 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_611])])]) ).
fof(c_0_1036,plain,
! [X25,X26,X27] :
( c_in(X25,c_Relation_ODomain(X26,X27,X27),X27)
| c_in(c_Pair(X25,X25,X27,X27),c_Transitive__Closure_Ortrancl(X26,X27),tc_prod(X27,X27)) ),
inference(variable_rename,[status(thm)],[c_0_612]) ).
fof(c_0_1037,plain,
! [X19,X20,X21,X22] :
( c_in(c_Pair(X19,X19,X22,X22),X20,tc_prod(X22,X22))
| ~ c_in(X19,X21,X22)
| ~ c_Relation_Orefl__on(X21,X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_613]) ).
fof(c_0_1038,plain,
! [X19,X20,X21,X22] :
( c_in(c_Pair(X20,X20,X22,X22),X19,tc_prod(X22,X22))
| ~ c_in(X20,X21,X22)
| ~ c_Relation_Orefl__on(X21,X19,X22) ),
inference(variable_rename,[status(thm)],[c_0_614]) ).
fof(c_0_1039,plain,
! [X19,X20,X21] :
( c_in(c_Pair(X19,X19,X21,X21),c_Relation_OId__on(X20,X21),tc_prod(X21,X21))
| ~ c_in(X19,X20,X21) ),
inference(variable_rename,[status(thm)],[c_0_615]) ).
fof(c_0_1040,plain,
! [X44,X45,X46,X47,X48] :
( ~ c_in(X44,X46,X47)
| c_in(hAPP(X45,X44),c_Set_Oimage(X45,X46,X47,X48),X48) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_616])])]) ).
fof(c_0_1041,plain,
! [X23,X24,X25,X26,X27] :
( ~ c_in(X23,X25,X26)
| c_in(hAPP(X24,X23),c_Set_Oimage(X24,X25,X26,X27),X27) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_617])])]) ).
fof(c_0_1042,plain,
! [X23,X24,X25,X26,X27] :
( c_in(hAPP(X24,X23),c_Set_Oimage(X24,X25,X26,X27),X27)
| ~ c_in(X23,X25,X26) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_618])])]) ).
fof(c_0_1043,plain,
! [X23,X24,X25,X26,X27] :
( c_in(hAPP(X24,X23),c_Set_Oimage(X24,X25,X27,X26),X26)
| ~ c_in(X23,X25,X27) ),
inference(variable_rename,[status(thm)],[c_0_619]) ).
fof(c_0_1044,plain,
! [X26,X27,X28,X29,X30] :
( c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(X29,X28,tc_fun(X30,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X27,X26,tc_fun(tc_prod(X30,X30),tc_bool)),X30)
| ~ c_Relation_Orefl__on(X28,X26,X30)
| ~ c_Relation_Orefl__on(X29,X27,X30) ),
inference(variable_rename,[status(thm)],[c_0_620]) ).
fof(c_0_1045,plain,
! [X26,X27,X28,X29,X30] :
( c_Relation_Orefl__on(c_Lattices_Olower__semilattice__class_Oinf(X29,X28,tc_fun(X30,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X27,X26,tc_fun(tc_prod(X30,X30),tc_bool)),X30)
| ~ c_Relation_Orefl__on(X28,X26,X30)
| ~ c_Relation_Orefl__on(X29,X27,X30) ),
inference(variable_rename,[status(thm)],[c_0_621]) ).
fof(c_0_1046,plain,
! [X24,X25,X26] :
( X24 = c_Pair(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X25,X24,X26),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X25,X24,X26),X26,X26)
| ~ c_in(X24,c_Relation_OId__on(X25,X26),tc_prod(X26,X26)) ),
inference(variable_rename,[status(thm)],[c_0_622]) ).
fof(c_0_1047,plain,
! [X39,X40,X41,X42,X43] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X42,X41,tc_fun(X43,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X40,X39,tc_fun(X43,tc_bool)),tc_fun(X43,tc_bool))
| ~ c_lessequals(X41,X39,tc_fun(X43,tc_bool))
| ~ c_lessequals(X42,X40,tc_fun(X43,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_623]) ).
fof(c_0_1048,plain,
! [X39,X40,X41,X42,X43] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X42,X41,tc_fun(X43,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X40,X39,tc_fun(X43,tc_bool)),tc_fun(X43,tc_bool))
| ~ c_lessequals(X41,X39,tc_fun(X43,tc_bool))
| ~ c_lessequals(X42,X40,tc_fun(X43,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_624]) ).
fof(c_0_1049,plain,
! [X18,X19,X20] :
( c_in(c_Pair(X18,X18,X20,X20),X19,tc_prod(X20,X20))
| ~ c_Nitpick_Orefl_H(X19,X20) ),
inference(variable_rename,[status(thm)],[c_0_625]) ).
fof(c_0_1050,plain,
! [X13,X14,X15] :
( X14 = X13
| X13 = X14
| c_in(c_Pair(X14,X13,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X15,X14),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_626])])]) ).
fof(c_0_1051,plain,
! [X17,X18,X19] :
( X17 = X18
| X17 = X18
| c_in(c_Pair(X17,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X19,X18),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_627])])]) ).
fof(c_0_1052,plain,
! [X8,X9] :
( c_in(c_Pair(X9,X8,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X9,X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X9 = X8 ),
inference(variable_rename,[status(thm)],[c_0_628]) ).
fof(c_0_1053,plain,
! [X20,X21,X22,X23] :
( hBOOL(hAPP(X21,X20))
| hBOOL(hAPP(X22,X20))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X22,X21,tc_fun(X23,tc_bool)),X20)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_629])])]) ).
fof(c_0_1054,plain,
! [X22,X23,X24,X25] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X24,X23,tc_fun(X25,tc_bool)),X22,tc_fun(X25,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X24,c_Lattices_Oupper__semilattice__class_Osup(X23,X22,tc_fun(X25,tc_bool)),tc_fun(X25,tc_bool))
| ~ c_lessequals(X22,X24,tc_fun(X25,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_630]) ).
fof(c_0_1055,plain,
! [X20,X21,X22,X23] :
( hBOOL(hAPP(X21,X20))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X22,X21,tc_fun(X23,tc_bool)),X20)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_631])])]) ).
fof(c_0_1056,plain,
! [X20,X21,X22,X23] :
( hBOOL(hAPP(X22,X20))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X22,X21,tc_fun(X23,tc_bool)),X20)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_632])])]) ).
fof(c_0_1057,plain,
! [X30,X31,X32,X33] :
( hBOOL(hAPP(X32,X31))
| ~ hBOOL(hAPP(X32,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X32,X30,X33)))
| ~ c_in(X31,c_Wellfounded_Oacc(X30,X33),X33) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_633])])]) ).
fof(c_0_1058,plain,
! [X30,X31,X32,X33] :
( hBOOL(hAPP(X32,X31))
| ~ hBOOL(hAPP(X32,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X32,X30,X33)))
| ~ c_in(X31,c_Wellfounded_Oacc(X30,X33),X33) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_634])])]) ).
fof(c_0_1059,plain,
! [X23,X24,X25,X26] :
( c_Relation_Otrans(c_Relation_Oinv__image(X23,X24,X26,X25),X25)
| ~ c_Relation_Otrans(X23,X26) ),
inference(variable_rename,[status(thm)],[c_0_635]) ).
fof(c_0_1060,plain,
! [X42,X43,X44,X45] :
( c_Finite__Set_Ofinite(c_Set_Oimage(X42,X43,X45,X44),X44)
| ~ c_Finite__Set_Ofinite(X43,X45) ),
inference(variable_rename,[status(thm)],[c_0_636]) ).
fof(c_0_1061,plain,
! [X23,X24,X25,X26] :
( c_Wellfounded_Owf(c_Relation_Oinv__image(X23,X24,X26,X25),X25)
| ~ c_Wellfounded_Owf(X23,X26) ),
inference(variable_rename,[status(thm)],[c_0_637]) ).
fof(c_0_1062,plain,
! [X23,X24,X25,X26] :
( c_Relation_Osym(c_Relation_Oinv__image(X23,X24,X26,X25),X25)
| ~ c_Relation_Osym(X23,X26) ),
inference(variable_rename,[status(thm)],[c_0_638]) ).
fof(c_0_1063,plain,
! [X26,X27,X28,X29] :
( c_lessequals(c_Relation_ODomain(X27,X29,X28),c_Relation_ODomain(X26,X29,X28),tc_fun(X29,tc_bool))
| ~ c_lessequals(X27,X26,tc_fun(tc_prod(X29,X28),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_639]) ).
fof(c_0_1064,plain,
! [X29,X30,X31,X32] :
( c_in(X31,c_Transitive__Closure_Otrancl(X29,X32),tc_prod(X32,X32))
| ~ c_lessequals(X30,X29,tc_fun(tc_prod(X32,X32),tc_bool))
| ~ c_in(X31,c_Transitive__Closure_Otrancl(X30,X32),tc_prod(X32,X32)) ),
inference(variable_rename,[status(thm)],[c_0_640]) ).
fof(c_0_1065,plain,
! [X22,X23,X24,X25] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X22,X24,X25),X23,tc_fun(X25,tc_bool)) = c_Set_Oinsert(X22,c_Lattices_Olower__semilattice__class_Oinf(X24,X23,tc_fun(X25,tc_bool)),X25)
| ~ c_in(X22,X23,X25) ),
inference(variable_rename,[status(thm)],[c_0_641]) ).
fof(c_0_1066,plain,
! [X20,X21,X22,X23] :
( c_Lattices_Olower__semilattice__class_Oinf(X22,c_Set_Oinsert(X20,X21,X23),tc_fun(X23,tc_bool)) = c_Set_Oinsert(X20,c_Lattices_Olower__semilattice__class_Oinf(X22,X21,tc_fun(X23,tc_bool)),X23)
| ~ c_in(X20,X22,X23) ),
inference(variable_rename,[status(thm)],[c_0_642]) ).
fof(c_0_1067,plain,
! [X25,X26,X27] :
( c_Transitive__Closure_Ortrancl(X25,X27) = c_Transitive__Closure_Ortrancl(X26,X27)
| ~ c_lessequals(X25,c_Transitive__Closure_Ortrancl(X26,X27),tc_fun(tc_prod(X27,X27),tc_bool))
| ~ c_lessequals(X26,X25,tc_fun(tc_prod(X27,X27),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_643]) ).
fof(c_0_1068,plain,
! [X22,X23,X24,X25] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X24,X23,tc_fun(X25,tc_bool)),X22,tc_fun(X25,tc_bool))
| ~ c_lessequals(X23,X22,tc_fun(X25,tc_bool))
| ~ c_lessequals(X24,X22,tc_fun(X25,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_644]) ).
fof(c_0_1069,plain,
! [X22,X23,X24,X25] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X24,X23,tc_fun(X25,tc_bool)),X22,tc_fun(X25,tc_bool))
| ~ c_lessequals(X23,X22,tc_fun(X25,tc_bool))
| ~ c_lessequals(X24,X22,tc_fun(X25,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_645]) ).
fof(c_0_1070,plain,
! [X22,X23,X24,X25] :
( c_lessequals(X22,c_Lattices_Olower__semilattice__class_Oinf(X24,X23,tc_fun(X25,tc_bool)),tc_fun(X25,tc_bool))
| ~ c_lessequals(X22,X23,tc_fun(X25,tc_bool))
| ~ c_lessequals(X22,X24,tc_fun(X25,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_646]) ).
fof(c_0_1071,plain,
! [X22,X23,X24,X25] :
( c_lessequals(X22,c_Lattices_Olower__semilattice__class_Oinf(X24,X23,tc_fun(X25,tc_bool)),tc_fun(X25,tc_bool))
| ~ c_lessequals(X22,X23,tc_fun(X25,tc_bool))
| ~ c_lessequals(X22,X24,tc_fun(X25,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_647]) ).
fof(c_0_1072,plain,
! [X9] :
( c_in(X9,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Relation_Oconverse(X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_648]) ).
fof(c_0_1073,plain,
! [X22,X23,X24,X25] :
( c_lessequals(X22,X23,tc_fun(X25,tc_bool))
| ~ c_lessequals(X22,c_Lattices_Olower__semilattice__class_Oinf(X24,X23,tc_fun(X25,tc_bool)),tc_fun(X25,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_649]) ).
fof(c_0_1074,plain,
! [X22,X23,X24,X25] :
( c_lessequals(X22,X24,tc_fun(X25,tc_bool))
| ~ c_lessequals(X22,c_Lattices_Olower__semilattice__class_Oinf(X24,X23,tc_fun(X25,tc_bool)),tc_fun(X25,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_650]) ).
fof(c_0_1075,plain,
! [X22,X23,X24,X25] :
( c_lessequals(X24,X22,tc_fun(X25,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X24,X23,tc_fun(X25,tc_bool)),X22,tc_fun(X25,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_651]) ).
fof(c_0_1076,plain,
! [X22,X23,X24,X25] :
( c_lessequals(X23,X22,tc_fun(X25,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X24,X23,tc_fun(X25,tc_bool)),X22,tc_fun(X25,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_652]) ).
fof(c_0_1077,plain,
! [X29,X30] :
( X29 = c_Pair(c_ATP__Linkup_Osko__Relation__XIdE__1__1(X29,X30),c_ATP__Linkup_Osko__Relation__XIdE__1__1(X29,X30),X30,X30)
| ~ c_in(X29,c_Relation_OId(X30),tc_prod(X30,X30)) ),
inference(variable_rename,[status(thm)],[c_0_653]) ).
fof(c_0_1078,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Odistrib__lattice(X24)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X22,X21,X24),X23,X24) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X22,X23,X24),c_Lattices_Olower__semilattice__class_Oinf(X21,X23,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_654]) ).
fof(c_0_1079,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Odistrib__lattice(X24)
| c_Lattices_Olower__semilattice__class_Oinf(X23,c_Lattices_Oupper__semilattice__class_Osup(X22,X21,X24),X24) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X23,X22,X24),c_Lattices_Olower__semilattice__class_Oinf(X23,X21,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_655]) ).
fof(c_0_1080,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Odistrib__lattice(X24)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X22,X21,X24),X23,X24) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X22,X23,X24),c_Lattices_Oupper__semilattice__class_Osup(X21,X23,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_656]) ).
fof(c_0_1081,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Odistrib__lattice(X24)
| c_Lattices_Oupper__semilattice__class_Osup(X23,c_Lattices_Olower__semilattice__class_Oinf(X22,X21,X24),X24) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X23,X22,X24),c_Lattices_Oupper__semilattice__class_Osup(X23,X21,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_657]) ).
fof(c_0_1082,plain,
! [X24,X25,X26,X27] :
( c_in(X24,X25,X27)
| c_in(X24,X26,X27)
| ~ c_in(X24,c_Lattices_Oupper__semilattice__class_Osup(X26,X25,tc_fun(X27,tc_bool)),X27) ),
inference(variable_rename,[status(thm)],[c_0_658]) ).
fof(c_0_1083,plain,
! [X20,X21,X22,X23] :
( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X22,X21,tc_fun(X23,tc_bool)),X20))
| ~ hBOOL(hAPP(X21,X20))
| ~ hBOOL(hAPP(X22,X20)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_659])])]) ).
fof(c_0_1084,plain,
! [X26,X27,X28] :
( c_lessequals(c_Transitive__Closure_Ortrancl(X27,X28),c_Transitive__Closure_Ortrancl(X26,X28),tc_fun(tc_prod(X28,X28),tc_bool))
| ~ c_lessequals(X27,c_Transitive__Closure_Ortrancl(X26,X28),tc_fun(tc_prod(X28,X28),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_660]) ).
fof(c_0_1085,plain,
! [X20,X21,X22,X23] :
( c_lessequals(X22,X21,tc_fun(X23,tc_bool))
| c_in(X20,X22,X23)
| ~ c_lessequals(X22,c_Set_Oinsert(X20,X21,X23),tc_fun(X23,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_661]) ).
fof(c_0_1086,plain,
! [X20,X21,X22,X23] :
( c_lessequals(X22,X21,tc_fun(X23,tc_bool))
| ~ c_lessequals(X22,c_Set_Oinsert(X20,X21,X23),tc_fun(X23,tc_bool))
| c_in(X20,X22,X23) ),
inference(variable_rename,[status(thm)],[c_0_662]) ).
fof(c_0_1087,plain,
! [X19,X20,X21,X22] :
( hBOOL(hAPP(X21,X20))
| X19 = X20
| ~ hBOOL(hAPP(c_Set_Oinsert(X19,X21,X22),X20)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_663])])]) ).
fof(c_0_1088,plain,
! [X39,X40,X41,X42] :
( c_lessequals(c_Set_Oinsert(X39,X41,X42),c_Set_Oinsert(X39,X40,X42),tc_fun(X42,tc_bool))
| ~ c_lessequals(X41,X40,tc_fun(X42,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_664]) ).
fof(c_0_1089,plain,
! [X13,X14,X15] :
( c_in(c_Arrow__Order__Mirabelle_Obelow(X15,X14,X13),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X15,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X14 = X13 ),
inference(variable_rename,[status(thm)],[c_0_665]) ).
fof(c_0_1090,plain,
! [X13,X14,X15] :
( c_in(c_Arrow__Order__Mirabelle_Oabove(X15,X14,X13),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X15,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X14 = X13 ),
inference(variable_rename,[status(thm)],[c_0_666]) ).
fof(c_0_1091,plain,
! [X9] :
( c_in(c_Relation_Oconverse(X9,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X9,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_667]) ).
fof(c_0_1092,plain,
! [X20,X21,X22,X23] :
( c_lessequals(c_Set_Oinsert(X20,X22,X23),X21,tc_fun(X23,tc_bool))
| ~ c_lessequals(X22,X21,tc_fun(X23,tc_bool))
| ~ c_in(X20,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_668]) ).
fof(c_0_1093,plain,
! [X26,X27,X28] :
( c_lessequals(c_Transitive__Closure_Ortrancl(X27,X28),c_Transitive__Closure_Ortrancl(X26,X28),tc_fun(tc_prod(X28,X28),tc_bool))
| ~ c_lessequals(X27,X26,tc_fun(tc_prod(X28,X28),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_669]) ).
fof(c_0_1094,plain,
! [X20,X21,X22,X23] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X22,X21,tc_fun(X23,tc_bool)),X20))
| ~ hBOOL(hAPP(X21,X20)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_670])])]) ).
fof(c_0_1095,plain,
! [X20,X21,X22,X23] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X22,X21,tc_fun(X23,tc_bool)),X20))
| ~ hBOOL(hAPP(X22,X20)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_671])])]) ).
fof(c_0_1096,plain,
! [X22,X23,X24] :
( c_in(c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X23,X22,X24),X22,tc_fun(X24,tc_bool))
| ~ c_in(X23,c_Complete__Lattice_OSup__class_OSup(X22,tc_fun(X24,tc_bool)),X24) ),
inference(variable_rename,[status(thm)],[c_0_672]) ).
fof(c_0_1097,plain,
! [X24,X25,X26,X27] :
( c_in(X24,X25,X27)
| ~ c_in(X24,c_Lattices_Olower__semilattice__class_Oinf(X26,X25,tc_fun(X27,tc_bool)),X27) ),
inference(variable_rename,[status(thm)],[c_0_673]) ).
fof(c_0_1098,plain,
! [X24,X25,X26,X27] :
( c_in(X24,X26,X27)
| ~ c_in(X24,c_Lattices_Olower__semilattice__class_Oinf(X26,X25,tc_fun(X27,tc_bool)),X27) ),
inference(variable_rename,[status(thm)],[c_0_674]) ).
fof(c_0_1099,plain,
! [X22,X23,X24] :
( c_in(X23,c_Complete__Lattice_OInf__class_OInf(X22,tc_fun(X24,tc_bool)),X24)
| ~ c_in(X23,c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X23,X22,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_675]) ).
fof(c_0_1100,plain,
! [X24,X25,X26,X27] :
( c_in(X24,c_Lattices_Olower__semilattice__class_Oinf(X26,X25,tc_fun(X27,tc_bool)),X27)
| ~ c_in(X24,X25,X27)
| ~ c_in(X24,X26,X27) ),
inference(variable_rename,[status(thm)],[c_0_676]) ).
fof(c_0_1101,plain,
! [X24,X25,X26,X27] :
( c_in(X24,c_Lattices_Olower__semilattice__class_Oinf(X26,X25,tc_fun(X27,tc_bool)),X27)
| ~ c_in(X24,X25,X27)
| ~ c_in(X24,X26,X27) ),
inference(variable_rename,[status(thm)],[c_0_677]) ).
fof(c_0_1102,plain,
! [X22,X23,X24,X25] :
( c_in(X24,X22,X25)
| ~ c_in(X22,X23,tc_fun(X25,tc_bool))
| ~ c_in(X24,c_Complete__Lattice_OInf__class_OInf(X23,tc_fun(X25,tc_bool)),X25) ),
inference(variable_rename,[status(thm)],[c_0_678]) ).
fof(c_0_1103,plain,
! [X18,X19,X20] :
( c_in(X18,c_Wellfounded_Oacc(X19,X20),X20)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X19,X18,X20),c_Wellfounded_Oacc(X19,X20),X20) ),
inference(variable_rename,[status(thm)],[c_0_679]) ).
fof(c_0_1104,plain,
! [X25,X26,X27] :
( ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X26,X25,X27),c_Wellfounded_Oacc(X26,X27),X27)
| c_in(X25,c_Wellfounded_Oacc(X26,X27),X27) ),
inference(variable_rename,[status(thm)],[c_0_680]) ).
fof(c_0_1105,plain,
! [X20,X21,X22,X23] :
( c_lessequals(X22,X21,tc_fun(X23,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X20,X22,X23),X21,tc_fun(X23,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_681]) ).
fof(c_0_1106,plain,
! [X18,X19] :
( c_Wellfounded_Owf(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X18,X19),X19,X19),X19)
| ~ c_Wellfounded_Owf(c_Relation_Oconverse(X18,X19,X19),X19) ),
inference(variable_rename,[status(thm)],[c_0_682]) ).
fof(c_0_1107,plain,
! [X20,X21,X22,X23] :
( c_lessequals(X22,c_Set_Oinsert(X20,X21,X23),tc_fun(X23,tc_bool))
| ~ c_lessequals(X22,X21,tc_fun(X23,tc_bool))
| c_in(X20,X22,X23) ),
inference(variable_rename,[status(thm)],[c_0_683]) ).
fof(c_0_1108,plain,
! [X20,X21,X22,X23] :
( c_lessequals(X22,c_Set_Oinsert(X20,X21,X23),tc_fun(X23,tc_bool))
| ~ c_lessequals(X22,X21,tc_fun(X23,tc_bool))
| c_in(X20,X22,X23) ),
inference(variable_rename,[status(thm)],[c_0_684]) ).
fof(c_0_1109,plain,
! [X22,X23,X24] :
( c_in(X23,c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X23,X22,X24),X24)
| ~ c_in(X23,c_Complete__Lattice_OSup__class_OSup(X22,tc_fun(X24,tc_bool)),X24) ),
inference(variable_rename,[status(thm)],[c_0_685]) ).
fof(c_0_1110,plain,
! [X30,X31,X32,X33] :
( hBOOL(hAPP(X32,X31))
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X32,X30,X33),c_Wellfounded_Oacc(X30,X33),X33)
| ~ c_in(X31,c_Wellfounded_Oacc(X30,X33),X33) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_686])])]) ).
fof(c_0_1111,plain,
! [X30,X31,X32,X33] :
( hBOOL(hAPP(X32,X31))
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X32,X30,X33),c_Wellfounded_Oacc(X30,X33),X33)
| ~ c_in(X31,c_Wellfounded_Oacc(X30,X33),X33) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_687])])]) ).
fof(c_0_1112,plain,
! [X20,X21,X22,X23] :
( c_in(X20,X21,X23)
| ~ c_lessequals(c_Set_Oinsert(X20,X22,X23),X21,tc_fun(X23,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_688]) ).
fof(c_0_1113,plain,
! [X11,X12,X13,X14] :
( ~ class_Lattices_Oupper__semilattice(X14)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X13,X12,X14),X11,X14)
| ~ c_lessequals(X12,X11,X14)
| ~ c_lessequals(X13,X11,X14) ),
inference(variable_rename,[status(thm)],[c_0_689]) ).
fof(c_0_1114,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Oupper__semilattice(X24)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X22,X21,X24),X23,X24)
| ~ c_lessequals(X21,X23,X24)
| ~ c_lessequals(X22,X23,X24) ),
inference(variable_rename,[status(thm)],[c_0_690]) ).
fof(c_0_1115,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Oupper__semilattice(X24)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X23,X22,X24),X21,X24)
| ~ c_lessequals(X22,X21,X24)
| ~ c_lessequals(X23,X21,X24) ),
inference(variable_rename,[status(thm)],[c_0_691]) ).
fof(c_0_1116,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Olower__semilattice(X24)
| c_lessequals(X23,c_Lattices_Olower__semilattice__class_Oinf(X22,X21,X24),X24)
| ~ c_lessequals(X23,X21,X24)
| ~ c_lessequals(X23,X22,X24) ),
inference(variable_rename,[status(thm)],[c_0_692]) ).
fof(c_0_1117,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Olower__semilattice(X24)
| c_lessequals(X23,c_Lattices_Olower__semilattice__class_Oinf(X22,X21,X24),X24)
| ~ c_lessequals(X23,X21,X24)
| ~ c_lessequals(X23,X22,X24) ),
inference(variable_rename,[status(thm)],[c_0_693]) ).
fof(c_0_1118,plain,
! [X11,X12,X13,X14] :
( ~ class_Lattices_Olower__semilattice(X14)
| c_lessequals(X11,c_Lattices_Olower__semilattice__class_Oinf(X13,X12,X14),X14)
| ~ c_lessequals(X11,X12,X14)
| ~ c_lessequals(X11,X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_694]) ).
fof(c_0_1119,plain,
! [X22,X23,X24,X25] :
( c_in(X24,c_Complete__Lattice_OSup__class_OSup(X23,tc_fun(X25,tc_bool)),X25)
| ~ c_in(X24,X22,X25)
| ~ c_in(X22,X23,tc_fun(X25,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_695]) ).
fof(c_0_1120,plain,
! [X26,X27,X28] :
( c_lessequals(c_Relation_OField(X27,X28),c_Relation_OField(X26,X28),tc_fun(X28,tc_bool))
| ~ c_lessequals(X27,X26,tc_fun(tc_prod(X28,X28),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_696]) ).
fof(c_0_1121,plain,
! [X35,X36,X37] :
( c_lessequals(c_Wellfounded_Oacc(X35,X37),c_Wellfounded_Oacc(X36,X37),tc_fun(X37,tc_bool))
| ~ c_lessequals(X36,X35,tc_fun(tc_prod(X37,X37),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_697]) ).
fof(c_0_1122,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Oupper__semilattice(X24)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X23,X22,X24),X21,X24) = c_Lattices_Oupper__semilattice__class_Osup(X23,c_Lattices_Oupper__semilattice__class_Osup(X22,X21,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_698]) ).
fof(c_0_1123,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Oupper__semilattice(X24)
| c_Lattices_Oupper__semilattice__class_Osup(X23,c_Lattices_Oupper__semilattice__class_Osup(X22,X21,X24),X24) = c_Lattices_Oupper__semilattice__class_Osup(X22,c_Lattices_Oupper__semilattice__class_Osup(X23,X21,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_699]) ).
fof(c_0_1124,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Olattice(X24)
| c_Lattices_Oupper__semilattice__class_Osup(X23,c_Lattices_Oupper__semilattice__class_Osup(X22,X21,X24),X24) = c_Lattices_Oupper__semilattice__class_Osup(X22,c_Lattices_Oupper__semilattice__class_Osup(X23,X21,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_700]) ).
fof(c_0_1125,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Olattice(X24)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X23,X22,X24),X21,X24) = c_Lattices_Oupper__semilattice__class_Osup(X23,c_Lattices_Oupper__semilattice__class_Osup(X22,X21,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_701]) ).
fof(c_0_1126,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Olattice(X24)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X23,X22,X24),X21,X24) = c_Lattices_Olower__semilattice__class_Oinf(X23,c_Lattices_Olower__semilattice__class_Oinf(X22,X21,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_702]) ).
fof(c_0_1127,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Olattice(X24)
| c_Lattices_Olower__semilattice__class_Oinf(X23,c_Lattices_Olower__semilattice__class_Oinf(X22,X21,X24),X24) = c_Lattices_Olower__semilattice__class_Oinf(X22,c_Lattices_Olower__semilattice__class_Oinf(X23,X21,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_703]) ).
fof(c_0_1128,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Olower__semilattice(X24)
| c_Lattices_Olower__semilattice__class_Oinf(X23,c_Lattices_Olower__semilattice__class_Oinf(X22,X21,X24),X24) = c_Lattices_Olower__semilattice__class_Oinf(X22,c_Lattices_Olower__semilattice__class_Oinf(X23,X21,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_704]) ).
fof(c_0_1129,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Olower__semilattice(X24)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X23,X22,X24),X21,X24) = c_Lattices_Olower__semilattice__class_Oinf(X23,c_Lattices_Olower__semilattice__class_Oinf(X22,X21,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_705]) ).
fof(c_0_1130,plain,
! [X24,X25,X26] :
( c_in(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X25,X24,X26),X25,X26)
| ~ c_in(X24,c_Relation_OId__on(X25,X26),tc_prod(X26,X26)) ),
inference(variable_rename,[status(thm)],[c_0_706]) ).
fof(c_0_1131,plain,
! [X11,X12] :
( c_in(c_Arrow__Order__Mirabelle_Omktop(X12,X11),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X12,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_707]) ).
fof(c_0_1132,plain,
! [X11,X12] :
( c_in(c_Arrow__Order__Mirabelle_Omkbot(X12,X11),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X12,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_708]) ).
fof(c_0_1133,plain,
! [X22,X23,X24,X25] :
( c_lessequals(X24,X22,tc_fun(X25,tc_bool))
| ~ c_lessequals(X23,X22,tc_fun(X25,tc_bool))
| ~ c_lessequals(X24,X23,tc_fun(X25,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_709]) ).
fof(c_0_1134,plain,
! [X20,X21,X22,X23] :
( c_Lattices_Olower__semilattice__class_Oinf(X22,c_Set_Oinsert(X20,X21,X23),tc_fun(X23,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X22,X21,tc_fun(X23,tc_bool))
| c_in(X20,X22,X23) ),
inference(variable_rename,[status(thm)],[c_0_710]) ).
fof(c_0_1135,plain,
! [X22,X23,X24,X25] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X22,X24,X25),X23,tc_fun(X25,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X24,X23,tc_fun(X25,tc_bool))
| c_in(X22,X23,X25) ),
inference(variable_rename,[status(thm)],[c_0_711]) ).
fof(c_0_1136,plain,
! [X26,X27,X28] :
( c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X27,X26,tc_fun(tc_prod(X28,X28),tc_bool)),X28)
| ~ c_Relation_Osym(X26,X28)
| ~ c_Relation_Osym(X27,X28) ),
inference(variable_rename,[status(thm)],[c_0_712]) ).
fof(c_0_1137,plain,
! [X26,X27,X28] :
( c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X27,X26,tc_fun(tc_prod(X28,X28),tc_bool)),X28)
| ~ c_Relation_Osym(X26,X28)
| ~ c_Relation_Osym(X27,X28) ),
inference(variable_rename,[status(thm)],[c_0_713]) ).
fof(c_0_1138,plain,
! [X26,X27,X28] :
( c_Relation_Otrans(c_Lattices_Olower__semilattice__class_Oinf(X27,X26,tc_fun(tc_prod(X28,X28),tc_bool)),X28)
| ~ c_Relation_Otrans(X26,X28)
| ~ c_Relation_Otrans(X27,X28) ),
inference(variable_rename,[status(thm)],[c_0_714]) ).
fof(c_0_1139,plain,
! [X11,X12,X13,X14] :
( ~ class_Lattices_Olower__semilattice(X14)
| c_lessequals(X11,X13,X14)
| ~ c_lessequals(X11,c_Lattices_Olower__semilattice__class_Oinf(X13,X12,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_715]) ).
fof(c_0_1140,plain,
! [X11,X12,X13,X14] :
( ~ class_Lattices_Olower__semilattice(X14)
| c_lessequals(X11,X12,X14)
| ~ c_lessequals(X11,c_Lattices_Olower__semilattice__class_Oinf(X13,X12,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_716]) ).
fof(c_0_1141,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Olower__semilattice(X24)
| c_lessequals(X23,X22,X24)
| ~ c_lessequals(X23,c_Lattices_Olower__semilattice__class_Oinf(X22,X21,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_717]) ).
fof(c_0_1142,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Olower__semilattice(X24)
| c_lessequals(X23,X21,X24)
| ~ c_lessequals(X23,c_Lattices_Olower__semilattice__class_Oinf(X22,X21,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_718]) ).
fof(c_0_1143,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Oupper__semilattice(X24)
| c_lessequals(X22,X21,X24)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X23,X22,X24),X21,X24) ),
inference(variable_rename,[status(thm)],[c_0_719]) ).
fof(c_0_1144,plain,
! [X21,X22,X23,X24] :
( ~ class_Lattices_Oupper__semilattice(X24)
| c_lessequals(X23,X21,X24)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X23,X22,X24),X21,X24) ),
inference(variable_rename,[status(thm)],[c_0_720]) ).
fof(c_0_1145,plain,
! [X11,X12,X13,X14] :
( ~ class_Lattices_Oupper__semilattice(X14)
| c_lessequals(X12,X11,X14)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X13,X12,X14),X11,X14) ),
inference(variable_rename,[status(thm)],[c_0_721]) ).
fof(c_0_1146,plain,
! [X11,X12,X13,X14] :
( ~ class_Lattices_Oupper__semilattice(X14)
| c_lessequals(X13,X11,X14)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X13,X12,X14),X11,X14) ),
inference(variable_rename,[status(thm)],[c_0_722]) ).
fof(c_0_1147,plain,
! [X19,X20,X21,X22] :
( c_in(X20,X21,X22)
| X20 = X19
| ~ c_in(X20,c_Set_Oinsert(X19,X21,X22),X22) ),
inference(variable_rename,[status(thm)],[c_0_723]) ).
fof(c_0_1148,plain,
! [X22,X23,X24] :
( c_in(X23,c_Complete__Lattice_OInf__class_OInf(X22,tc_fun(X24,tc_bool)),X24)
| c_in(c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X23,X22,X24),X22,tc_fun(X24,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_724]) ).
fof(c_0_1149,plain,
! [X19,X20,X21] :
( c_Relation_Orefl__on(X20,X19,X21)
| ~ c_Relation_Orefl__on(X20,c_Relation_Oconverse(X19,X21,X21),X21) ),
inference(variable_rename,[status(thm)],[c_0_725]) ).
fof(c_0_1150,plain,
! [X19,X20,X21] :
( c_Relation_Ototal__on(X20,X19,X21)
| ~ c_Relation_Ototal__on(X20,c_Relation_Oconverse(X19,X21,X21),X21) ),
inference(variable_rename,[status(thm)],[c_0_726]) ).
fof(c_0_1151,plain,
! [X20,X21,X22,X23] :
( c_lessequals(X22,c_Set_Oinsert(X20,X21,X23),tc_fun(X23,tc_bool))
| ~ c_lessequals(X22,X21,tc_fun(X23,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_727]) ).
fof(c_0_1152,plain,
! [X18,X19] :
( c_Relation_Otrans(c_Lattices_Oupper__semilattice__class_Osup(X18,c_Relation_OId(X19),tc_fun(tc_prod(X19,X19),tc_bool)),X19)
| ~ c_Relation_Otrans(X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_728]) ).
fof(c_0_1153,plain,
! [X24,X25,X26,X27] :
( c_in(X24,c_Lattices_Oupper__semilattice__class_Osup(X26,X25,tc_fun(X27,tc_bool)),X27)
| ~ c_in(X24,X26,X27) ),
inference(variable_rename,[status(thm)],[c_0_729]) ).
fof(c_0_1154,plain,
! [X24,X25,X26,X27] :
( c_in(X24,c_Lattices_Oupper__semilattice__class_Osup(X26,X25,tc_fun(X27,tc_bool)),X27)
| ~ c_in(X24,X25,X27) ),
inference(variable_rename,[status(thm)],[c_0_730]) ).
fof(c_0_1155,plain,
! [X37,X38,X39] :
( c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X38,X37,tc_fun(tc_prod(X39,X39),tc_bool)),X39)
| ~ c_Wellfounded_Owf(X38,X39) ),
inference(variable_rename,[status(thm)],[c_0_731]) ).
fof(c_0_1156,plain,
! [X37,X38,X39] :
( c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X37,X38,tc_fun(tc_prod(X39,X39),tc_bool)),X39)
| ~ c_Wellfounded_Owf(X38,X39) ),
inference(variable_rename,[status(thm)],[c_0_732]) ).
fof(c_0_1157,plain,
! [X19,X20,X21,X22] :
( hBOOL(hAPP(c_Set_Oinsert(X19,X21,X22),X20))
| ~ hBOOL(hAPP(X21,X20)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_733])])]) ).
fof(c_0_1158,plain,
! [X20,X21,X22,X23] :
( c_Set_Oinsert(X20,X22,X23) != c_Set_Oinsert(X20,X21,X23)
| c_in(X20,X21,X23)
| c_in(X20,X22,X23)
| X22 = X21 ),
inference(variable_rename,[status(thm)],[c_0_734]) ).
fof(c_0_1159,plain,
! [X30,X31,X32] :
( hBOOL(hAPP(X32,X30))
| ~ hBOOL(hAPP(X32,v_sko__Wellfounded__Xacc__Xinduct__1(X32,X31)))
| ~ c_in(X30,c_Wellfounded_Oacc(X31,t_a),t_a) ),
inference(variable_rename,[status(thm)],[c_0_735]) ).
fof(c_0_1160,plain,
! [X30,X31,X32] :
( hBOOL(hAPP(X32,X30))
| ~ hBOOL(hAPP(X32,v_sko__Wellfounded__Xacc__Xinducts__1(X32,X31)))
| ~ c_in(X30,c_Wellfounded_Oacc(X31,t_a),t_a) ),
inference(variable_rename,[status(thm)],[c_0_736]) ).
fof(c_0_1161,plain,
! [X43,X44,X45] :
( c_Finite__Set_Ofinite(X44,X45)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X44,X43,tc_fun(X45,tc_bool)),X45) ),
inference(variable_rename,[status(thm)],[c_0_737]) ).
fof(c_0_1162,plain,
! [X43,X44,X45] :
( c_Finite__Set_Ofinite(X43,X45)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X44,X43,tc_fun(X45,tc_bool)),X45) ),
inference(variable_rename,[status(thm)],[c_0_738]) ).
fof(c_0_1163,plain,
! [X20,X21,X22] :
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X21,tc_fun(X22,tc_bool)),X20,tc_fun(X22,tc_bool))
| ~ c_in(X20,X21,tc_fun(X22,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_739]) ).
fof(c_0_1164,plain,
! [X20,X21,X22] :
( c_lessequals(X20,c_Complete__Lattice_OSup__class_OSup(X21,tc_fun(X22,tc_bool)),tc_fun(X22,tc_bool))
| ~ c_in(X20,X21,tc_fun(X22,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_740]) ).
fof(c_0_1165,plain,
! [X32,X33,X34,X35] :
( c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X34,X33,X35),X34,X35)
| ~ c_in(X32,X34,X35)
| ~ c_Wellfounded_Owf(X33,X35) ),
inference(variable_rename,[status(thm)],[c_0_741]) ).
fof(c_0_1166,plain,
! [X32,X33,X34,X35] :
( c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X34,X33,X35),X34,X35)
| ~ c_in(X32,X34,X35)
| ~ c_Wellfounded_Owf(X33,X35) ),
inference(variable_rename,[status(thm)],[c_0_742]) ).
fof(c_0_1167,plain,
! [X33,X34,X35,X36] :
( c_in(X33,X34,X36)
| ~ c_in(X33,X35,X36)
| ~ c_lessequals(X35,X34,tc_fun(X36,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_743]) ).
fof(c_0_1168,plain,
! [X20,X21,X22,X23] :
( c_in(X20,X21,X23)
| ~ c_lessequals(X22,X21,tc_fun(X23,tc_bool))
| ~ c_in(X20,X22,X23) ),
inference(variable_rename,[status(thm)],[c_0_744]) ).
fof(c_0_1169,plain,
! [X24,X25,X26,X27] :
( c_in(X24,X25,X27)
| ~ c_in(X24,X26,X27)
| ~ c_lessequals(X26,X25,tc_fun(X27,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_745]) ).
fof(c_0_1170,plain,
! [X20,X21,X22,X23] :
( c_in(X20,X21,X23)
| ~ c_in(X20,X22,X23)
| ~ c_lessequals(X22,X21,tc_fun(X23,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_746]) ).
fof(c_0_1171,plain,
! [X11,X12,X13,X14] :
( ~ class_Lattices_Olower__semilattice(X14)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X13,X12,X14),X11,X14)
| ~ c_lessequals(X13,X11,X14) ),
inference(variable_rename,[status(thm)],[c_0_747]) ).
fof(c_0_1172,plain,
! [X11,X12,X13,X14] :
( ~ class_Lattices_Olower__semilattice(X14)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X13,X12,X14),X11,X14)
| ~ c_lessequals(X12,X11,X14) ),
inference(variable_rename,[status(thm)],[c_0_748]) ).
fof(c_0_1173,plain,
! [X11,X12,X13,X14] :
( ~ class_Lattices_Oupper__semilattice(X14)
| c_lessequals(X11,c_Lattices_Oupper__semilattice__class_Osup(X13,X12,X14),X14)
| ~ c_lessequals(X11,X12,X14) ),
inference(variable_rename,[status(thm)],[c_0_749]) ).
fof(c_0_1174,plain,
! [X11,X12,X13,X14] :
( ~ class_Lattices_Oupper__semilattice(X14)
| c_lessequals(X11,c_Lattices_Oupper__semilattice__class_Osup(X13,X12,X14),X14)
| ~ c_lessequals(X11,X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_750]) ).
fof(c_0_1175,plain,
! [X19,X20,X21,X22] :
( c_in(X20,c_Set_Oinsert(X19,X21,X22),X22)
| ~ c_in(X20,X21,X22) ),
inference(variable_rename,[status(thm)],[c_0_751]) ).
fof(c_0_1176,plain,
! [X20,X21,X22,X23] :
( c_in(X21,c_Set_Oinsert(X20,X22,X23),X23)
| ~ c_in(X21,X22,X23) ),
inference(variable_rename,[status(thm)],[c_0_752]) ).
fof(c_0_1177,plain,
! [X19,X20,X21] :
( c_Relation_Orefl__on(X20,c_Relation_Oconverse(X19,X21,X21),X21)
| ~ c_Relation_Orefl__on(X20,X19,X21) ),
inference(variable_rename,[status(thm)],[c_0_753]) ).
fof(c_0_1178,plain,
! [X19,X20,X21] :
( c_Relation_Ototal__on(X20,c_Relation_Oconverse(X19,X21,X21),X21)
| ~ c_Relation_Ototal__on(X20,X19,X21) ),
inference(variable_rename,[status(thm)],[c_0_754]) ).
fof(c_0_1179,plain,
! [X20,X21,X22] :
( X21 = X20
| ~ c_lessequals(X20,X21,tc_fun(X22,tc_bool))
| ~ c_lessequals(X21,X20,tc_fun(X22,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_755])])]) ).
fof(c_0_1180,plain,
! [X20,X21,X22] :
( X21 = X20
| ~ c_lessequals(X20,X21,tc_fun(X22,tc_bool))
| ~ c_lessequals(X21,X20,tc_fun(X22,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_756])])]) ).
fof(c_0_1181,plain,
! [X29,X30,X31] :
( c_Wellfounded_Owf(X30,X31)
| ~ c_lessequals(X30,X29,tc_fun(tc_prod(X31,X31),tc_bool))
| ~ c_Wellfounded_Owf(X29,X31) ),
inference(variable_rename,[status(thm)],[c_0_757]) ).
fof(c_0_1182,plain,
! [X28,X29,X30,X31,X32] :
( ~ class_HOL_Oord(X31)
| c_lessequals(hAPP(X30,X28),hAPP(X29,X28),X31)
| ~ c_lessequals(X30,X29,tc_fun(X32,X31)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_758])])]) ).
fof(c_0_1183,plain,
! [X21,X22,X23,X24] :
( ~ class_Orderings_Opreorder(X24)
| c_lessequals(X23,X21,X24)
| ~ c_lessequals(X22,X21,X24)
| ~ c_lessequals(X23,X22,X24) ),
inference(variable_rename,[status(thm)],[c_0_759]) ).
fof(c_0_1184,plain,
! [X21,X22,X23,X24] :
( ~ class_Orderings_Oorder(X24)
| c_lessequals(X21,X23,X24)
| ~ c_lessequals(X21,X22,X24)
| ~ c_lessequals(X22,X23,X24) ),
inference(variable_rename,[status(thm)],[c_0_760]) ).
fof(c_0_1185,plain,
! [X29,X30,X31] :
( c_in(X30,c_Transitive__Closure_Ortrancl(X29,X31),tc_prod(X31,X31))
| ~ c_in(X30,X29,tc_prod(X31,X31)) ),
inference(variable_rename,[status(thm)],[c_0_761]) ).
fof(c_0_1186,plain,
! [X29,X30,X31] :
( c_in(X30,c_Transitive__Closure_Otrancl(X29,X31),tc_prod(X31,X31))
| ~ c_in(X30,X29,tc_prod(X31,X31)) ),
inference(variable_rename,[status(thm)],[c_0_762]) ).
fof(c_0_1187,plain,
! [X40,X41,X42] :
( c_Finite__Set_Ofinite(c_Complete__Lattice_OInf__class_OInf(X41,tc_fun(X42,tc_bool)),X42)
| ~ c_Finite__Set_Ofinite(X40,X42)
| ~ c_in(X40,X41,tc_fun(X42,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_763]) ).
fof(c_0_1188,plain,
! [X19,X20,X21] :
( c_Complete__Lattice_OSup__class_OSup(c_Equiv__Relations_Oquotient(X20,X19,X21),tc_fun(X21,tc_bool)) = X20
| ~ c_Equiv__Relations_Oequiv(X20,X19,X21) ),
inference(variable_rename,[status(thm)],[c_0_764]) ).
fof(c_0_1189,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Oupper__semilattice(X15)
| c_Lattices_Oupper__semilattice__class_Osup(X14,c_Lattices_Oupper__semilattice__class_Osup(X14,X13,X15),X15) = c_Lattices_Oupper__semilattice__class_Osup(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_765]) ).
fof(c_0_1190,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olattice(X15)
| c_Lattices_Oupper__semilattice__class_Osup(X14,c_Lattices_Oupper__semilattice__class_Osup(X14,X13,X15),X15) = c_Lattices_Oupper__semilattice__class_Osup(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_766]) ).
fof(c_0_1191,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olattice(X15)
| c_Lattices_Olower__semilattice__class_Oinf(X14,c_Lattices_Olower__semilattice__class_Oinf(X14,X13,X15),X15) = c_Lattices_Olower__semilattice__class_Oinf(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_767]) ).
fof(c_0_1192,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olower__semilattice(X15)
| c_Lattices_Olower__semilattice__class_Oinf(X14,c_Lattices_Olower__semilattice__class_Oinf(X14,X13,X15),X15) = c_Lattices_Olower__semilattice__class_Oinf(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_768]) ).
fof(c_0_1193,plain,
! [X43,X44,X45] :
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X44,X43,tc_fun(X45,tc_bool)),X45)
| ~ c_Finite__Set_Ofinite(X43,X45)
| ~ c_Finite__Set_Ofinite(X44,X45) ),
inference(variable_rename,[status(thm)],[c_0_769]) ).
fof(c_0_1194,plain,
! [X43,X44,X45] :
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X44,X43,tc_fun(X45,tc_bool)),X45)
| ~ c_Finite__Set_Ofinite(X43,X45)
| ~ c_Finite__Set_Ofinite(X44,X45) ),
inference(variable_rename,[status(thm)],[c_0_770]) ).
fof(c_0_1195,plain,
! [X19,X20,X21] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X21)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X19,X20,X21),X21) = c_Lattices_Olower__semilattice__class_Oinf(X19,c_Complete__Lattice_OInf__class_OInf(X20,X21),X21) ),
inference(variable_rename,[status(thm)],[c_0_771]) ).
fof(c_0_1196,plain,
! [X19,X20,X21] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X21)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X19,X20,X21),X21) = c_Lattices_Oupper__semilattice__class_Osup(X19,c_Complete__Lattice_OSup__class_OSup(X20,X21),X21) ),
inference(variable_rename,[status(thm)],[c_0_772]) ).
fof(c_0_1197,plain,
! [X18,X19] :
( c_Relation_Otrans(X18,X19)
| ~ c_Relation_Otrans(c_Relation_Oconverse(X18,X19,X19),X19) ),
inference(variable_rename,[status(thm)],[c_0_773]) ).
fof(c_0_1198,plain,
! [X19,X20,X21] :
( c_Finite__Set_Ofinite(X20,X21)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X19,X20,X21),X21) ),
inference(variable_rename,[status(thm)],[c_0_774]) ).
fof(c_0_1199,plain,
! [X18,X19] :
( c_Relation_Osym(X18,X19)
| ~ c_Relation_Osym(c_Relation_Oconverse(X18,X19,X19),X19) ),
inference(variable_rename,[status(thm)],[c_0_775]) ).
fof(c_0_1200,plain,
! [X20,X21,X22] :
( c_Lattices_Oupper__semilattice__class_Osup(X21,X20,tc_fun(X22,tc_bool)) != X20
| c_lessequals(X21,X20,tc_fun(X22,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_776]) ).
fof(c_0_1201,plain,
! [X20,X21,X22] :
( c_Lattices_Olower__semilattice__class_Oinf(X21,X20,tc_fun(X22,tc_bool)) = X21
| ~ c_lessequals(X21,X20,tc_fun(X22,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_777]) ).
fof(c_0_1202,plain,
! [X20,X21,X22] :
( c_Lattices_Olower__semilattice__class_Oinf(X21,X20,tc_fun(X22,tc_bool)) = X20
| ~ c_lessequals(X20,X21,tc_fun(X22,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_778]) ).
fof(c_0_1203,plain,
! [X20,X21,X22] :
( c_Lattices_Oupper__semilattice__class_Osup(X21,X20,tc_fun(X22,tc_bool)) = X20
| ~ c_lessequals(X21,X20,tc_fun(X22,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_779]) ).
fof(c_0_1204,plain,
! [X20,X21,X22] :
( c_Lattices_Oupper__semilattice__class_Osup(X21,X20,tc_fun(X22,tc_bool)) = X21
| ~ c_lessequals(X20,X21,tc_fun(X22,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_780]) ).
fof(c_0_1205,plain,
! [X32,X33,X34,X35] :
( hBOOL(hAPP(X33,X32))
| ~ c_lessequals(X34,X33,tc_fun(X35,tc_bool))
| ~ hBOOL(hAPP(X34,X32)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_781])])]) ).
fof(c_0_1206,plain,
! [X32,X33,X34,X35] :
( hBOOL(hAPP(X33,X32))
| ~ hBOOL(hAPP(X34,X32))
| ~ c_lessequals(X34,X33,tc_fun(X35,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_782])])]) ).
fof(c_0_1207,plain,
! [X43,X44,X45] :
( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X44,X43,tc_fun(X45,tc_bool)),X45)
| ~ c_Finite__Set_Ofinite(X43,X45) ),
inference(variable_rename,[status(thm)],[c_0_783]) ).
fof(c_0_1208,plain,
! [X43,X44,X45] :
( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X44,X43,tc_fun(X45,tc_bool)),X45)
| ~ c_Finite__Set_Ofinite(X44,X45) ),
inference(variable_rename,[status(thm)],[c_0_784]) ).
fof(c_0_1209,plain,
! [X18,X19] :
( c_Wellfounded_Owf(X18,X19)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X18,X19),c_Wellfounded_Oacc(X18,X19),X19) ),
inference(variable_rename,[status(thm)],[c_0_785]) ).
fof(c_0_1210,plain,
! [X18,X19] :
( c_Wellfounded_Owf(X18,X19)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X18,X19),c_Wellfounded_Oacc(X18,X19),X19) ),
inference(variable_rename,[status(thm)],[c_0_786]) ).
fof(c_0_1211,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Oorder(X15)
| X14 = X13
| ~ c_lessequals(X14,X13,X15)
| ~ c_lessequals(X13,X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_787]) ).
fof(c_0_1212,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Oorder(X15)
| X14 = X13
| ~ c_lessequals(X13,X14,X15)
| ~ c_lessequals(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_788]) ).
fof(c_0_1213,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Oorder(X15)
| X14 = X13
| ~ c_lessequals(X13,X14,X15)
| ~ c_lessequals(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_789]) ).
fof(c_0_1214,plain,
! [X19,X20,X21] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X21)
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X20,X21),X19,X21)
| ~ c_in(X19,X20,X21) ),
inference(variable_rename,[status(thm)],[c_0_790]) ).
fof(c_0_1215,plain,
! [X19,X20,X21] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X21)
| c_lessequals(X19,c_Complete__Lattice_OSup__class_OSup(X20,X21),X21)
| ~ c_in(X19,X20,X21) ),
inference(variable_rename,[status(thm)],[c_0_791]) ).
fof(c_0_1216,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olattice(X15)
| c_Lattices_Oupper__semilattice__class_Osup(X14,c_Lattices_Olower__semilattice__class_Oinf(X14,X13,X15),X15) = X14 ),
inference(variable_rename,[status(thm)],[c_0_792]) ).
fof(c_0_1217,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olattice(X15)
| c_Lattices_Olower__semilattice__class_Oinf(X14,c_Lattices_Oupper__semilattice__class_Osup(X14,X13,X15),X15) = X14 ),
inference(variable_rename,[status(thm)],[c_0_793]) ).
fof(c_0_1218,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Oupper__semilattice(X15)
| c_lessequals(X14,c_Lattices_Oupper__semilattice__class_Osup(X14,X13,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_794]) ).
fof(c_0_1219,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Oupper__semilattice(X15)
| c_lessequals(X13,c_Lattices_Oupper__semilattice__class_Osup(X14,X13,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_795]) ).
fof(c_0_1220,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olattice(X15)
| c_lessequals(X13,c_Lattices_Oupper__semilattice__class_Osup(X14,X13,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_796]) ).
fof(c_0_1221,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olattice(X15)
| c_lessequals(X14,c_Lattices_Oupper__semilattice__class_Osup(X14,X13,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_797]) ).
fof(c_0_1222,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olattice(X15)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X14,X13,X15),X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_798]) ).
fof(c_0_1223,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olattice(X15)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X14,X13,X15),X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_799]) ).
fof(c_0_1224,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olower__semilattice(X15)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X14,X13,X15),X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_800]) ).
fof(c_0_1225,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olower__semilattice(X15)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X14,X13,X15),X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_801]) ).
fof(c_0_1226,plain,
! [X20,X21,X22] :
( c_Finite__Set_Ofinite(X21,X22)
| ~ c_Finite__Set_Ofinite(X20,X22)
| ~ c_lessequals(X21,X20,tc_fun(X22,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_802]) ).
fof(c_0_1227,plain,
! [X20,X21,X22] :
( c_Finite__Set_Ofinite(X21,X22)
| ~ c_lessequals(X21,X20,tc_fun(X22,tc_bool))
| ~ c_Finite__Set_Ofinite(X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_803]) ).
fof(c_0_1228,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olower__semilattice(X15)
| c_Lattices_Olower__semilattice__class_Oinf(X14,X13,X15) != X14
| c_lessequals(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_804]) ).
fof(c_0_1229,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Oupper__semilattice(X15)
| c_Lattices_Oupper__semilattice__class_Osup(X14,X13,X15) != X13
| c_lessequals(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_805]) ).
fof(c_0_1230,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olower__semilattice(X15)
| c_Lattices_Olower__semilattice__class_Oinf(X14,X13,X15) = X14
| ~ c_lessequals(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_806]) ).
fof(c_0_1231,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olower__semilattice(X15)
| c_Lattices_Olower__semilattice__class_Oinf(X14,X13,X15) = X13
| ~ c_lessequals(X13,X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_807]) ).
fof(c_0_1232,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Oupper__semilattice(X15)
| c_Lattices_Oupper__semilattice__class_Osup(X14,X13,X15) = X14
| ~ c_lessequals(X13,X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_808]) ).
fof(c_0_1233,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Oupper__semilattice(X15)
| c_Lattices_Oupper__semilattice__class_Osup(X14,X13,X15) = X13
| ~ c_lessequals(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_809]) ).
fof(c_0_1234,plain,
! [X8,X9] :
( c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X9,X8),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X9 = X8 ),
inference(variable_rename,[status(thm)],[c_0_810]) ).
fof(c_0_1235,plain,
! [X18,X19] :
( c_Relation_Otrans(c_Relation_Oconverse(X18,X19,X19),X19)
| ~ c_Relation_Otrans(X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_811]) ).
fof(c_0_1236,plain,
! [X19,X20,X21] :
( c_Finite__Set_Ofinite(c_Set_Oinsert(X19,X20,X21),X21)
| ~ c_Finite__Set_Ofinite(X20,X21) ),
inference(variable_rename,[status(thm)],[c_0_812]) ).
fof(c_0_1237,plain,
! [X18,X19] :
( c_Relation_Osym(c_Relation_Oconverse(X18,X19,X19),X19)
| ~ c_Relation_Osym(X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_813]) ).
fof(c_0_1238,plain,
! [X19,X20,X21] :
( c_Set_Oinsert(X19,X20,X21) = X20
| ~ c_in(X19,X20,X21) ),
inference(variable_rename,[status(thm)],[c_0_814]) ).
fof(c_0_1239,plain,
! [X19,X20,X21] :
( c_Relation_Orefl__on(X20,X19,X21)
| ~ c_Equiv__Relations_Oequiv(X20,X19,X21) ),
inference(variable_rename,[status(thm)],[c_0_815]) ).
fof(c_0_1240,plain,
! [X13,X14,X15] :
( ~ class_Orderings_Olinorder(X15)
| c_lessequals(X13,X14,X15)
| c_lessequals(X14,X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_816]) ).
fof(c_0_1241,plain,
! [X12,X13,X14] :
( hBOOL(hAPP(X13,X12))
| ~ c_in(X12,X13,X14) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_817])])]) ).
fof(c_0_1242,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olower__semilattice(X15)
| c_Lattices_Olower__semilattice__class_Oinf(X14,X13,X15) = c_Lattices_Olower__semilattice__class_Oinf(X13,X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_818]) ).
fof(c_0_1243,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olattice(X15)
| c_Lattices_Olower__semilattice__class_Oinf(X14,X13,X15) = c_Lattices_Olower__semilattice__class_Oinf(X13,X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_819]) ).
fof(c_0_1244,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Oupper__semilattice(X15)
| c_Lattices_Oupper__semilattice__class_Osup(X14,X13,X15) = c_Lattices_Oupper__semilattice__class_Osup(X13,X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_820]) ).
fof(c_0_1245,plain,
! [X13,X14,X15] :
( ~ class_Lattices_Olattice(X15)
| c_Lattices_Oupper__semilattice__class_Osup(X14,X13,X15) = c_Lattices_Oupper__semilattice__class_Osup(X13,X14,X15) ),
inference(variable_rename,[status(thm)],[c_0_821]) ).
fof(c_0_1246,plain,
! [X18,X19,X20] :
( c_in(X18,c_Wellfounded_Oacc(X19,X20),X20)
| ~ c_Wellfounded_Owf(X19,X20) ),
inference(variable_rename,[status(thm)],[c_0_822]) ).
fof(c_0_1247,plain,
! [X12,X13,X14] :
( c_in(X12,X13,X14)
| ~ hBOOL(hAPP(X13,X12)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_823])])]) ).
fof(c_0_1248,plain,
! [X18,X19] :
( c_Relation_Oconverse(X18,X19,X19) != X18
| c_Relation_Osym(X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_824]) ).
fof(c_0_1249,plain,
! [X19,X20,X21] :
( c_Relation_Otrans(X19,X21)
| ~ c_Equiv__Relations_Oequiv(X20,X19,X21) ),
inference(variable_rename,[status(thm)],[c_0_825]) ).
fof(c_0_1250,plain,
! [X19,X20,X21] :
( c_Relation_Osym(X19,X21)
| ~ c_Equiv__Relations_Oequiv(X20,X19,X21) ),
inference(variable_rename,[status(thm)],[c_0_826]) ).
fof(c_0_1251,plain,
! [X4,X5,X6] :
( X5 = X4
| ~ c_fequal(X5,X4,X6) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_827])])]) ).
fof(c_0_1252,plain,
! [X18,X19] :
( c_Relation_Oconverse(X18,X19,X19) = X18
| ~ c_Relation_Osym(X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_828]) ).
fof(c_0_1253,plain,
! [X18,X19] :
( c_Relation_Osym(c_Transitive__Closure_Ortrancl(X18,X19),X19)
| ~ c_Relation_Osym(X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_829]) ).
fof(c_0_1254,plain,
! [X18,X19] :
( c_Relation_Osym(c_Transitive__Closure_Otrancl(X18,X19),X19)
| ~ c_Relation_Osym(X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_830]) ).
fof(c_0_1255,plain,
! [X18,X19] :
( c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X18,X19),X19)
| ~ c_Wellfounded_Owf(X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_831]) ).
fof(c_0_1256,plain,
! [X11,X12] :
( ~ class_Lattices_Oupper__semilattice(X12)
| c_Lattices_Oupper__semilattice__class_Osup(X11,X11,X12) = X11 ),
inference(variable_rename,[status(thm)],[c_0_832]) ).
fof(c_0_1257,plain,
! [X11,X12] :
( ~ class_Lattices_Olower__semilattice(X12)
| c_Lattices_Olower__semilattice__class_Oinf(X11,X11,X12) = X11 ),
inference(variable_rename,[status(thm)],[c_0_833]) ).
fof(c_0_1258,plain,
! [X11,X12] :
( ~ class_Orderings_Opreorder(X12)
| c_lessequals(X11,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_834]) ).
fof(c_0_1259,plain,
! [X11,X12] :
( ~ class_Orderings_Oorder(X12)
| c_lessequals(X11,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_835]) ).
fof(c_0_1260,plain,
! [X6,X7] :
( class_Finite__Set_Ofinite_Ofinite(tc_prod(X6,X7))
| ~ class_Finite__Set_Ofinite_Ofinite(X7)
| ~ class_Finite__Set_Ofinite_Ofinite(X6) ),
inference(variable_rename,[status(thm)],[c_0_836]) ).
fof(c_0_1261,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_837]) ).
fof(c_0_1262,plain,
! [X18,X19] :
( c_Transitive__Closure_Otrancl(X18,X19) = X18
| ~ c_Relation_Otrans(X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_838]) ).
fof(c_0_1263,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_839]) ).
fof(c_0_1264,plain,
! [X6,X7] :
( class_Lattices_Oupper__semilattice(tc_fun(X6,X7))
| ~ class_Lattices_Olattice(X7) ),
inference(variable_rename,[status(thm)],[c_0_840]) ).
fof(c_0_1265,plain,
! [X6,X7] :
( class_Lattices_Olower__semilattice(tc_fun(X6,X7))
| ~ class_Lattices_Olattice(X7) ),
inference(variable_rename,[status(thm)],[c_0_841]) ).
fof(c_0_1266,plain,
! [X6,X7] :
( class_Lattices_Odistrib__lattice(tc_fun(X6,X7))
| ~ class_Lattices_Odistrib__lattice(X7) ),
inference(variable_rename,[status(thm)],[c_0_842]) ).
fof(c_0_1267,plain,
! [X6,X7] :
( class_Orderings_Opreorder(tc_fun(X6,X7))
| ~ class_Orderings_Opreorder(X7) ),
inference(variable_rename,[status(thm)],[c_0_843]) ).
fof(c_0_1268,plain,
! [X6,X7] :
( class_Lattices_Olattice(tc_fun(X6,X7))
| ~ class_Lattices_Olattice(X7) ),
inference(variable_rename,[status(thm)],[c_0_844]) ).
fof(c_0_1269,plain,
! [X6,X7] :
( class_Orderings_Oorder(tc_fun(X6,X7))
| ~ class_Orderings_Oorder(X7) ),
inference(variable_rename,[status(thm)],[c_0_845]) ).
fof(c_0_1270,plain,
! [X6,X7] :
( class_HOL_Oord(tc_fun(X6,X7))
| ~ class_HOL_Oord(X7) ),
inference(variable_rename,[status(thm)],[c_0_846]) ).
fof(c_0_1271,plain,
! [X19,X20] :
( ~ class_Finite__Set_Ofinite_Ofinite(X20)
| c_Finite__Set_Ofinite(X19,X20) ),
inference(variable_rename,[status(thm)],[c_0_847]) ).
cnf(c_0_1272,plain,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X1,X2,X5,X6,X3,X4,X7),X3,X7),X5,tc_prod(X3,X7))
| ~ c_in(c_Pair(X1,X2,X3,X4),c_Relation_Orel__comp(X5,X6,X3,X7,X4),tc_prod(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_848]) ).
cnf(c_0_1273,plain,
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X1,X2,X5,X6,X3,X4,X7),X2,X7,X4),X6,tc_prod(X7,X4))
| ~ c_in(c_Pair(X1,X2,X3,X4),c_Relation_Orel__comp(X5,X6,X3,X7,X4),tc_prod(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_849]) ).
cnf(c_0_1274,plain,
( c_Recdef_Ocut(X1,X2,X3,X4,X5) = c_Recdef_Ocut(X6,X2,X3,X4,X5)
| hAPP(X1,c_List_Osko__Recdef__Xcuts__eq__1__1(X1,X6,X2,X3,X4,X5)) != hAPP(X6,c_List_Osko__Recdef__Xcuts__eq__1__1(X1,X6,X2,X3,X4,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_850]) ).
cnf(c_0_1275,plain,
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,X1,X2,X2,X2),c_Relation_Orel__comp(X3,X1,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_851]) ).
cnf(c_0_1276,plain,
( c_in(c_Pair(c_List_Osko__Recdef__Xcuts__eq__1__1(X1,X2,X3,X4,X5,X6),X4,X5,X5),X3,tc_prod(X5,X5))
| c_Recdef_Ocut(X1,X3,X4,X5,X6) = c_Recdef_Ocut(X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_852]) ).
cnf(c_0_1277,plain,
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,X1,X3,X3,X3),c_Relation_Orel__comp(X2,X1,X3,X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)),X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_853]) ).
cnf(c_0_1278,plain,
( c_lessequals(c_Product__Type_OSigma(X1,X4,X3,X6),c_Product__Type_OSigma(X2,X5,X3,X6),tc_fun(tc_prod(X3,X6),tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(hAPP(X4,c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(X1,X4,X5,X3,X6)),hAPP(X5,c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(X1,X4,X5,X3,X6)),tc_fun(X6,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_854]) ).
cnf(c_0_1279,plain,
( c_in(X1,c_FuncSet_OPi(X2,X3,X4,X5),tc_fun(X4,X5))
| ~ c_in(hAPP(X1,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X2,X3,X1,X4,X5)),hAPP(X3,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X2,X3,X1,X4,X5)),X5) ),
inference(split_conjunct,[status(thm)],[c_0_855]) ).
cnf(c_0_1280,plain,
( c_in(X1,c_FuncSet_OPi(X2,X3,X4,X5),tc_fun(X4,X5))
| ~ c_in(hAPP(X1,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X2,X3,X1,X4,X5)),hAPP(X3,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X2,X3,X1,X4,X5)),X5) ),
inference(split_conjunct,[status(thm)],[c_0_856]) ).
cnf(c_0_1281,plain,
( c_in(X1,c_FuncSet_OPi(X2,c_COMBK(X3,tc_fun(X5,tc_bool),X4),X4,X5),tc_fun(X4,X5))
| ~ c_in(hAPP(X1,c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X2,X3,X1,X4,X5)),X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_857]) ).
cnf(c_0_1282,plain,
( c_lessequals(c_Relation_Orel__comp(X1,X6,X5,X4,X8),c_Product__Type_OSigma(X2,c_COMBK(X7,tc_fun(X8,tc_bool),X5),X5,X8),tc_fun(tc_prod(X5,X8),tc_bool))
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X3,tc_fun(X4,tc_bool),X5),X5,X4),tc_fun(tc_prod(X5,X4),tc_bool))
| ~ c_lessequals(X6,c_Product__Type_OSigma(X3,c_COMBK(X7,tc_fun(X8,tc_bool),X4),X4,X8),tc_fun(tc_prod(X4,X8),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_858]) ).
cnf(c_0_1283,plain,
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X3,X1,X2,X4,X5),X1,X4,X5),X2,tc_prod(X4,X5))
| ~ c_in(X1,c_Relation_OImage(X2,X3,X4,X5),X5) ),
inference(split_conjunct,[status(thm)],[c_0_859]) ).
cnf(c_0_1284,plain,
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X3,X1,X2,X4,X5),X1,X4,X5),X2,tc_prod(X4,X5))
| ~ c_in(X1,c_Relation_OImage(X2,X3,X4,X5),X5) ),
inference(split_conjunct,[status(thm)],[c_0_860]) ).
cnf(c_0_1285,plain,
( c_lessequals(c_Relation_Orel__comp(X1,X5,X3,X4,X7),c_Relation_Orel__comp(X2,X6,X3,X4,X7),tc_fun(tc_prod(X3,X7),tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool))
| ~ c_lessequals(X5,X6,tc_fun(tc_prod(X4,X7),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_861]) ).
cnf(c_0_1286,plain,
( c_lessequals(c_Transitive__Closure_Ortrancl(X3,X1),X2,tc_fun(tc_prod(X1,X1),tc_bool))
| ~ c_lessequals(c_Relation_OId(X1),X2,tc_fun(tc_prod(X1,X1),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Ortrancl(X3,X1),X2,tc_fun(tc_prod(X1,X1),tc_bool)),X3,X1,X1,X1),X2,tc_fun(tc_prod(X1,X1),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_862]) ).
cnf(c_0_1287,plain,
( c_lessequals(c_Transitive__Closure_Otrancl(X1,X3),X2,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Otrancl(X1,X3),X2,tc_fun(tc_prod(X3,X3),tc_bool)),X1,X3,X3,X3),X2,tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_863]) ).
cnf(c_0_1288,plain,
( c_in(c_Pair(X1,X6,X3,X7),c_Relation_Orel__comp(X5,X8,X3,X4,X7),tc_prod(X3,X7))
| ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
| ~ c_in(c_Pair(X2,X6,X4,X7),X8,tc_prod(X4,X7)) ),
inference(split_conjunct,[status(thm)],[c_0_864]) ).
cnf(c_0_1289,plain,
( hAPP(X5,X1) = hAPP(X6,X1)
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| c_Recdef_Ocut(X5,X4,X2,X3,X7) != c_Recdef_Ocut(X6,X4,X2,X3,X7) ),
inference(split_conjunct,[status(thm)],[c_0_865]) ).
cnf(c_0_1290,plain,
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_Wellfounded_Owf(X3,X2)
| ~ c_lessequals(c_Relation_Orel__comp(X1,X3,X2,X2,X2),X1,tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_866]) ).
cnf(c_0_1291,plain,
( c_Wellfounded_Owf(X1,X2)
| ~ c_Wellfounded_Owf(c_Relation_Orel__comp(X1,X1,X2,X2,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_867]) ).
cnf(c_0_1292,plain,
( c_in(c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(X1,X4,X5,X3,X6),X1,X3)
| c_lessequals(c_Product__Type_OSigma(X1,X4,X3,X6),c_Product__Type_OSigma(X2,X5,X3,X6),tc_fun(tc_prod(X3,X6),tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_868]) ).
cnf(c_0_1293,plain,
( X1 = X2
| X4 = X5
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_869]) ).
cnf(c_0_1294,plain,
( X1 = X2
| X4 = X5
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_870]) ).
cnf(c_0_1295,plain,
( c_in(c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X1,X2,X3,X4,X5),X1,X4)
| c_in(X3,c_FuncSet_OPi(X1,c_COMBK(X2,tc_fun(X5,tc_bool),X4),X4,X5),tc_fun(X4,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_871]) ).
cnf(c_0_1296,plain,
( hAPP(c_Recdef_Ocut(X5,X4,X2,X3,X6),X1) = hAPP(X5,X1)
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_872]) ).
cnf(c_0_1297,plain,
( hAPP(c_Recdef_Ocut(X5,X4,X2,X3,X6),X1) = hAPP(X5,X1)
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_873]) ).
cnf(c_0_1298,plain,
( c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X3,X1,X2,X4,X5),X3,X4)
| ~ c_in(X1,c_Relation_OImage(X2,X3,X4,X5),X5) ),
inference(split_conjunct,[status(thm)],[c_0_874]) ).
cnf(c_0_1299,plain,
( c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X3,X1,X2,X4,X5),X3,X4)
| ~ c_in(X1,c_Relation_OImage(X2,X3,X4,X5),X5) ),
inference(split_conjunct,[status(thm)],[c_0_875]) ).
cnf(c_0_1300,plain,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X4,X1,X2,X3),X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_876]) ).
cnf(c_0_1301,plain,
( c_Relation_Orefl__on(X2,X1,X3)
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1(X2,X1,X3),c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1(X2,X1,X3),X3,X3),X1,tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_877]) ).
cnf(c_0_1302,plain,
( c_Relation_Orefl__on(X2,X1,X3)
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1(X2,X1,X3),c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1(X2,X1,X3),X3,X3),X1,tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_878]) ).
cnf(c_0_1303,plain,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X4,X1,X2,X3),X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_879]) ).
cnf(c_0_1304,plain,
( c_in(c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X1,X2,X3,X4,X5),X1,X4)
| c_in(X3,c_FuncSet_OPi(X1,X2,X4,X5),tc_fun(X4,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_880]) ).
cnf(c_0_1305,plain,
( c_in(c_FuncSet_Osko__FuncSet__XPi__I__1__1(X1,X2,X3,X4,X5),X1,X4)
| c_in(X3,c_FuncSet_OPi(X1,X2,X4,X5),tc_fun(X4,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_881]) ).
cnf(c_0_1306,plain,
( c_lessequals(X4,X6,tc_fun(X5,tc_bool))
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(c_Product__Type_OSigma(X4,c_COMBK(X2,tc_fun(X3,tc_bool),X5),X5,X3),c_Product__Type_OSigma(X6,c_COMBK(X2,tc_fun(X3,tc_bool),X5),X5,X3),tc_fun(tc_prod(X5,X3),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_882]) ).
cnf(c_0_1307,plain,
( c_lessequals(X2,c_Relation_Orel__comp(c_Relation_Oconverse(X2,X3,X3),X2,X3,X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Relation_Orefl__on(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_883]) ).
cnf(c_0_1308,plain,
( c_lessequals(c_Relation_Orel__comp(c_Relation_Oconverse(X1,X2,X2),X1,X2,X2,X2),X1,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_Relation_Osym(X1,X2)
| ~ c_Relation_Otrans(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_884]) ).
cnf(c_0_1309,plain,
( ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)),X3)
| ~ c_in(c_Pair(X2,X1,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_885]) ).
cnf(c_0_1310,plain,
( X1 = X2
| X4 = X5
| X4 = X1
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_886]) ).
cnf(c_0_1311,plain,
( X1 = X2
| X4 = X5
| X5 = X1
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_887]) ).
cnf(c_0_1312,plain,
( X1 = X2
| X4 = X5
| X5 = X2
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_888]) ).
cnf(c_0_1313,plain,
( X1 = X2
| X4 = X5
| X4 = X2
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_889]) ).
cnf(c_0_1314,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_890]) ).
cnf(c_0_1315,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X2
| X1 = X2
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_891]) ).
cnf(c_0_1316,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X2
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_892]) ).
cnf(c_0_1317,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| X1 = X2
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_893]) ).
cnf(c_0_1318,plain,
( c_lessequals(c_Relation_Orel__comp(X1,X1,X2,X2,X2),X1,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_Relation_Otrans(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_894]) ).
cnf(c_0_1319,plain,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X4,X1,X2,X3),X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_895]) ).
cnf(c_0_1320,plain,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X4,X1,X2,X3),X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_896]) ).
cnf(c_0_1321,plain,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X4,X1,X2,X3),X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_897]) ).
cnf(c_0_1322,plain,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X4,X1,X2,X3),X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_898]) ).
cnf(c_0_1323,plain,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_899]) ).
cnf(c_0_1324,plain,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_900]) ).
cnf(c_0_1325,plain,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_901]) ).
cnf(c_0_1326,plain,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_902]) ).
cnf(c_0_1327,plain,
( X1 = X2
| c_in(X1,X5,X3)
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_lessequals(X4,c_Product__Type_OSigma(X5,c_COMBK(X5,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_903]) ).
cnf(c_0_1328,plain,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),X4,tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_904]) ).
cnf(c_0_1329,plain,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_905]) ).
cnf(c_0_1330,plain,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),X4,tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_906]) ).
cnf(c_0_1331,plain,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_907]) ).
cnf(c_0_1332,plain,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_908]) ).
cnf(c_0_1333,plain,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),X4,tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_909]) ).
cnf(c_0_1334,plain,
( c_Wellfounded_Owf(c_Relation_Orel__comp(X1,X1,X2,X2,X2),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_910]) ).
cnf(c_0_1335,plain,
( c_lessequals(c_Transitive__Closure_Otrancl(X1,X3),c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_911]) ).
cnf(c_0_1336,plain,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),X4,tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_912]) ).
cnf(c_0_1337,plain,
( c_in(c_Pair(X3,X5,X2,X2),X1,tc_prod(X2,X2))
| ~ c_Relation_Otrans(X1,X2)
| ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X5,X2,X2),X1,tc_prod(X2,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_913]) ).
cnf(c_0_1338,plain,
( c_in(c_Pair(X3,X5,X2,X2),X1,tc_prod(X2,X2))
| ~ c_Relation_Otrans(X1,X2)
| ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X5,X2,X2),X1,tc_prod(X2,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_914]) ).
cnf(c_0_1339,plain,
( c_in(c_Pair(hAPP(X5,X1),hAPP(X5,X2),X6,X6),X4,tc_prod(X6,X6))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_Oinv__image(X4,X5,X6,X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_915]) ).
cnf(c_0_1340,plain,
( c_Equiv__Relations_Oequiv(c_Relation_ODomain(X1,X2,X2),X1,X2)
| c_Relation_Orel__comp(c_Relation_Oconverse(X1,X2,X2),X1,X2,X2,X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_916]) ).
cnf(c_0_1341,plain,
( c_in(c_Pair(X2,X3,X6,X6),c_Relation_Oinv__image(X5,X1,X4,X6),tc_prod(X6,X6))
| ~ c_in(c_Pair(hAPP(X1,X2),hAPP(X1,X3),X4,X4),X5,tc_prod(X4,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_917]) ).
cnf(c_0_1342,plain,
( c_lessequals(c_Relation_OImage(X1,X6,X5,X4),X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X3,tc_fun(X4,tc_bool),X5),X5,X4),tc_fun(tc_prod(X5,X4),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_918]) ).
cnf(c_0_1343,plain,
( c_in(c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1(X2,X3,X1,X4),X3,X4)
| c_Wellfounded_Owf(X1,X4)
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X3,tc_fun(X4,tc_bool),X4),X4,X4),tc_fun(tc_prod(X4,X4),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_919]) ).
cnf(c_0_1344,plain,
( c_in(c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1(X2,X3,X1,X4),X2,X4)
| c_Wellfounded_Owf(X1,X4)
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X3,tc_fun(X4,tc_bool),X4),X4,X4),tc_fun(tc_prod(X4,X4),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_920]) ).
cnf(c_0_1345,plain,
( c_in(c_Pair(X1,X2,X3,X3),c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X4,X3),X3,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X4,X3,X3),X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_921]) ).
cnf(c_0_1346,plain,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X4,X3,X3),X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X4,X3),X3,X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_922]) ).
cnf(c_0_1347,plain,
( c_lessequals(c_Set_Oimage(X1,X2,X5,X4),X3,tc_fun(X4,tc_bool))
| ~ c_in(X1,c_FuncSet_OPi(X2,c_COMBK(X3,tc_fun(X4,tc_bool),X5),X5,X4),tc_fun(X5,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_923]) ).
cnf(c_0_1348,plain,
( X2 = X3
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_924]) ).
cnf(c_0_1349,plain,
( ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_925]) ).
cnf(c_0_1350,plain,
( c_lessequals(c_Product__Type_OSigma(X4,c_COMBK(X2,tc_fun(X3,tc_bool),X6),X6,X3),c_Product__Type_OSigma(X5,c_COMBK(X2,tc_fun(X3,tc_bool),X6),X6,X3),tc_fun(tc_prod(X6,X3),tc_bool))
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X4,X5,tc_fun(X6,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_926]) ).
cnf(c_0_1351,plain,
( c_in(c_Pair(X2,X1,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X4,X3,X3),X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_927]) ).
cnf(c_0_1352,plain,
( c_Wellfounded_Owf(X4,X3)
| ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_928]) ).
cnf(c_0_1353,plain,
( ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X3,X2,X2),X1,tc_prod(X2,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_929]) ).
cnf(c_0_1354,plain,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X1,X2,X3,X4),X3,X4),X2,tc_prod(X3,X4))
| ~ c_in(X1,c_Relation_ODomain(X2,X3,X4),X3) ),
inference(split_conjunct,[status(thm)],[c_0_930]) ).
cnf(c_0_1355,plain,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X1,X2,X3,X4),X3,X4),X2,tc_prod(X3,X4))
| ~ c_in(X1,c_Relation_ODomain(X2,X3,X4),X3) ),
inference(split_conjunct,[status(thm)],[c_0_931]) ).
cnf(c_0_1356,plain,
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X1,X2,X4,X3),X1,X3,X4),X2,tc_prod(X3,X4))
| ~ c_in(X1,c_Relation_ORange(X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_932]) ).
cnf(c_0_1357,plain,
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X1,X2,X4,X3),X1,X3,X4),X2,tc_prod(X3,X4))
| ~ c_in(X1,c_Relation_ORange(X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_933]) ).
cnf(c_0_1358,plain,
( X1 = X2
| X4 = X2
| X5 = X2
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_934]) ).
cnf(c_0_1359,plain,
( X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X4
| X1 = X4
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X2,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_935]) ).
cnf(c_0_1360,plain,
( X1 = X2
| X5 = X1
| X4 = X1
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_936]) ).
cnf(c_0_1361,plain,
( X1 = X2
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X2
| X1 = X4
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_937]) ).
cnf(c_0_1362,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_938]) ).
cnf(c_0_1363,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_939]) ).
cnf(c_0_1364,plain,
( c_Finite__Set_Ofinite(X4,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,c_Product__Type_OSigma(X1,c_COMBK(X1,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_in(X4,c_Equiv__Relations_Oquotient(X1,X3,X2),tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_940]) ).
cnf(c_0_1365,plain,
( c_in(c_Pair(X3,X4,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X4,X3,X2,X2),X1,tc_prod(X2,X2)),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_941]) ).
cnf(c_0_1366,plain,
( c_in(X2,hAPP(X6,X1),X4)
| ~ c_in(c_Pair(X1,X2,X3,X4),c_Product__Type_OSigma(X5,X6,X3,X4),tc_prod(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_942]) ).
cnf(c_0_1367,plain,
( c_in(c_Pair(X2,X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X4,X3,X3),X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_943]) ).
cnf(c_0_1368,plain,
( X4 = X5
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(X4,c_Equiv__Relations_Oquotient(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_in(X5,c_Equiv__Relations_Oquotient(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_in(X6,X4,X3)
| ~ c_in(X7,X5,X3)
| ~ c_in(c_Pair(X6,X7,X3,X3),X2,tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_944]) ).
cnf(c_0_1369,plain,
( X1 = X2
| X4 = X5
| X4 = X2
| X5 = X2
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_945]) ).
cnf(c_0_1370,plain,
( X1 = X2
| X4 = X5
| X5 = X1
| X4 = X1
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_946]) ).
cnf(c_0_1371,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X2
| X1 = X2
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_947]) ).
cnf(c_0_1372,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| X1 = X2
| X1 = X4
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_948]) ).
cnf(c_0_1373,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| X1 = X2
| X2 = X1
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_949]) ).
cnf(c_0_1374,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X2
| X1 = X2
| X2 = X4
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_950]) ).
cnf(c_0_1375,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_951]) ).
cnf(c_0_1376,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X1
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_952]) ).
cnf(c_0_1377,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_953]) ).
cnf(c_0_1378,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X2,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X4
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_954]) ).
cnf(c_0_1379,plain,
( c_in(X1,X5,X3)
| ~ c_in(c_Pair(X1,X2,X3,X4),c_Product__Type_OSigma(X5,X6,X3,X4),tc_prod(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_955]) ).
cnf(c_0_1380,plain,
( c_in(c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1(X2,X1,X3),X2,X3)
| c_Relation_Orefl__on(X2,X1,X3)
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_956]) ).
cnf(c_0_1381,plain,
( c_in(c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1(X2,X1,X3),X2,X3)
| c_Relation_Orefl__on(X2,X1,X3)
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_957]) ).
cnf(c_0_1382,plain,
( c_in(c_Pair(X2,X1,X4,X3),X5,tc_prod(X4,X3))
| ~ c_in(c_Pair(X1,X2,X3,X4),c_Relation_Oconverse(X5,X4,X3),tc_prod(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_958]) ).
cnf(c_0_1383,plain,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X1,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X1,X2),X2,X2),c_Transitive__Closure_Otrancl(X1,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X3,X3,X2,X2),X1,tc_prod(X2,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_959]) ).
cnf(c_0_1384,plain,
( c_in(c_Pair(X2,X1,X4,X3),c_Relation_Oconverse(X5,X3,X4),tc_prod(X4,X3))
| ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_960]) ).
cnf(c_0_1385,plain,
( c_in(c_Pair(X2,X1,X4,X3),c_Relation_Oconverse(X5,X3,X4),tc_prod(X4,X3))
| ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_961]) ).
cnf(c_0_1386,plain,
( c_in(hAPP(X1,X6),X3,X4)
| ~ c_in(X1,c_FuncSet_OPi(X2,c_COMBK(X3,tc_fun(X4,tc_bool),X5),X5,X4),tc_fun(X5,X4))
| ~ c_in(X6,X2,X5) ),
inference(split_conjunct,[status(thm)],[c_0_962]) ).
cnf(c_0_1387,plain,
( X1 = X2
| c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_963]) ).
cnf(c_0_1388,plain,
( X1 = X2
| c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_964]) ).
cnf(c_0_1389,plain,
( X1 = X2
| c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_965]) ).
cnf(c_0_1390,plain,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_966]) ).
cnf(c_0_1391,plain,
( c_in(X4,c_Relation_OImage(X6,X2,X3,X5),X5)
| ~ c_in(X1,X2,X3)
| ~ c_in(c_Pair(X1,X4,X3,X5),X6,tc_prod(X3,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_967]) ).
cnf(c_0_1392,plain,
( c_in(X4,c_Relation_OImage(X6,X2,X3,X5),X5)
| ~ c_in(X1,X2,X3)
| ~ c_in(c_Pair(X1,X4,X3,X5),X6,tc_prod(X3,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_968]) ).
cnf(c_0_1393,plain,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_969]) ).
cnf(c_0_1394,plain,
( c_in(c_Pair(X4,X3,X2,X2),X1,tc_prod(X2,X2))
| ~ c_Relation_Osym(X1,X2)
| ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_970]) ).
cnf(c_0_1395,plain,
( c_in(c_Pair(X4,X3,X2,X2),X1,tc_prod(X2,X2))
| ~ c_Relation_Osym(X1,X2)
| ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_971]) ).
cnf(c_0_1396,plain,
( X2 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X3,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_972]) ).
cnf(c_0_1397,plain,
( X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X3,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_973]) ).
cnf(c_0_1398,plain,
( X1 = X2
| X1 = X3
| c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_974]) ).
cnf(c_0_1399,plain,
( X1 = X2
| X3 = X2
| c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_975]) ).
cnf(c_0_1400,plain,
( X1 = X2
| X3 = X1
| c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_976]) ).
cnf(c_0_1401,plain,
( X1 = X2
| X3 = X2
| c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_977]) ).
cnf(c_0_1402,plain,
( ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(X3,X4,X2)
| ~ c_in(c_Pair(X5,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(X5,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_978]) ).
cnf(c_0_1403,plain,
( ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(X3,X4,X2)
| ~ c_in(c_Pair(X5,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(X5,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_979]) ).
cnf(c_0_1404,plain,
( hBOOL(hAPP(X5,X4))
| hBOOL(hAPP(X5,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_Pair(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X5,X2,X3),X3,X3),X2,tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_980]) ).
cnf(c_0_1405,plain,
( hBOOL(hAPP(X5,X4))
| hBOOL(hAPP(X5,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_Pair(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X5,X2,X3),X3,X3),X2,tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_981]) ).
cnf(c_0_1406,plain,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X3)
| ~ c_in(X6,c_Equiv__Relations_Oquotient(X5,X4,X3),tc_fun(X3,tc_bool))
| ~ c_in(X6,c_Equiv__Relations_Oquotient(X5,X4,X3),tc_fun(X3,tc_bool))
| ~ c_in(X1,X6,X3)
| ~ c_in(X2,X6,X3) ),
inference(split_conjunct,[status(thm)],[c_0_982]) ).
cnf(c_0_1407,plain,
( X4 = X5
| c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3))
| c_in(c_Pair(X5,X4,X3,X3),X2,tc_prod(X3,X3))
| ~ c_Relation_Ototal__on(X1,X2,X3)
| ~ c_in(X4,X1,X3)
| ~ c_in(X5,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_983]) ).
cnf(c_0_1408,plain,
( c_Relation_Orel__comp(c_Relation_Oconverse(X2,X3,X3),X2,X3,X3,X3) = X2
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_984]) ).
cnf(c_0_1409,plain,
( c_lessequals(c_Relation_OImage(X1,X5,X3,X4),c_Relation_OImage(X2,X6,X3,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool))
| ~ c_lessequals(X5,X6,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_985]) ).
cnf(c_0_1410,plain,
( X1 = X2
| ~ c_in(X3,X4,X5)
| c_Product__Type_OSigma(X1,c_COMBK(X4,tc_fun(X5,tc_bool),X6),X6,X5) != c_Product__Type_OSigma(X2,c_COMBK(X4,tc_fun(X5,tc_bool),X6),X6,X5) ),
inference(split_conjunct,[status(thm)],[c_0_986]) ).
cnf(c_0_1411,plain,
( X2 = X3
| c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_987]) ).
cnf(c_0_1412,plain,
( c_in(c_Pair(X1,X4,X3,X6),c_Product__Type_OSigma(X2,X5,X3,X6),tc_prod(X3,X6))
| ~ c_in(X1,X2,X3)
| ~ c_in(X4,hAPP(X5,X1),X6) ),
inference(split_conjunct,[status(thm)],[c_0_988]) ).
cnf(c_0_1413,plain,
( c_in(c_Pair(X1,X4,X3,X6),c_Product__Type_OSigma(X2,X5,X3,X6),tc_prod(X3,X6))
| ~ c_in(X1,X2,X3)
| ~ c_in(X4,hAPP(X5,X1),X6) ),
inference(split_conjunct,[status(thm)],[c_0_989]) ).
cnf(c_0_1414,plain,
( X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_990]) ).
cnf(c_0_1415,plain,
( X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_991]) ).
cnf(c_0_1416,plain,
( c_in(X3,c_Wellfounded_Oacc(X2,t_a),t_a)
| hBOOL(hAPP(X4,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X4,X2),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
inference(split_conjunct,[status(thm)],[c_0_992]) ).
cnf(c_0_1417,plain,
( c_in(X3,c_Wellfounded_Oacc(X2,t_a),t_a)
| hBOOL(hAPP(X4,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X4,X2),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
inference(split_conjunct,[status(thm)],[c_0_993]) ).
cnf(c_0_1418,plain,
( c_lessequals(c_Set_Oimage(X4,X1,X3,X5),c_Set_Oimage(X4,X2,X3,X5),tc_fun(X5,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_994]) ).
cnf(c_0_1419,plain,
( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_995]) ).
cnf(c_0_1420,plain,
( c_in(X4,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_Pair(X4,X1,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_996]) ).
cnf(c_0_1421,plain,
( c_in(X1,c_Wellfounded_Oacc(X4,X3),X3)
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(X2,c_Wellfounded_Oacc(X4,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_997]) ).
cnf(c_0_1422,plain,
( hBOOL(hAPP(X4,X3))
| hBOOL(hAPP(X4,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X4,X2),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
inference(split_conjunct,[status(thm)],[c_0_998]) ).
cnf(c_0_1423,plain,
( hBOOL(hAPP(X4,X3))
| hBOOL(hAPP(X4,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X4,X2),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
inference(split_conjunct,[status(thm)],[c_0_999]) ).
cnf(c_0_1424,plain,
( c_in(X4,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_Pair(X4,X1,X3,X3),X2,tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1000]) ).
cnf(c_0_1425,plain,
( c_in(X4,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_Pair(X4,X1,X3,X3),X2,tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1001]) ).
cnf(c_0_1426,plain,
( c_in(X1,c_Relation_ODomain(X2,X3,X3),X3)
| X1 = X4
| ~ c_in(c_Pair(X1,X4,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1002]) ).
cnf(c_0_1427,plain,
( c_in(hAPP(X1,X6),hAPP(X3,X6),X5)
| ~ c_in(X1,c_FuncSet_OPi(X2,X3,X4,X5),tc_fun(X4,X5))
| ~ c_in(X6,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1003]) ).
cnf(c_0_1428,plain,
( c_in(hAPP(X1,X6),hAPP(X3,X6),X5)
| ~ c_in(X1,c_FuncSet_OPi(X2,X3,X4,X5),tc_fun(X4,X5))
| ~ c_in(X6,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1004]) ).
cnf(c_0_1429,plain,
( c_Nitpick_Orefl_H(X1,X2)
| ~ c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X1,X2),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X1,X2),X2,X2),X1,tc_prod(X2,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1005]) ).
cnf(c_0_1430,plain,
( c_in(hAPP(X1,X6),X5,X4)
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ c_in(X6,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1006]) ).
cnf(c_0_1431,plain,
( c_in(X2,c_Relation_ORange(X5,X3,X4),X4)
| ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1007]) ).
cnf(c_0_1432,plain,
( c_in(X2,c_Relation_ORange(X5,X3,X4),X4)
| ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1008]) ).
cnf(c_0_1433,plain,
( c_in(X1,c_Relation_ODomain(X5,X3,X4),X3)
| ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1009]) ).
cnf(c_0_1434,plain,
( c_in(X1,c_Relation_ODomain(X5,X3,X4),X3)
| ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1010]) ).
cnf(c_0_1435,plain,
( v_thesis____
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1011]) ).
cnf(c_0_1436,plain,
( c_in(X5,X1,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1012]) ).
cnf(c_0_1437,plain,
( c_in(X4,X1,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1013]) ).
cnf(c_0_1438,plain,
( c_in(X5,X1,X3)
| ~ c_Relation_Orefl__on(X1,X2,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1014]) ).
cnf(c_0_1439,plain,
( c_in(X4,X1,X3)
| ~ c_Relation_Orefl__on(X1,X2,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1015]) ).
cnf(c_0_1440,plain,
( c_lessequals(X2,c_Product__Type_OSigma(X1,c_COMBK(X1,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1016]) ).
cnf(c_0_1441,plain,
( c_lessequals(X2,c_Product__Type_OSigma(X1,c_COMBK(X1,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Relation_Orefl__on(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1017]) ).
cnf(c_0_1442,plain,
( c_in(X1,X4,X3)
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId__on(X4,X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1018]) ).
cnf(c_0_1443,plain,
( X1 = X2
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId__on(X4,X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1019]) ).
cnf(c_0_1444,plain,
( c_Finite__Set_Ofinite(X3,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,c_Set_Oimage(X4,X1,X2,X5),tc_fun(X5,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1020]) ).
cnf(c_0_1445,plain,
( ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_Pair(X3,X3,X2,X2),X1,tc_prod(X2,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1021]) ).
cnf(c_0_1446,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X3),c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1022]) ).
cnf(c_0_1447,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X4),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4),X4)
| ~ class_Lattices_Olattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1023]) ).
cnf(c_0_1448,plain,
( X1 = X2
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId(X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1024]) ).
cnf(c_0_1449,plain,
( c_Set_Oinsert(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5) = c_Set_Oimage(X4,X2,X3,X5)
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1025]) ).
cnf(c_0_1450,plain,
( c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X1,X2,X3),X2,X3,X3),X1,tc_prod(X3,X3))
| c_in(X2,c_Wellfounded_Oacc(X1,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1026]) ).
cnf(c_0_1451,plain,
( c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X2,X1,X3),X1,X3,X3),X2,tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1027]) ).
cnf(c_0_1452,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X1 = X2
| X2 = X1
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1028]) ).
cnf(c_0_1453,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X1 = X2
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1029]) ).
cnf(c_0_1454,plain,
( c_in(c_List_Osko__Equiv__Relations__XquotientE__1__1(X2,X1,X3,X4),X2,X4)
| ~ c_in(X1,c_Equiv__Relations_Oquotient(X2,X3,X4),tc_fun(X4,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1030]) ).
cnf(c_0_1455,plain,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1031]) ).
cnf(c_0_1456,plain,
( c_in(X1,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3),tc_prod(X3,X3))
| ~ c_in(X1,c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1032]) ).
cnf(c_0_1457,plain,
( c_in(X1,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(tc_prod(X3,X3),tc_bool)),X3),tc_prod(X3,X3))
| ~ c_in(X1,c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1033]) ).
cnf(c_0_1458,plain,
( X1 = X2
| c_Pair(X3,X1,X4,X5) != c_Pair(X6,X2,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_1034]) ).
cnf(c_0_1459,plain,
( X1 = X2
| c_Pair(X1,X3,X4,X5) != c_Pair(X2,X6,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_1035]) ).
cnf(c_0_1460,plain,
( c_in(c_Pair(X1,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| c_in(X1,c_Relation_ODomain(X3,X2,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1036]) ).
cnf(c_0_1461,plain,
( c_in(c_Pair(X4,X4,X3,X3),X2,tc_prod(X3,X3))
| ~ c_Relation_Orefl__on(X1,X2,X3)
| ~ c_in(X4,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1037]) ).
cnf(c_0_1462,plain,
( c_in(c_Pair(X4,X4,X3,X3),X2,tc_prod(X3,X3))
| ~ c_Relation_Orefl__on(X1,X2,X3)
| ~ c_in(X4,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1038]) ).
cnf(c_0_1463,plain,
( c_in(c_Pair(X1,X1,X3,X3),c_Relation_OId__on(X2,X3),tc_prod(X3,X3))
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1039]) ).
cnf(c_0_1464,plain,
( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
| ~ c_in(X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1040]) ).
cnf(c_0_1465,plain,
( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
| ~ c_in(X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1041]) ).
cnf(c_0_1466,plain,
( c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1042]) ).
cnf(c_0_1467,plain,
( c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1043]) ).
cnf(c_0_1468,plain,
( c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Relation_Orefl__on(X1,X2,X3)
| ~ c_Relation_Orefl__on(X4,X5,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1044]) ).
cnf(c_0_1469,plain,
( c_Relation_Orefl__on(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Relation_Orefl__on(X1,X2,X3)
| ~ c_Relation_Orefl__on(X4,X5,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1045]) ).
cnf(c_0_1470,plain,
( X1 = c_Pair(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X2,X1,X3),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X2,X1,X3),X3,X3)
| ~ c_in(X1,c_Relation_OId__on(X2,X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1046]) ).
cnf(c_0_1471,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1047]) ).
cnf(c_0_1472,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1048]) ).
cnf(c_0_1473,plain,
( c_in(c_Pair(X3,X3,X2,X2),X1,tc_prod(X2,X2))
| ~ c_Nitpick_Orefl_H(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1049]) ).
cnf(c_0_1474,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X3,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X1
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_1050]) ).
cnf(c_0_1475,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X3,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_1051]) ).
cnf(c_0_1476,plain,
( X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_1052]) ).
cnf(c_0_1477,plain,
( hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1053]) ).
cnf(c_0_1478,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1054]) ).
cnf(c_0_1479,plain,
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1055]) ).
cnf(c_0_1480,plain,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1056]) ).
cnf(c_0_1481,plain,
( hBOOL(hAPP(X4,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X4,X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1057]) ).
cnf(c_0_1482,plain,
( hBOOL(hAPP(X4,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X4,X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1058]) ).
cnf(c_0_1483,plain,
( c_Relation_Otrans(c_Relation_Oinv__image(X1,X3,X2,X4),X4)
| ~ c_Relation_Otrans(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1059]) ).
cnf(c_0_1484,plain,
( c_Finite__Set_Ofinite(c_Set_Oimage(X3,X1,X2,X4),X4)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1060]) ).
cnf(c_0_1485,plain,
( c_Wellfounded_Owf(c_Relation_Oinv__image(X1,X3,X2,X4),X4)
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1061]) ).
cnf(c_0_1486,plain,
( c_Relation_Osym(c_Relation_Oinv__image(X1,X3,X2,X4),X4)
| ~ c_Relation_Osym(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1062]) ).
cnf(c_0_1487,plain,
( c_lessequals(c_Relation_ODomain(X1,X3,X4),c_Relation_ODomain(X2,X3,X4),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1063]) ).
cnf(c_0_1488,plain,
( c_in(X1,c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(X1,c_Transitive__Closure_Otrancl(X2,X3),tc_prod(X3,X3))
| ~ c_lessequals(X2,X4,tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1064]) ).
cnf(c_0_1489,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1065]) ).
cnf(c_0_1490,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1066]) ).
cnf(c_0_1491,plain,
( c_Transitive__Closure_Ortrancl(X2,X3) = c_Transitive__Closure_Ortrancl(X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(X2,c_Transitive__Closure_Ortrancl(X1,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1067]) ).
cnf(c_0_1492,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1068]) ).
cnf(c_0_1493,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1069]) ).
cnf(c_0_1494,plain,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1070]) ).
cnf(c_0_1495,plain,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1071]) ).
cnf(c_0_1496,plain,
( c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Relation_Oconverse(X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1072]) ).
cnf(c_0_1497,plain,
( c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1073]) ).
cnf(c_0_1498,plain,
( c_lessequals(X1,X2,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1074]) ).
cnf(c_0_1499,plain,
( c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1075]) ).
cnf(c_0_1500,plain,
( c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1076]) ).
cnf(c_0_1501,plain,
( X1 = c_Pair(c_ATP__Linkup_Osko__Relation__XIdE__1__1(X1,X2),c_ATP__Linkup_Osko__Relation__XIdE__1__1(X1,X2),X2,X2)
| ~ c_in(X1,c_Relation_OId(X2),tc_prod(X2,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1077]) ).
cnf(c_0_1502,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ class_Lattices_Odistrib__lattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1078]) ).
cnf(c_0_1503,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X4),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4)
| ~ class_Lattices_Odistrib__lattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1079]) ).
cnf(c_0_1504,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ class_Lattices_Odistrib__lattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1080]) ).
cnf(c_0_1505,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X4),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4)
| ~ class_Lattices_Odistrib__lattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1081]) ).
cnf(c_0_1506,plain,
( c_in(X1,X2,X4)
| c_in(X1,X3,X4)
| ~ c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1082]) ).
cnf(c_0_1507,plain,
( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1083]) ).
cnf(c_0_1508,plain,
( c_lessequals(c_Transitive__Closure_Ortrancl(X1,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(X1,c_Transitive__Closure_Ortrancl(X2,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1084]) ).
cnf(c_0_1509,plain,
( c_in(X2,X1,X4)
| c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1085]) ).
cnf(c_0_1510,plain,
( c_in(X1,X2,X3)
| c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1086]) ).
cnf(c_0_1511,plain,
( X1 = X4
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1087]) ).
cnf(c_0_1512,plain,
( c_lessequals(c_Set_Oinsert(X4,X1,X3),c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1088]) ).
cnf(c_0_1513,plain,
( X1 = X2
| c_in(c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1089]) ).
cnf(c_0_1514,plain,
( X1 = X2
| c_in(c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1090]) ).
cnf(c_0_1515,plain,
( c_in(c_Relation_Oconverse(X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1091]) ).
cnf(c_0_1516,plain,
( c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1092]) ).
cnf(c_0_1517,plain,
( c_lessequals(c_Transitive__Closure_Ortrancl(X1,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1093]) ).
cnf(c_0_1518,plain,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1094]) ).
cnf(c_0_1519,plain,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1095]) ).
cnf(c_0_1520,plain,
( c_in(c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X1,X2,X3),X2,tc_fun(X3,tc_bool))
| ~ c_in(X1,c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X3,tc_bool)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1096]) ).
cnf(c_0_1521,plain,
( c_in(X1,X3,X4)
| ~ c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1097]) ).
cnf(c_0_1522,plain,
( c_in(X1,X2,X4)
| ~ c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1098]) ).
cnf(c_0_1523,plain,
( c_in(X1,c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1099]) ).
cnf(c_0_1524,plain,
( c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3)
| ~ c_in(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1100]) ).
cnf(c_0_1525,plain,
( c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3)
| ~ c_in(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1101]) ).
cnf(c_0_1526,plain,
( c_in(X1,X4,X3)
| ~ c_in(X1,c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X4,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1102]) ).
cnf(c_0_1527,plain,
( c_in(X2,c_Wellfounded_Oacc(X1,X3),X3)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X1,X2,X3),c_Wellfounded_Oacc(X1,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1103]) ).
cnf(c_0_1528,plain,
( c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X2,X1,X3),c_Wellfounded_Oacc(X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1104]) ).
cnf(c_0_1529,plain,
( c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1105]) ).
cnf(c_0_1530,plain,
( c_Wellfounded_Owf(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X1,X2),X2,X2),X2)
| ~ c_Wellfounded_Owf(c_Relation_Oconverse(X1,X2,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1106]) ).
cnf(c_0_1531,plain,
( c_in(X1,X2,X3)
| c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1107]) ).
cnf(c_0_1532,plain,
( c_in(X1,X2,X3)
| c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1108]) ).
cnf(c_0_1533,plain,
( c_in(X1,c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X1,X2,X3),X3)
| ~ c_in(X1,c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X3,tc_bool)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1109]) ).
cnf(c_0_1534,plain,
( c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X4,X2,X3),c_Wellfounded_Oacc(X2,X3),X3)
| hBOOL(hAPP(X4,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1110]) ).
cnf(c_0_1535,plain,
( c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X4,X2,X3),c_Wellfounded_Oacc(X2,X3),X3)
| hBOOL(hAPP(X4,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1111]) ).
cnf(c_0_1536,plain,
( c_in(X1,X4,X3)
| ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1112]) ).
cnf(c_0_1537,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1113]) ).
cnf(c_0_1538,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1114]) ).
cnf(c_0_1539,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1115]) ).
cnf(c_0_1540,plain,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1116]) ).
cnf(c_0_1541,plain,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1117]) ).
cnf(c_0_1542,plain,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1118]) ).
cnf(c_0_1543,plain,
( c_in(X4,c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1119]) ).
cnf(c_0_1544,plain,
( c_lessequals(c_Relation_OField(X1,X3),c_Relation_OField(X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1120]) ).
cnf(c_0_1545,plain,
( c_lessequals(c_Wellfounded_Oacc(X2,X3),c_Wellfounded_Oacc(X1,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1121]) ).
cnf(c_0_1546,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1122]) ).
cnf(c_0_1547,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4)
| ~ class_Lattices_Oupper__semilattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1123]) ).
cnf(c_0_1548,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4)
| ~ class_Lattices_Olattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1124]) ).
cnf(c_0_1549,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1125]) ).
cnf(c_0_1550,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1126]) ).
cnf(c_0_1551,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4)
| ~ class_Lattices_Olattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1127]) ).
cnf(c_0_1552,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1128]) ).
cnf(c_0_1553,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1129]) ).
cnf(c_0_1554,plain,
( c_in(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X2,X1,X3),X2,X3)
| ~ c_in(X1,c_Relation_OId__on(X2,X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1130]) ).
cnf(c_0_1555,plain,
( c_in(c_Arrow__Order__Mirabelle_Omktop(X1,X2),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1131]) ).
cnf(c_0_1556,plain,
( c_in(c_Arrow__Order__Mirabelle_Omkbot(X1,X2),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1132]) ).
cnf(c_0_1557,plain,
( c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1133]) ).
cnf(c_0_1558,plain,
( c_in(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1134]) ).
cnf(c_0_1559,plain,
( c_in(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1135]) ).
cnf(c_0_1560,plain,
( c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Osym(X1,X2)
| ~ c_Relation_Osym(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1136]) ).
cnf(c_0_1561,plain,
( c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Osym(X1,X2)
| ~ c_Relation_Osym(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1137]) ).
cnf(c_0_1562,plain,
( c_Relation_Otrans(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Otrans(X1,X2)
| ~ c_Relation_Otrans(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1138]) ).
cnf(c_0_1563,plain,
( c_lessequals(X1,X2,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1139]) ).
cnf(c_0_1564,plain,
( c_lessequals(X1,X3,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1140]) ).
cnf(c_0_1565,plain,
( c_lessequals(X1,X2,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1141]) ).
cnf(c_0_1566,plain,
( c_lessequals(X1,X3,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1142]) ).
cnf(c_0_1567,plain,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1143]) ).
cnf(c_0_1568,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1144]) ).
cnf(c_0_1569,plain,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1145]) ).
cnf(c_0_1570,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1146]) ).
cnf(c_0_1571,plain,
( X1 = X2
| c_in(X1,X3,X4)
| ~ c_in(X1,c_Set_Oinsert(X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1147]) ).
cnf(c_0_1572,plain,
( c_in(c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X1,X2,X3),X2,tc_fun(X3,tc_bool))
| c_in(X1,c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X3,tc_bool)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1148]) ).
cnf(c_0_1573,plain,
( c_Relation_Orefl__on(X1,X2,X3)
| ~ c_Relation_Orefl__on(X1,c_Relation_Oconverse(X2,X3,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1149]) ).
cnf(c_0_1574,plain,
( c_Relation_Ototal__on(X1,X2,X3)
| ~ c_Relation_Ototal__on(X1,c_Relation_Oconverse(X2,X3,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1150]) ).
cnf(c_0_1575,plain,
( c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1151]) ).
cnf(c_0_1576,plain,
( c_Relation_Otrans(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Otrans(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1152]) ).
cnf(c_0_1577,plain,
( c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1153]) ).
cnf(c_0_1578,plain,
( c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1154]) ).
cnf(c_0_1579,plain,
( c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1155]) ).
cnf(c_0_1580,plain,
( c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1156]) ).
cnf(c_0_1581,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1157]) ).
cnf(c_0_1582,plain,
( X1 = X2
| c_in(X3,X1,X4)
| c_in(X3,X2,X4)
| c_Set_Oinsert(X3,X1,X4) != c_Set_Oinsert(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1158]) ).
cnf(c_0_1583,plain,
( hBOOL(hAPP(X3,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ hBOOL(hAPP(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X3,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1159]) ).
cnf(c_0_1584,plain,
( hBOOL(hAPP(X3,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ hBOOL(hAPP(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X3,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1160]) ).
cnf(c_0_1585,plain,
( c_Finite__Set_Ofinite(X1,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1161]) ).
cnf(c_0_1586,plain,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1162]) ).
cnf(c_0_1587,plain,
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1163]) ).
cnf(c_0_1588,plain,
( c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1164]) ).
cnf(c_0_1589,plain,
( c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X4,X1,X2),X4,X2)
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(X3,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1165]) ).
cnf(c_0_1590,plain,
( c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X4,X1,X2),X4,X2)
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(X3,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1166]) ).
cnf(c_0_1591,plain,
( c_in(X4,X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1167]) ).
cnf(c_0_1592,plain,
( c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1168]) ).
cnf(c_0_1593,plain,
( c_in(X4,X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1169]) ).
cnf(c_0_1594,plain,
( c_in(X4,X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1170]) ).
cnf(c_0_1595,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1171]) ).
cnf(c_0_1596,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X1,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1172]) ).
cnf(c_0_1597,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1173]) ).
cnf(c_0_1598,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1174]) ).
cnf(c_0_1599,plain,
( c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1175]) ).
cnf(c_0_1600,plain,
( c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1176]) ).
cnf(c_0_1601,plain,
( c_Relation_Orefl__on(X1,c_Relation_Oconverse(X2,X3,X3),X3)
| ~ c_Relation_Orefl__on(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1177]) ).
cnf(c_0_1602,plain,
( c_Relation_Ototal__on(X1,c_Relation_Oconverse(X2,X3,X3),X3)
| ~ c_Relation_Ototal__on(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1178]) ).
cnf(c_0_1603,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1179]) ).
cnf(c_0_1604,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1180]) ).
cnf(c_0_1605,plain,
( c_Wellfounded_Owf(X3,X2)
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_lessequals(X3,X1,tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1181]) ).
cnf(c_0_1606,plain,
( c_lessequals(hAPP(X1,X5),hAPP(X2,X5),X4)
| ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
inference(split_conjunct,[status(thm)],[c_0_1182]) ).
cnf(c_0_1607,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1183]) ).
cnf(c_0_1608,plain,
( c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1184]) ).
cnf(c_0_1609,plain,
( c_in(X1,c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
| ~ c_in(X1,X2,tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1185]) ).
cnf(c_0_1610,plain,
( c_in(X1,c_Transitive__Closure_Otrancl(X2,X3),tc_prod(X3,X3))
| ~ c_in(X1,X2,tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1186]) ).
cnf(c_0_1611,plain,
( c_Finite__Set_Ofinite(c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1187]) ).
cnf(c_0_1612,plain,
( c_Complete__Lattice_OSup__class_OSup(c_Equiv__Relations_Oquotient(X1,X2,X3),tc_fun(X3,tc_bool)) = X1
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1188]) ).
cnf(c_0_1613,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1189]) ).
cnf(c_0_1614,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1190]) ).
cnf(c_0_1615,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1191]) ).
cnf(c_0_1616,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1192]) ).
cnf(c_0_1617,plain,
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1193]) ).
cnf(c_0_1618,plain,
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1194]) ).
cnf(c_0_1619,plain,
( c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X1,X2,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Complete__Lattice_OInf__class_OInf(X2,X3),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1195]) ).
cnf(c_0_1620,plain,
( c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Complete__Lattice_OSup__class_OSup(X2,X3),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1196]) ).
cnf(c_0_1621,plain,
( c_Relation_Otrans(X1,X2)
| ~ c_Relation_Otrans(c_Relation_Oconverse(X1,X2,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1197]) ).
cnf(c_0_1622,plain,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1198]) ).
cnf(c_0_1623,plain,
( c_Relation_Osym(X1,X2)
| ~ c_Relation_Osym(c_Relation_Oconverse(X1,X2,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1199]) ).
cnf(c_0_1624,plain,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_1200]) ).
cnf(c_0_1625,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1201]) ).
cnf(c_0_1626,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1202]) ).
cnf(c_0_1627,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1203]) ).
cnf(c_0_1628,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1204]) ).
cnf(c_0_1629,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1205]) ).
cnf(c_0_1630,plain,
( hBOOL(hAPP(X2,X4))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X1,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1206]) ).
cnf(c_0_1631,plain,
( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1207]) ).
cnf(c_0_1632,plain,
( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1208]) ).
cnf(c_0_1633,plain,
( c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X1,X2),c_Wellfounded_Oacc(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1209]) ).
cnf(c_0_1634,plain,
( c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X1,X2),c_Wellfounded_Oacc(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1210]) ).
cnf(c_0_1635,plain,
( X2 = X1
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1211]) ).
cnf(c_0_1636,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1212]) ).
cnf(c_0_1637,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1213]) ).
cnf(c_0_1638,plain,
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X2,X3),X1,X3)
| ~ c_in(X1,X2,X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1214]) ).
cnf(c_0_1639,plain,
( c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X2,X3),X3)
| ~ c_in(X1,X2,X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1215]) ).
cnf(c_0_1640,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) = X1
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1216]) ).
cnf(c_0_1641,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = X1
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1217]) ).
cnf(c_0_1642,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1218]) ).
cnf(c_0_1643,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1219]) ).
cnf(c_0_1644,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1220]) ).
cnf(c_0_1645,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1221]) ).
cnf(c_0_1646,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X1,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1222]) ).
cnf(c_0_1647,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X2,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1223]) ).
cnf(c_0_1648,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1224]) ).
cnf(c_0_1649,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X1,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1225]) ).
cnf(c_0_1650,plain,
( c_Finite__Set_Ofinite(X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1226]) ).
cnf(c_0_1651,plain,
( c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1227]) ).
cnf(c_0_1652,plain,
( c_lessequals(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) != X1
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1228]) ).
cnf(c_0_1653,plain,
( c_lessequals(X1,X2,X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) != X2
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1229]) ).
cnf(c_0_1654,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1230]) ).
cnf(c_0_1655,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3) = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1231]) ).
cnf(c_0_1656,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1232]) ).
cnf(c_0_1657,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1233]) ).
cnf(c_0_1658,plain,
( X1 = X2
| c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X1,X2),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1234]) ).
cnf(c_0_1659,plain,
( c_Relation_Otrans(c_Relation_Oconverse(X1,X2,X2),X2)
| ~ c_Relation_Otrans(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1235]) ).
cnf(c_0_1660,plain,
( c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X1,X2),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1236]) ).
cnf(c_0_1661,plain,
( c_Relation_Osym(c_Relation_Oconverse(X1,X2,X2),X2)
| ~ c_Relation_Osym(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1237]) ).
cnf(c_0_1662,plain,
( c_Set_Oinsert(X1,X2,X3) = X2
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1238]) ).
cnf(c_0_1663,plain,
( c_Relation_Orefl__on(X1,X2,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1239]) ).
cnf(c_0_1664,plain,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1240]) ).
cnf(c_0_1665,plain,
( hBOOL(hAPP(X2,X1))
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1241]) ).
cnf(c_0_1666,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1242]) ).
cnf(c_0_1667,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1243]) ).
cnf(c_0_1668,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1244]) ).
cnf(c_0_1669,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1245]) ).
cnf(c_0_1670,plain,
( c_in(X3,c_Wellfounded_Oacc(X1,X2),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1246]) ).
cnf(c_0_1671,plain,
( c_in(X2,X1,X3)
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1247]) ).
cnf(c_0_1672,plain,
( c_Relation_Osym(X1,X2)
| c_Relation_Oconverse(X1,X2,X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_1248]) ).
cnf(c_0_1673,plain,
( c_Relation_Otrans(X2,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1249]) ).
cnf(c_0_1674,plain,
( c_Relation_Osym(X2,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1250]) ).
cnf(c_0_1675,plain,
( X1 = X2
| ~ c_fequal(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1251]) ).
cnf(c_0_1676,plain,
( c_Relation_Oconverse(X1,X2,X2) = X1
| ~ c_Relation_Osym(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1252]) ).
cnf(c_0_1677,plain,
( c_Relation_Osym(c_Transitive__Closure_Ortrancl(X1,X2),X2)
| ~ c_Relation_Osym(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1253]) ).
cnf(c_0_1678,plain,
( c_Relation_Osym(c_Transitive__Closure_Otrancl(X1,X2),X2)
| ~ c_Relation_Osym(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1254]) ).
cnf(c_0_1679,plain,
( c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X1,X2),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1255]) ).
cnf(c_0_1680,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X2) = X1
| ~ class_Lattices_Oupper__semilattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1256]) ).
cnf(c_0_1681,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X1,X2) = X1
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1257]) ).
cnf(c_0_1682,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1258]) ).
cnf(c_0_1683,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1259]) ).
cnf(c_0_1684,plain,
( class_Finite__Set_Ofinite_Ofinite(tc_prod(X1,X2))
| ~ class_Finite__Set_Ofinite_Ofinite(X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1260]) ).
cnf(c_0_1685,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_1261]) ).
cnf(c_0_1686,plain,
( c_Transitive__Closure_Otrancl(X1,X2) = X1
| ~ c_Relation_Otrans(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1262]) ).
cnf(c_0_1687,plain,
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1263]) ).
cnf(c_0_1688,plain,
( class_Lattices_Oupper__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1264]) ).
cnf(c_0_1689,plain,
( class_Lattices_Olower__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1265]) ).
cnf(c_0_1690,plain,
( class_Lattices_Odistrib__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1266]) ).
cnf(c_0_1691,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1267]) ).
cnf(c_0_1692,plain,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1268]) ).
cnf(c_0_1693,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1269]) ).
cnf(c_0_1694,plain,
( class_HOL_Oord(tc_fun(X2,X1))
| ~ class_HOL_Oord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1270]) ).
cnf(c_0_1695,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1271]) ).
cnf(c_0_1696,plain,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X1,X2,X5,X6,X3,X4,X7),X3,X7),X5,tc_prod(X3,X7))
| ~ c_in(c_Pair(X1,X2,X3,X4),c_Relation_Orel__comp(X5,X6,X3,X7,X4),tc_prod(X3,X4)) ),
c_0_1272,
[final] ).
cnf(c_0_1697,plain,
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X1,X2,X5,X6,X3,X4,X7),X2,X7,X4),X6,tc_prod(X7,X4))
| ~ c_in(c_Pair(X1,X2,X3,X4),c_Relation_Orel__comp(X5,X6,X3,X7,X4),tc_prod(X3,X4)) ),
c_0_1273,
[final] ).
cnf(c_0_1698,plain,
( c_Recdef_Ocut(X1,X2,X3,X4,X5) = c_Recdef_Ocut(X6,X2,X3,X4,X5)
| hAPP(X1,c_List_Osko__Recdef__Xcuts__eq__1__1(X1,X6,X2,X3,X4,X5)) != hAPP(X6,c_List_Osko__Recdef__Xcuts__eq__1__1(X1,X6,X2,X3,X4,X5)) ),
c_0_1274,
[final] ).
cnf(c_0_1699,plain,
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,X1,X2,X2,X2),c_Relation_Orel__comp(X3,X1,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
c_0_1275,
[final] ).
cnf(c_0_1700,plain,
( c_in(c_Pair(c_List_Osko__Recdef__Xcuts__eq__1__1(X1,X2,X3,X4,X5,X6),X4,X5,X5),X3,tc_prod(X5,X5))
| c_Recdef_Ocut(X1,X3,X4,X5,X6) = c_Recdef_Ocut(X2,X3,X4,X5,X6) ),
c_0_1276,
[final] ).
cnf(c_0_1701,plain,
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,X1,X3,X3,X3),c_Relation_Orel__comp(X2,X1,X3,X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)),X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3) ),
c_0_1277,
[final] ).
cnf(c_0_1702,plain,
( c_lessequals(c_Product__Type_OSigma(X1,X4,X3,X6),c_Product__Type_OSigma(X2,X5,X3,X6),tc_fun(tc_prod(X3,X6),tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(hAPP(X4,c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(X1,X4,X5,X3,X6)),hAPP(X5,c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(X1,X4,X5,X3,X6)),tc_fun(X6,tc_bool)) ),
c_0_1278,
[final] ).
cnf(c_0_1703,plain,
( c_in(X1,c_FuncSet_OPi(X2,X3,X4,X5),tc_fun(X4,X5))
| ~ c_in(hAPP(X1,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X2,X3,X1,X4,X5)),hAPP(X3,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X2,X3,X1,X4,X5)),X5) ),
c_0_1279,
[final] ).
cnf(c_0_1704,plain,
( c_in(X1,c_FuncSet_OPi(X2,X3,X4,X5),tc_fun(X4,X5))
| ~ c_in(hAPP(X1,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X2,X3,X1,X4,X5)),hAPP(X3,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X2,X3,X1,X4,X5)),X5) ),
c_0_1280,
[final] ).
cnf(c_0_1705,plain,
( c_in(X1,c_FuncSet_OPi(X2,c_COMBK(X3,tc_fun(X5,tc_bool),X4),X4,X5),tc_fun(X4,X5))
| ~ c_in(hAPP(X1,c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X2,X3,X1,X4,X5)),X3,X5) ),
c_0_1281,
[final] ).
cnf(c_0_1706,plain,
( c_lessequals(c_Relation_Orel__comp(X1,X6,X5,X4,X8),c_Product__Type_OSigma(X2,c_COMBK(X7,tc_fun(X8,tc_bool),X5),X5,X8),tc_fun(tc_prod(X5,X8),tc_bool))
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X3,tc_fun(X4,tc_bool),X5),X5,X4),tc_fun(tc_prod(X5,X4),tc_bool))
| ~ c_lessequals(X6,c_Product__Type_OSigma(X3,c_COMBK(X7,tc_fun(X8,tc_bool),X4),X4,X8),tc_fun(tc_prod(X4,X8),tc_bool)) ),
c_0_1282,
[final] ).
cnf(c_0_1707,plain,
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X3,X1,X2,X4,X5),X1,X4,X5),X2,tc_prod(X4,X5))
| ~ c_in(X1,c_Relation_OImage(X2,X3,X4,X5),X5) ),
c_0_1283,
[final] ).
cnf(c_0_1708,plain,
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X3,X1,X2,X4,X5),X1,X4,X5),X2,tc_prod(X4,X5))
| ~ c_in(X1,c_Relation_OImage(X2,X3,X4,X5),X5) ),
c_0_1284,
[final] ).
cnf(c_0_1709,plain,
( c_lessequals(c_Relation_Orel__comp(X1,X5,X3,X4,X7),c_Relation_Orel__comp(X2,X6,X3,X4,X7),tc_fun(tc_prod(X3,X7),tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool))
| ~ c_lessequals(X5,X6,tc_fun(tc_prod(X4,X7),tc_bool)) ),
c_0_1285,
[final] ).
cnf(c_0_1710,plain,
( c_lessequals(c_Transitive__Closure_Ortrancl(X3,X1),X2,tc_fun(tc_prod(X1,X1),tc_bool))
| ~ c_lessequals(c_Relation_OId(X1),X2,tc_fun(tc_prod(X1,X1),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Ortrancl(X3,X1),X2,tc_fun(tc_prod(X1,X1),tc_bool)),X3,X1,X1,X1),X2,tc_fun(tc_prod(X1,X1),tc_bool)) ),
c_0_1286,
[final] ).
cnf(c_0_1711,plain,
( c_lessequals(c_Transitive__Closure_Otrancl(X1,X3),X2,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Otrancl(X1,X3),X2,tc_fun(tc_prod(X3,X3),tc_bool)),X1,X3,X3,X3),X2,tc_fun(tc_prod(X3,X3),tc_bool)) ),
c_0_1287,
[final] ).
cnf(c_0_1712,plain,
( c_in(c_Pair(X1,X6,X3,X7),c_Relation_Orel__comp(X5,X8,X3,X4,X7),tc_prod(X3,X7))
| ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
| ~ c_in(c_Pair(X2,X6,X4,X7),X8,tc_prod(X4,X7)) ),
c_0_1288,
[final] ).
cnf(c_0_1713,plain,
( hAPP(X5,X1) = hAPP(X6,X1)
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| c_Recdef_Ocut(X5,X4,X2,X3,X7) != c_Recdef_Ocut(X6,X4,X2,X3,X7) ),
c_0_1289,
[final] ).
cnf(c_0_1714,plain,
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_Wellfounded_Owf(X3,X2)
| ~ c_lessequals(c_Relation_Orel__comp(X1,X3,X2,X2,X2),X1,tc_fun(tc_prod(X2,X2),tc_bool)) ),
c_0_1290,
[final] ).
cnf(c_0_1715,plain,
( c_Wellfounded_Owf(X1,X2)
| ~ c_Wellfounded_Owf(c_Relation_Orel__comp(X1,X1,X2,X2,X2),X2) ),
c_0_1291,
[final] ).
cnf(c_0_1716,plain,
( c_in(c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(X1,X4,X5,X3,X6),X1,X3)
| c_lessequals(c_Product__Type_OSigma(X1,X4,X3,X6),c_Product__Type_OSigma(X2,X5,X3,X6),tc_fun(tc_prod(X3,X6),tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1292,
[final] ).
cnf(c_0_1717,plain,
( X1 = X2
| X4 = X5
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1293,
[final] ).
cnf(c_0_1718,plain,
( X1 = X2
| X4 = X5
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1294,
[final] ).
cnf(c_0_1719,plain,
( c_in(c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X1,X2,X3,X4,X5),X1,X4)
| c_in(X3,c_FuncSet_OPi(X1,c_COMBK(X2,tc_fun(X5,tc_bool),X4),X4,X5),tc_fun(X4,X5)) ),
c_0_1295,
[final] ).
cnf(c_0_1720,plain,
( hAPP(c_Recdef_Ocut(X5,X4,X2,X3,X6),X1) = hAPP(X5,X1)
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)) ),
c_0_1296,
[final] ).
cnf(c_0_1721,plain,
( hAPP(c_Recdef_Ocut(X5,X4,X2,X3,X6),X1) = hAPP(X5,X1)
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)) ),
c_0_1297,
[final] ).
cnf(c_0_1722,plain,
( c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X3,X1,X2,X4,X5),X3,X4)
| ~ c_in(X1,c_Relation_OImage(X2,X3,X4,X5),X5) ),
c_0_1298,
[final] ).
cnf(c_0_1723,plain,
( c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X3,X1,X2,X4,X5),X3,X4)
| ~ c_in(X1,c_Relation_OImage(X2,X3,X4,X5),X5) ),
c_0_1299,
[final] ).
cnf(c_0_1724,plain,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X4,X1,X2,X3),X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
c_0_1300,
[final] ).
cnf(c_0_1725,plain,
( c_Relation_Orefl__on(X2,X1,X3)
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1(X2,X1,X3),c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1(X2,X1,X3),X3,X3),X1,tc_prod(X3,X3)) ),
c_0_1301,
[final] ).
cnf(c_0_1726,plain,
( c_Relation_Orefl__on(X2,X1,X3)
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1(X2,X1,X3),c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1(X2,X1,X3),X3,X3),X1,tc_prod(X3,X3)) ),
c_0_1302,
[final] ).
cnf(c_0_1727,plain,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X4,X1,X2,X3),X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
c_0_1303,
[final] ).
cnf(c_0_1728,plain,
( c_in(c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X1,X2,X3,X4,X5),X1,X4)
| c_in(X3,c_FuncSet_OPi(X1,X2,X4,X5),tc_fun(X4,X5)) ),
c_0_1304,
[final] ).
cnf(c_0_1729,plain,
( c_in(c_FuncSet_Osko__FuncSet__XPi__I__1__1(X1,X2,X3,X4,X5),X1,X4)
| c_in(X3,c_FuncSet_OPi(X1,X2,X4,X5),tc_fun(X4,X5)) ),
c_0_1305,
[final] ).
cnf(c_0_1730,plain,
( c_lessequals(X4,X6,tc_fun(X5,tc_bool))
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(c_Product__Type_OSigma(X4,c_COMBK(X2,tc_fun(X3,tc_bool),X5),X5,X3),c_Product__Type_OSigma(X6,c_COMBK(X2,tc_fun(X3,tc_bool),X5),X5,X3),tc_fun(tc_prod(X5,X3),tc_bool)) ),
c_0_1306,
[final] ).
cnf(c_0_1731,plain,
( c_lessequals(X2,c_Relation_Orel__comp(c_Relation_Oconverse(X2,X3,X3),X2,X3,X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Relation_Orefl__on(X1,X2,X3) ),
c_0_1307,
[final] ).
cnf(c_0_1732,plain,
( c_lessequals(c_Relation_Orel__comp(c_Relation_Oconverse(X1,X2,X2),X1,X2,X2,X2),X1,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_Relation_Osym(X1,X2)
| ~ c_Relation_Otrans(X1,X2) ),
c_0_1308,
[final] ).
cnf(c_0_1733,plain,
( ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)),X3)
| ~ c_in(c_Pair(X2,X1,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
c_0_1309,
[final] ).
cnf(c_0_1734,plain,
( X1 = X2
| X4 = X5
| X4 = X1
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1310,
[final] ).
cnf(c_0_1735,plain,
( X1 = X2
| X4 = X5
| X5 = X1
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1311,
[final] ).
cnf(c_0_1736,plain,
( X1 = X2
| X4 = X5
| X5 = X2
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1312,
[final] ).
cnf(c_0_1737,plain,
( X1 = X2
| X4 = X5
| X4 = X2
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1313,
[final] ).
cnf(c_0_1738,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1314,
[final] ).
cnf(c_0_1739,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X2
| X1 = X2
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1315,
[final] ).
cnf(c_0_1740,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X2
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1316,
[final] ).
cnf(c_0_1741,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| X1 = X2
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1317,
[final] ).
cnf(c_0_1742,plain,
( c_lessequals(c_Relation_Orel__comp(X1,X1,X2,X2,X2),X1,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_Relation_Otrans(X1,X2) ),
c_0_1318,
[final] ).
cnf(c_0_1743,plain,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X4,X1,X2,X3),X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
c_0_1319,
[final] ).
cnf(c_0_1744,plain,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X4,X1,X2,X3),X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
c_0_1320,
[final] ).
cnf(c_0_1745,plain,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X4,X1,X2,X3),X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
c_0_1321,
[final] ).
cnf(c_0_1746,plain,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X4,X1,X2,X3),X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
c_0_1322,
[final] ).
cnf(c_0_1747,plain,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
c_0_1323,
[final] ).
cnf(c_0_1748,plain,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
c_0_1324,
[final] ).
cnf(c_0_1749,plain,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
c_0_1325,
[final] ).
cnf(c_0_1750,plain,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
c_0_1326,
[final] ).
cnf(c_0_1751,plain,
( X1 = X2
| c_in(X1,X5,X3)
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_lessequals(X4,c_Product__Type_OSigma(X5,c_COMBK(X5,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
c_0_1327,
[final] ).
cnf(c_0_1752,plain,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),X4,tc_prod(X3,X3)) ),
c_0_1328,
[final] ).
cnf(c_0_1753,plain,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
c_0_1329,
[final] ).
cnf(c_0_1754,plain,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),X4,tc_prod(X3,X3)) ),
c_0_1330,
[final] ).
cnf(c_0_1755,plain,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
c_0_1331,
[final] ).
cnf(c_0_1756,plain,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
c_0_1332,
[final] ).
cnf(c_0_1757,plain,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),X4,tc_prod(X3,X3)) ),
c_0_1333,
[final] ).
cnf(c_0_1758,plain,
( c_Wellfounded_Owf(c_Relation_Orel__comp(X1,X1,X2,X2,X2),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
c_0_1334,
[final] ).
cnf(c_0_1759,plain,
( c_lessequals(c_Transitive__Closure_Otrancl(X1,X3),c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
c_0_1335,
[final] ).
cnf(c_0_1760,plain,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),X4,tc_prod(X3,X3)) ),
c_0_1336,
[final] ).
cnf(c_0_1761,plain,
( c_in(c_Pair(X3,X5,X2,X2),X1,tc_prod(X2,X2))
| ~ c_Relation_Otrans(X1,X2)
| ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X5,X2,X2),X1,tc_prod(X2,X2)) ),
c_0_1337,
[final] ).
cnf(c_0_1762,plain,
( c_in(c_Pair(X3,X5,X2,X2),X1,tc_prod(X2,X2))
| ~ c_Relation_Otrans(X1,X2)
| ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X5,X2,X2),X1,tc_prod(X2,X2)) ),
c_0_1338,
[final] ).
cnf(c_0_1763,plain,
( c_in(c_Pair(hAPP(X5,X1),hAPP(X5,X2),X6,X6),X4,tc_prod(X6,X6))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_Oinv__image(X4,X5,X6,X3),tc_prod(X3,X3)) ),
c_0_1339,
[final] ).
cnf(c_0_1764,plain,
( c_Equiv__Relations_Oequiv(c_Relation_ODomain(X1,X2,X2),X1,X2)
| c_Relation_Orel__comp(c_Relation_Oconverse(X1,X2,X2),X1,X2,X2,X2) != X1 ),
c_0_1340,
[final] ).
cnf(c_0_1765,plain,
( c_in(c_Pair(X2,X3,X6,X6),c_Relation_Oinv__image(X5,X1,X4,X6),tc_prod(X6,X6))
| ~ c_in(c_Pair(hAPP(X1,X2),hAPP(X1,X3),X4,X4),X5,tc_prod(X4,X4)) ),
c_0_1341,
[final] ).
cnf(c_0_1766,plain,
( c_lessequals(c_Relation_OImage(X1,X6,X5,X4),X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X3,tc_fun(X4,tc_bool),X5),X5,X4),tc_fun(tc_prod(X5,X4),tc_bool)) ),
c_0_1342,
[final] ).
cnf(c_0_1767,plain,
( c_in(c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1(X2,X3,X1,X4),X3,X4)
| c_Wellfounded_Owf(X1,X4)
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X3,tc_fun(X4,tc_bool),X4),X4,X4),tc_fun(tc_prod(X4,X4),tc_bool)) ),
c_0_1343,
[final] ).
cnf(c_0_1768,plain,
( c_in(c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1(X2,X3,X1,X4),X2,X4)
| c_Wellfounded_Owf(X1,X4)
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X3,tc_fun(X4,tc_bool),X4),X4,X4),tc_fun(tc_prod(X4,X4),tc_bool)) ),
c_0_1344,
[final] ).
cnf(c_0_1769,plain,
( c_in(c_Pair(X1,X2,X3,X3),c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X4,X3),X3,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X4,X3,X3),X3),tc_prod(X3,X3)) ),
c_0_1345,
[final] ).
cnf(c_0_1770,plain,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X4,X3,X3),X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X4,X3),X3,X3),tc_prod(X3,X3)) ),
c_0_1346,
[final] ).
cnf(c_0_1771,plain,
( c_lessequals(c_Set_Oimage(X1,X2,X5,X4),X3,tc_fun(X4,tc_bool))
| ~ c_in(X1,c_FuncSet_OPi(X2,c_COMBK(X3,tc_fun(X4,tc_bool),X5),X5,X4),tc_fun(X5,X4)) ),
c_0_1347,
[final] ).
cnf(c_0_1772,plain,
( X2 = X3
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1348,
[final] ).
cnf(c_0_1773,plain,
( ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1349,
[final] ).
cnf(c_0_1774,plain,
( c_lessequals(c_Product__Type_OSigma(X4,c_COMBK(X2,tc_fun(X3,tc_bool),X6),X6,X3),c_Product__Type_OSigma(X5,c_COMBK(X2,tc_fun(X3,tc_bool),X6),X6,X3),tc_fun(tc_prod(X6,X3),tc_bool))
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X4,X5,tc_fun(X6,tc_bool)) ),
c_0_1350,
[final] ).
cnf(c_0_1775,plain,
( c_in(c_Pair(X2,X1,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X4,X3,X3),X3),tc_prod(X3,X3)) ),
c_0_1351,
[final] ).
cnf(c_0_1776,plain,
( c_Wellfounded_Owf(X4,X3)
| ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)),X3) ),
c_0_1352,
[final] ).
cnf(c_0_1777,plain,
( ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X3,X2,X2),X1,tc_prod(X2,X2)) ),
c_0_1353,
[final] ).
cnf(c_0_1778,plain,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X1,X2,X3,X4),X3,X4),X2,tc_prod(X3,X4))
| ~ c_in(X1,c_Relation_ODomain(X2,X3,X4),X3) ),
c_0_1354,
[final] ).
cnf(c_0_1779,plain,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X1,X2,X3,X4),X3,X4),X2,tc_prod(X3,X4))
| ~ c_in(X1,c_Relation_ODomain(X2,X3,X4),X3) ),
c_0_1355,
[final] ).
cnf(c_0_1780,plain,
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X1,X2,X4,X3),X1,X3,X4),X2,tc_prod(X3,X4))
| ~ c_in(X1,c_Relation_ORange(X2,X3,X4),X4) ),
c_0_1356,
[final] ).
cnf(c_0_1781,plain,
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X1,X2,X4,X3),X1,X3,X4),X2,tc_prod(X3,X4))
| ~ c_in(X1,c_Relation_ORange(X2,X3,X4),X4) ),
c_0_1357,
[final] ).
cnf(c_0_1782,plain,
( X1 = X2
| X4 = X2
| X5 = X2
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1358,
[final] ).
cnf(c_0_1783,plain,
( X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X4
| X1 = X4
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X2,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1359,
[final] ).
cnf(c_0_1784,plain,
( X1 = X2
| X5 = X1
| X4 = X1
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1360,
[final] ).
cnf(c_0_1785,plain,
( X1 = X2
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X2
| X1 = X4
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1361,
[final] ).
cnf(c_0_1786,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1362,
[final] ).
cnf(c_0_1787,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1363,
[final] ).
cnf(c_0_1788,plain,
( c_Finite__Set_Ofinite(X4,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,c_Product__Type_OSigma(X1,c_COMBK(X1,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_in(X4,c_Equiv__Relations_Oquotient(X1,X3,X2),tc_fun(X2,tc_bool)) ),
c_0_1364,
[final] ).
cnf(c_0_1789,plain,
( c_in(c_Pair(X3,X4,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X4,X3,X2,X2),X1,tc_prod(X2,X2)),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
c_0_1365,
[final] ).
cnf(c_0_1790,plain,
( c_in(X2,hAPP(X6,X1),X4)
| ~ c_in(c_Pair(X1,X2,X3,X4),c_Product__Type_OSigma(X5,X6,X3,X4),tc_prod(X3,X4)) ),
c_0_1366,
[final] ).
cnf(c_0_1791,plain,
( c_in(c_Pair(X2,X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X4,X3,X3),X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
c_0_1367,
[final] ).
cnf(c_0_1792,plain,
( X4 = X5
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(X4,c_Equiv__Relations_Oquotient(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_in(X5,c_Equiv__Relations_Oquotient(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_in(X6,X4,X3)
| ~ c_in(X7,X5,X3)
| ~ c_in(c_Pair(X6,X7,X3,X3),X2,tc_prod(X3,X3)) ),
c_0_1368,
[final] ).
cnf(c_0_1793,plain,
( X1 = X2
| X4 = X5
| X4 = X2
| X5 = X2
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1369,
[final] ).
cnf(c_0_1794,plain,
( X1 = X2
| X4 = X5
| X5 = X1
| X4 = X1
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1370,
[final] ).
cnf(c_0_1795,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X2
| X1 = X2
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1371,
[final] ).
cnf(c_0_1796,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| X1 = X2
| X1 = X4
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
c_0_1372,
[final] ).
cnf(c_0_1797,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| X1 = X2
| X2 = X1
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1373,
[final] ).
cnf(c_0_1798,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X2
| X1 = X2
| X2 = X4
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
c_0_1374,
[final] ).
cnf(c_0_1799,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1375,
[final] ).
cnf(c_0_1800,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X1
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1376,
[final] ).
cnf(c_0_1801,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1377,
[final] ).
cnf(c_0_1802,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X2,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X4
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1378,
[final] ).
cnf(c_0_1803,plain,
( c_in(X1,X5,X3)
| ~ c_in(c_Pair(X1,X2,X3,X4),c_Product__Type_OSigma(X5,X6,X3,X4),tc_prod(X3,X4)) ),
c_0_1379,
[final] ).
cnf(c_0_1804,plain,
( c_in(c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1(X2,X1,X3),X2,X3)
| c_Relation_Orefl__on(X2,X1,X3)
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
c_0_1380,
[final] ).
cnf(c_0_1805,plain,
( c_in(c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1(X2,X1,X3),X2,X3)
| c_Relation_Orefl__on(X2,X1,X3)
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
c_0_1381,
[final] ).
cnf(c_0_1806,plain,
( c_in(c_Pair(X2,X1,X4,X3),X5,tc_prod(X4,X3))
| ~ c_in(c_Pair(X1,X2,X3,X4),c_Relation_Oconverse(X5,X4,X3),tc_prod(X3,X4)) ),
c_0_1382,
[final] ).
cnf(c_0_1807,plain,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X1,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X1,X2),X2,X2),c_Transitive__Closure_Otrancl(X1,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X3,X3,X2,X2),X1,tc_prod(X2,X2)) ),
c_0_1383,
[final] ).
cnf(c_0_1808,plain,
( c_in(c_Pair(X2,X1,X4,X3),c_Relation_Oconverse(X5,X3,X4),tc_prod(X4,X3))
| ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)) ),
c_0_1384,
[final] ).
cnf(c_0_1809,plain,
( c_in(c_Pair(X2,X1,X4,X3),c_Relation_Oconverse(X5,X3,X4),tc_prod(X4,X3))
| ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)) ),
c_0_1385,
[final] ).
cnf(c_0_1810,plain,
( c_in(hAPP(X1,X6),X3,X4)
| ~ c_in(X1,c_FuncSet_OPi(X2,c_COMBK(X3,tc_fun(X4,tc_bool),X5),X5,X4),tc_fun(X5,X4))
| ~ c_in(X6,X2,X5) ),
c_0_1386,
[final] ).
cnf(c_0_1811,plain,
( X1 = X2
| c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
c_0_1387,
[final] ).
cnf(c_0_1812,plain,
( X1 = X2
| c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
c_0_1388,
[final] ).
cnf(c_0_1813,plain,
( X1 = X2
| c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
c_0_1389,
[final] ).
cnf(c_0_1814,plain,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
c_0_1390,
[final] ).
cnf(c_0_1815,plain,
( c_in(X4,c_Relation_OImage(X6,X2,X3,X5),X5)
| ~ c_in(X1,X2,X3)
| ~ c_in(c_Pair(X1,X4,X3,X5),X6,tc_prod(X3,X5)) ),
c_0_1391,
[final] ).
cnf(c_0_1816,plain,
( c_in(X4,c_Relation_OImage(X6,X2,X3,X5),X5)
| ~ c_in(X1,X2,X3)
| ~ c_in(c_Pair(X1,X4,X3,X5),X6,tc_prod(X3,X5)) ),
c_0_1392,
[final] ).
cnf(c_0_1817,plain,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)) ),
c_0_1393,
[final] ).
cnf(c_0_1818,plain,
( c_in(c_Pair(X4,X3,X2,X2),X1,tc_prod(X2,X2))
| ~ c_Relation_Osym(X1,X2)
| ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2)) ),
c_0_1394,
[final] ).
cnf(c_0_1819,plain,
( c_in(c_Pair(X4,X3,X2,X2),X1,tc_prod(X2,X2))
| ~ c_Relation_Osym(X1,X2)
| ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2)) ),
c_0_1395,
[final] ).
cnf(c_0_1820,plain,
( X2 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X3,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1396,
[final] ).
cnf(c_0_1821,plain,
( X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X3,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1397,
[final] ).
cnf(c_0_1822,plain,
( X1 = X2
| X1 = X3
| c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1398,
[final] ).
cnf(c_0_1823,plain,
( X1 = X2
| X3 = X2
| c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1399,
[final] ).
cnf(c_0_1824,plain,
( X1 = X2
| X3 = X1
| c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1400,
[final] ).
cnf(c_0_1825,plain,
( X1 = X2
| X3 = X2
| c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1401,
[final] ).
cnf(c_0_1826,plain,
( ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(X3,X4,X2)
| ~ c_in(c_Pair(X5,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(X5,X4,X2) ),
c_0_1402,
[final] ).
cnf(c_0_1827,plain,
( ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(X3,X4,X2)
| ~ c_in(c_Pair(X5,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(X5,X4,X2) ),
c_0_1403,
[final] ).
cnf(c_0_1828,plain,
( hBOOL(hAPP(X5,X4))
| hBOOL(hAPP(X5,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_Pair(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X5,X2,X3),X3,X3),X2,tc_prod(X3,X3)) ),
c_0_1404,
[final] ).
cnf(c_0_1829,plain,
( hBOOL(hAPP(X5,X4))
| hBOOL(hAPP(X5,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_Pair(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X5,X2,X3),X3,X3),X2,tc_prod(X3,X3)) ),
c_0_1405,
[final] ).
cnf(c_0_1830,plain,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X3)
| ~ c_in(X6,c_Equiv__Relations_Oquotient(X5,X4,X3),tc_fun(X3,tc_bool))
| ~ c_in(X6,c_Equiv__Relations_Oquotient(X5,X4,X3),tc_fun(X3,tc_bool))
| ~ c_in(X1,X6,X3)
| ~ c_in(X2,X6,X3) ),
c_0_1406,
[final] ).
cnf(c_0_1831,plain,
( X4 = X5
| c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3))
| c_in(c_Pair(X5,X4,X3,X3),X2,tc_prod(X3,X3))
| ~ c_Relation_Ototal__on(X1,X2,X3)
| ~ c_in(X4,X1,X3)
| ~ c_in(X5,X1,X3) ),
c_0_1407,
[final] ).
cnf(c_0_1832,plain,
( c_Relation_Orel__comp(c_Relation_Oconverse(X2,X3,X3),X2,X3,X3,X3) = X2
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
c_0_1408,
[final] ).
cnf(c_0_1833,plain,
( c_lessequals(c_Relation_OImage(X1,X5,X3,X4),c_Relation_OImage(X2,X6,X3,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool))
| ~ c_lessequals(X5,X6,tc_fun(X3,tc_bool)) ),
c_0_1409,
[final] ).
cnf(c_0_1834,plain,
( X1 = X2
| ~ c_in(X3,X4,X5)
| c_Product__Type_OSigma(X1,c_COMBK(X4,tc_fun(X5,tc_bool),X6),X6,X5) != c_Product__Type_OSigma(X2,c_COMBK(X4,tc_fun(X5,tc_bool),X6),X6,X5) ),
c_0_1410,
[final] ).
cnf(c_0_1835,plain,
( X2 = X3
| c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
c_0_1411,
[final] ).
cnf(c_0_1836,plain,
( c_in(c_Pair(X1,X4,X3,X6),c_Product__Type_OSigma(X2,X5,X3,X6),tc_prod(X3,X6))
| ~ c_in(X1,X2,X3)
| ~ c_in(X4,hAPP(X5,X1),X6) ),
c_0_1412,
[final] ).
cnf(c_0_1837,plain,
( c_in(c_Pair(X1,X4,X3,X6),c_Product__Type_OSigma(X2,X5,X3,X6),tc_prod(X3,X6))
| ~ c_in(X1,X2,X3)
| ~ c_in(X4,hAPP(X5,X1),X6) ),
c_0_1413,
[final] ).
cnf(c_0_1838,plain,
( X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1414,
[final] ).
cnf(c_0_1839,plain,
( X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1415,
[final] ).
cnf(c_0_1840,plain,
( c_in(X3,c_Wellfounded_Oacc(X2,t_a),t_a)
| hBOOL(hAPP(X4,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X4,X2),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
c_0_1416,
[final] ).
cnf(c_0_1841,plain,
( c_in(X3,c_Wellfounded_Oacc(X2,t_a),t_a)
| hBOOL(hAPP(X4,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X4,X2),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
c_0_1417,
[final] ).
cnf(c_0_1842,plain,
( c_lessequals(c_Set_Oimage(X4,X1,X3,X5),c_Set_Oimage(X4,X2,X3,X5),tc_fun(X5,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1418,
[final] ).
cnf(c_0_1843,plain,
( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool)) ),
c_0_1419,
[final] ).
cnf(c_0_1844,plain,
( c_in(X4,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_Pair(X4,X1,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3)) ),
c_0_1420,
[final] ).
cnf(c_0_1845,plain,
( c_in(X1,c_Wellfounded_Oacc(X4,X3),X3)
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(X2,c_Wellfounded_Oacc(X4,X3),X3) ),
c_0_1421,
[final] ).
cnf(c_0_1846,plain,
( hBOOL(hAPP(X4,X3))
| hBOOL(hAPP(X4,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X4,X2),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
c_0_1422,
[final] ).
cnf(c_0_1847,plain,
( hBOOL(hAPP(X4,X3))
| hBOOL(hAPP(X4,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X4,X2),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
c_0_1423,
[final] ).
cnf(c_0_1848,plain,
( c_in(X4,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_Pair(X4,X1,X3,X3),X2,tc_prod(X3,X3)) ),
c_0_1424,
[final] ).
cnf(c_0_1849,plain,
( c_in(X4,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_Pair(X4,X1,X3,X3),X2,tc_prod(X3,X3)) ),
c_0_1425,
[final] ).
cnf(c_0_1850,plain,
( c_in(X1,c_Relation_ODomain(X2,X3,X3),X3)
| X1 = X4
| ~ c_in(c_Pair(X1,X4,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3)) ),
c_0_1426,
[final] ).
cnf(c_0_1851,plain,
( c_in(hAPP(X1,X6),hAPP(X3,X6),X5)
| ~ c_in(X1,c_FuncSet_OPi(X2,X3,X4,X5),tc_fun(X4,X5))
| ~ c_in(X6,X2,X4) ),
c_0_1427,
[final] ).
cnf(c_0_1852,plain,
( c_in(hAPP(X1,X6),hAPP(X3,X6),X5)
| ~ c_in(X1,c_FuncSet_OPi(X2,X3,X4,X5),tc_fun(X4,X5))
| ~ c_in(X6,X2,X4) ),
c_0_1428,
[final] ).
cnf(c_0_1853,plain,
( c_Nitpick_Orefl_H(X1,X2)
| ~ c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X1,X2),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X1,X2),X2,X2),X1,tc_prod(X2,X2)) ),
c_0_1429,
[final] ).
cnf(c_0_1854,plain,
( c_in(hAPP(X1,X6),X5,X4)
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ c_in(X6,X2,X3) ),
c_0_1430,
[final] ).
cnf(c_0_1855,plain,
( c_in(X2,c_Relation_ORange(X5,X3,X4),X4)
| ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)) ),
c_0_1431,
[final] ).
cnf(c_0_1856,plain,
( c_in(X2,c_Relation_ORange(X5,X3,X4),X4)
| ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)) ),
c_0_1432,
[final] ).
cnf(c_0_1857,plain,
( c_in(X1,c_Relation_ODomain(X5,X3,X4),X3)
| ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)) ),
c_0_1433,
[final] ).
cnf(c_0_1858,plain,
( c_in(X1,c_Relation_ODomain(X5,X3,X4),X3)
| ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)) ),
c_0_1434,
[final] ).
cnf(c_0_1859,plain,
( v_thesis____
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
c_0_1435,
[final] ).
cnf(c_0_1860,plain,
( c_in(X5,X1,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
c_0_1436,
[final] ).
cnf(c_0_1861,plain,
( c_in(X4,X1,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
c_0_1437,
[final] ).
cnf(c_0_1862,plain,
( c_in(X5,X1,X3)
| ~ c_Relation_Orefl__on(X1,X2,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
c_0_1438,
[final] ).
cnf(c_0_1863,plain,
( c_in(X4,X1,X3)
| ~ c_Relation_Orefl__on(X1,X2,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
c_0_1439,
[final] ).
cnf(c_0_1864,plain,
( c_lessequals(X2,c_Product__Type_OSigma(X1,c_COMBK(X1,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
c_0_1440,
[final] ).
cnf(c_0_1865,plain,
( c_lessequals(X2,c_Product__Type_OSigma(X1,c_COMBK(X1,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Relation_Orefl__on(X1,X2,X3) ),
c_0_1441,
[final] ).
cnf(c_0_1866,plain,
( c_in(X1,X4,X3)
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId__on(X4,X3),tc_prod(X3,X3)) ),
c_0_1442,
[final] ).
cnf(c_0_1867,plain,
( X1 = X2
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId__on(X4,X3),tc_prod(X3,X3)) ),
c_0_1443,
[final] ).
cnf(c_0_1868,plain,
( c_Finite__Set_Ofinite(X3,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,c_Set_Oimage(X4,X1,X2,X5),tc_fun(X5,tc_bool)) ),
c_0_1444,
[final] ).
cnf(c_0_1869,plain,
( ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_Pair(X3,X3,X2,X2),X1,tc_prod(X2,X2)) ),
c_0_1445,
[final] ).
cnf(c_0_1870,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X3),c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3),X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_1446,
[final] ).
cnf(c_0_1871,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X4),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4),X4)
| ~ class_Lattices_Olattice(X4) ),
c_0_1447,
[final] ).
cnf(c_0_1872,plain,
( X1 = X2
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId(X3),tc_prod(X3,X3)) ),
c_0_1448,
[final] ).
cnf(c_0_1873,plain,
( c_Set_Oinsert(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5) = c_Set_Oimage(X4,X2,X3,X5)
| ~ c_in(X1,X2,X3) ),
c_0_1449,
[final] ).
cnf(c_0_1874,plain,
( c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X1,X2,X3),X2,X3,X3),X1,tc_prod(X3,X3))
| c_in(X2,c_Wellfounded_Oacc(X1,X3),X3) ),
c_0_1450,
[final] ).
cnf(c_0_1875,plain,
( c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X2,X1,X3),X1,X3,X3),X2,tc_prod(X3,X3)) ),
c_0_1451,
[final] ).
cnf(c_0_1876,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X1 = X2
| X2 = X1
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
c_0_1452,
[final] ).
cnf(c_0_1877,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X1 = X2
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
c_0_1453,
[final] ).
cnf(c_0_1878,plain,
( c_in(c_List_Osko__Equiv__Relations__XquotientE__1__1(X2,X1,X3,X4),X2,X4)
| ~ c_in(X1,c_Equiv__Relations_Oquotient(X2,X3,X4),tc_fun(X4,tc_bool)) ),
c_0_1454,
[final] ).
cnf(c_0_1879,plain,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
c_0_1455,
[final] ).
cnf(c_0_1880,plain,
( c_in(X1,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3),tc_prod(X3,X3))
| ~ c_in(X1,c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3)) ),
c_0_1456,
[final] ).
cnf(c_0_1881,plain,
( c_in(X1,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(tc_prod(X3,X3),tc_bool)),X3),tc_prod(X3,X3))
| ~ c_in(X1,c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3)) ),
c_0_1457,
[final] ).
cnf(c_0_1882,plain,
( X1 = X2
| c_Pair(X3,X1,X4,X5) != c_Pair(X6,X2,X4,X5) ),
c_0_1458,
[final] ).
cnf(c_0_1883,plain,
( X1 = X2
| c_Pair(X1,X3,X4,X5) != c_Pair(X2,X6,X4,X5) ),
c_0_1459,
[final] ).
cnf(c_0_1884,plain,
( c_in(c_Pair(X1,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| c_in(X1,c_Relation_ODomain(X3,X2,X2),X2) ),
c_0_1460,
[final] ).
cnf(c_0_1885,plain,
( c_in(c_Pair(X4,X4,X3,X3),X2,tc_prod(X3,X3))
| ~ c_Relation_Orefl__on(X1,X2,X3)
| ~ c_in(X4,X1,X3) ),
c_0_1461,
[final] ).
cnf(c_0_1886,plain,
( c_in(c_Pair(X4,X4,X3,X3),X2,tc_prod(X3,X3))
| ~ c_Relation_Orefl__on(X1,X2,X3)
| ~ c_in(X4,X1,X3) ),
c_0_1462,
[final] ).
cnf(c_0_1887,plain,
( c_in(c_Pair(X1,X1,X3,X3),c_Relation_OId__on(X2,X3),tc_prod(X3,X3))
| ~ c_in(X1,X2,X3) ),
c_0_1463,
[final] ).
cnf(c_0_1888,plain,
( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
| ~ c_in(X2,X3,X4) ),
c_0_1464,
[final] ).
cnf(c_0_1889,plain,
( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
| ~ c_in(X2,X3,X4) ),
c_0_1465,
[final] ).
cnf(c_0_1890,plain,
( c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
| ~ c_in(X1,X2,X3) ),
c_0_1466,
[final] ).
cnf(c_0_1891,plain,
( c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
| ~ c_in(X1,X2,X3) ),
c_0_1467,
[final] ).
cnf(c_0_1892,plain,
( c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Relation_Orefl__on(X1,X2,X3)
| ~ c_Relation_Orefl__on(X4,X5,X3) ),
c_0_1468,
[final] ).
cnf(c_0_1893,plain,
( c_Relation_Orefl__on(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Relation_Orefl__on(X1,X2,X3)
| ~ c_Relation_Orefl__on(X4,X5,X3) ),
c_0_1469,
[final] ).
cnf(c_0_1894,plain,
( c_Pair(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X2,X1,X3),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X2,X1,X3),X3,X3) = X1
| ~ c_in(X1,c_Relation_OId__on(X2,X3),tc_prod(X3,X3)) ),
c_0_1470,
[final] ).
cnf(c_0_1895,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
c_0_1471,
[final] ).
cnf(c_0_1896,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
c_0_1472,
[final] ).
cnf(c_0_1897,plain,
( c_in(c_Pair(X3,X3,X2,X2),X1,tc_prod(X2,X2))
| ~ c_Nitpick_Orefl_H(X1,X2) ),
c_0_1473,
[final] ).
cnf(c_0_1898,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X3,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X1
| X1 = X2 ),
c_0_1474,
[final] ).
cnf(c_0_1899,plain,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X3,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X1 = X2 ),
c_0_1475,
[final] ).
cnf(c_0_1900,plain,
( X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1476,
[final] ).
cnf(c_0_1901,plain,
( hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
c_0_1477,
[final] ).
cnf(c_0_1902,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1478,
[final] ).
cnf(c_0_1903,plain,
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
c_0_1479,
[final] ).
cnf(c_0_1904,plain,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
c_0_1480,
[final] ).
cnf(c_0_1905,plain,
( hBOOL(hAPP(X4,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X4,X2,X3))) ),
c_0_1481,
[final] ).
cnf(c_0_1906,plain,
( hBOOL(hAPP(X4,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X4,X2,X3))) ),
c_0_1482,
[final] ).
cnf(c_0_1907,plain,
( c_Relation_Otrans(c_Relation_Oinv__image(X1,X3,X2,X4),X4)
| ~ c_Relation_Otrans(X1,X2) ),
c_0_1483,
[final] ).
cnf(c_0_1908,plain,
( c_Finite__Set_Ofinite(c_Set_Oimage(X3,X1,X2,X4),X4)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_1484,
[final] ).
cnf(c_0_1909,plain,
( c_Wellfounded_Owf(c_Relation_Oinv__image(X1,X3,X2,X4),X4)
| ~ c_Wellfounded_Owf(X1,X2) ),
c_0_1485,
[final] ).
cnf(c_0_1910,plain,
( c_Relation_Osym(c_Relation_Oinv__image(X1,X3,X2,X4),X4)
| ~ c_Relation_Osym(X1,X2) ),
c_0_1486,
[final] ).
cnf(c_0_1911,plain,
( c_lessequals(c_Relation_ODomain(X1,X3,X4),c_Relation_ODomain(X2,X3,X4),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)) ),
c_0_1487,
[final] ).
cnf(c_0_1912,plain,
( c_in(X1,c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(X1,c_Transitive__Closure_Otrancl(X2,X3),tc_prod(X3,X3))
| ~ c_lessequals(X2,X4,tc_fun(tc_prod(X3,X3),tc_bool)) ),
c_0_1488,
[final] ).
cnf(c_0_1913,plain,
( c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),X3) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,X3) ),
c_0_1489,
[final] ).
cnf(c_0_1914,plain,
( c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,X3) ),
c_0_1490,
[final] ).
cnf(c_0_1915,plain,
( c_Transitive__Closure_Ortrancl(X2,X3) = c_Transitive__Closure_Ortrancl(X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(X2,c_Transitive__Closure_Ortrancl(X1,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
c_0_1491,
[final] ).
cnf(c_0_1916,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
c_0_1492,
[final] ).
cnf(c_0_1917,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
c_0_1493,
[final] ).
cnf(c_0_1918,plain,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
c_0_1494,
[final] ).
cnf(c_0_1919,plain,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
c_0_1495,
[final] ).
cnf(c_0_1920,plain,
( c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Relation_Oconverse(X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
c_0_1496,
[final] ).
cnf(c_0_1921,plain,
( c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
c_0_1497,
[final] ).
cnf(c_0_1922,plain,
( c_lessequals(X1,X2,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
c_0_1498,
[final] ).
cnf(c_0_1923,plain,
( c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) ),
c_0_1499,
[final] ).
cnf(c_0_1924,plain,
( c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) ),
c_0_1500,
[final] ).
cnf(c_0_1925,plain,
( c_Pair(c_ATP__Linkup_Osko__Relation__XIdE__1__1(X1,X2),c_ATP__Linkup_Osko__Relation__XIdE__1__1(X1,X2),X2,X2) = X1
| ~ c_in(X1,c_Relation_OId(X2),tc_prod(X2,X2)) ),
c_0_1501,
[final] ).
cnf(c_0_1926,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Odistrib__lattice(X3) ),
c_0_1502,
[final] ).
cnf(c_0_1927,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X4),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4)
| ~ class_Lattices_Odistrib__lattice(X4) ),
c_0_1503,
[final] ).
cnf(c_0_1928,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3)
| ~ class_Lattices_Odistrib__lattice(X3) ),
c_0_1504,
[final] ).
cnf(c_0_1929,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X4),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Odistrib__lattice(X4) ),
c_0_1505,
[final] ).
cnf(c_0_1930,plain,
( c_in(X1,X2,X4)
| c_in(X1,X3,X4)
| ~ c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4) ),
c_0_1506,
[final] ).
cnf(c_0_1931,plain,
( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X3,X2)) ),
c_0_1507,
[final] ).
cnf(c_0_1932,plain,
( c_lessequals(c_Transitive__Closure_Ortrancl(X1,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(X1,c_Transitive__Closure_Ortrancl(X2,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
c_0_1508,
[final] ).
cnf(c_0_1933,plain,
( c_in(X2,X1,X4)
| c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) ),
c_0_1509,
[final] ).
cnf(c_0_1934,plain,
( c_in(X1,X2,X3)
| c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) ),
c_0_1510,
[final] ).
cnf(c_0_1935,plain,
( X1 = X4
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
c_0_1511,
[final] ).
cnf(c_0_1936,plain,
( c_lessequals(c_Set_Oinsert(X4,X1,X3),c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1512,
[final] ).
cnf(c_0_1937,plain,
( X1 = X2
| c_in(c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
c_0_1513,
[final] ).
cnf(c_0_1938,plain,
( X1 = X2
| c_in(c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
c_0_1514,
[final] ).
cnf(c_0_1939,plain,
( c_in(c_Relation_Oconverse(X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
c_0_1515,
[final] ).
cnf(c_0_1940,plain,
( c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
c_0_1516,
[final] ).
cnf(c_0_1941,plain,
( c_lessequals(c_Transitive__Closure_Ortrancl(X1,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)) ),
c_0_1517,
[final] ).
cnf(c_0_1942,plain,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_1518,
[final] ).
cnf(c_0_1943,plain,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_1519,
[final] ).
cnf(c_0_1944,plain,
( c_in(c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X1,X2,X3),X2,tc_fun(X3,tc_bool))
| ~ c_in(X1,c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X3,tc_bool)),X3) ),
c_0_1520,
[final] ).
cnf(c_0_1945,plain,
( c_in(X1,X3,X4)
| ~ c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4) ),
c_0_1521,
[final] ).
cnf(c_0_1946,plain,
( c_in(X1,X2,X4)
| ~ c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4) ),
c_0_1522,
[final] ).
cnf(c_0_1947,plain,
( c_in(X1,c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X1,X2,X3),X3) ),
c_0_1523,
[final] ).
cnf(c_0_1948,plain,
( c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3)
| ~ c_in(X1,X4,X3) ),
c_0_1524,
[final] ).
cnf(c_0_1949,plain,
( c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3)
| ~ c_in(X1,X4,X3) ),
c_0_1525,
[final] ).
cnf(c_0_1950,plain,
( c_in(X1,X4,X3)
| ~ c_in(X1,c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X4,X2,tc_fun(X3,tc_bool)) ),
c_0_1526,
[final] ).
cnf(c_0_1951,plain,
( c_in(X2,c_Wellfounded_Oacc(X1,X3),X3)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X1,X2,X3),c_Wellfounded_Oacc(X1,X3),X3) ),
c_0_1527,
[final] ).
cnf(c_0_1952,plain,
( c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X2,X1,X3),c_Wellfounded_Oacc(X2,X3),X3) ),
c_0_1528,
[final] ).
cnf(c_0_1953,plain,
( c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
c_0_1529,
[final] ).
cnf(c_0_1954,plain,
( c_Wellfounded_Owf(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X1,X2),X2,X2),X2)
| ~ c_Wellfounded_Owf(c_Relation_Oconverse(X1,X2,X2),X2) ),
c_0_1530,
[final] ).
cnf(c_0_1955,plain,
( c_in(X1,X2,X3)
| c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
c_0_1531,
[final] ).
cnf(c_0_1956,plain,
( c_in(X1,X2,X3)
| c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
c_0_1532,
[final] ).
cnf(c_0_1957,plain,
( c_in(X1,c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X1,X2,X3),X3)
| ~ c_in(X1,c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X3,tc_bool)),X3) ),
c_0_1533,
[final] ).
cnf(c_0_1958,plain,
( c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X4,X2,X3),c_Wellfounded_Oacc(X2,X3),X3)
| hBOOL(hAPP(X4,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3) ),
c_0_1534,
[final] ).
cnf(c_0_1959,plain,
( c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X4,X2,X3),c_Wellfounded_Oacc(X2,X3),X3)
| hBOOL(hAPP(X4,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3) ),
c_0_1535,
[final] ).
cnf(c_0_1960,plain,
( c_in(X1,X4,X3)
| ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
c_0_1536,
[final] ).
cnf(c_0_1961,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1537,
[final] ).
cnf(c_0_1962,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1538,
[final] ).
cnf(c_0_1963,plain,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1539,
[final] ).
cnf(c_0_1964,plain,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_1540,
[final] ).
cnf(c_0_1965,plain,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_1541,
[final] ).
cnf(c_0_1966,plain,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_1542,
[final] ).
cnf(c_0_1967,plain,
( c_in(X4,c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
c_0_1543,
[final] ).
cnf(c_0_1968,plain,
( c_lessequals(c_Relation_OField(X1,X3),c_Relation_OField(X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)) ),
c_0_1544,
[final] ).
cnf(c_0_1969,plain,
( c_lessequals(c_Wellfounded_Oacc(X2,X3),c_Wellfounded_Oacc(X1,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)) ),
c_0_1545,
[final] ).
cnf(c_0_1970,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1546,
[final] ).
cnf(c_0_1971,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4)
| ~ class_Lattices_Oupper__semilattice(X4) ),
c_0_1547,
[final] ).
cnf(c_0_1972,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4)
| ~ class_Lattices_Olattice(X4) ),
c_0_1548,
[final] ).
cnf(c_0_1973,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_1549,
[final] ).
cnf(c_0_1974,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_1550,
[final] ).
cnf(c_0_1975,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4)
| ~ class_Lattices_Olattice(X4) ),
c_0_1551,
[final] ).
cnf(c_0_1976,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
c_0_1552,
[final] ).
cnf(c_0_1977,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_1553,
[final] ).
cnf(c_0_1978,plain,
( c_in(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X2,X1,X3),X2,X3)
| ~ c_in(X1,c_Relation_OId__on(X2,X3),tc_prod(X3,X3)) ),
c_0_1554,
[final] ).
cnf(c_0_1979,plain,
( c_in(c_Arrow__Order__Mirabelle_Omktop(X1,X2),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
c_0_1555,
[final] ).
cnf(c_0_1980,plain,
( c_in(c_Arrow__Order__Mirabelle_Omkbot(X1,X2),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
c_0_1556,
[final] ).
cnf(c_0_1981,plain,
( c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
c_0_1557,
[final] ).
cnf(c_0_1982,plain,
( c_in(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)) ),
c_0_1558,
[final] ).
cnf(c_0_1983,plain,
( c_in(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)) ),
c_0_1559,
[final] ).
cnf(c_0_1984,plain,
( c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Osym(X1,X2)
| ~ c_Relation_Osym(X3,X2) ),
c_0_1560,
[final] ).
cnf(c_0_1985,plain,
( c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Osym(X1,X2)
| ~ c_Relation_Osym(X3,X2) ),
c_0_1561,
[final] ).
cnf(c_0_1986,plain,
( c_Relation_Otrans(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Otrans(X1,X2)
| ~ c_Relation_Otrans(X3,X2) ),
c_0_1562,
[final] ).
cnf(c_0_1987,plain,
( c_lessequals(X1,X2,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
c_0_1563,
[final] ).
cnf(c_0_1988,plain,
( c_lessequals(X1,X3,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
c_0_1564,
[final] ).
cnf(c_0_1989,plain,
( c_lessequals(X1,X2,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
c_0_1565,
[final] ).
cnf(c_0_1990,plain,
( c_lessequals(X1,X3,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
c_0_1566,
[final] ).
cnf(c_0_1991,plain,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1567,
[final] ).
cnf(c_0_1992,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1568,
[final] ).
cnf(c_0_1993,plain,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1569,
[final] ).
cnf(c_0_1994,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1570,
[final] ).
cnf(c_0_1995,plain,
( X1 = X2
| c_in(X1,X3,X4)
| ~ c_in(X1,c_Set_Oinsert(X2,X3,X4),X4) ),
c_0_1571,
[final] ).
cnf(c_0_1996,plain,
( c_in(c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X1,X2,X3),X2,tc_fun(X3,tc_bool))
| c_in(X1,c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X3,tc_bool)),X3) ),
c_0_1572,
[final] ).
cnf(c_0_1997,plain,
( c_Relation_Orefl__on(X1,X2,X3)
| ~ c_Relation_Orefl__on(X1,c_Relation_Oconverse(X2,X3,X3),X3) ),
c_0_1573,
[final] ).
cnf(c_0_1998,plain,
( c_Relation_Ototal__on(X1,X2,X3)
| ~ c_Relation_Ototal__on(X1,c_Relation_Oconverse(X2,X3,X3),X3) ),
c_0_1574,
[final] ).
cnf(c_0_1999,plain,
( c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1575,
[final] ).
cnf(c_0_2000,plain,
( c_Relation_Otrans(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Otrans(X1,X2) ),
c_0_1576,
[final] ).
cnf(c_0_2001,plain,
( c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3) ),
c_0_1577,
[final] ).
cnf(c_0_2002,plain,
( c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3) ),
c_0_1578,
[final] ).
cnf(c_0_2003,plain,
( c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
c_0_1579,
[final] ).
cnf(c_0_2004,plain,
( c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
c_0_1580,
[final] ).
cnf(c_0_2005,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_1581,
[final] ).
cnf(c_0_2006,plain,
( X1 = X2
| c_in(X3,X1,X4)
| c_in(X3,X2,X4)
| c_Set_Oinsert(X3,X1,X4) != c_Set_Oinsert(X3,X2,X4) ),
c_0_1582,
[final] ).
cnf(c_0_2007,plain,
( hBOOL(hAPP(X3,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ hBOOL(hAPP(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X3,X2))) ),
c_0_1583,
[final] ).
cnf(c_0_2008,plain,
( hBOOL(hAPP(X3,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ hBOOL(hAPP(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X3,X2))) ),
c_0_1584,
[final] ).
cnf(c_0_2009,plain,
( c_Finite__Set_Ofinite(X1,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3) ),
c_0_1585,
[final] ).
cnf(c_0_2010,plain,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3) ),
c_0_1586,
[final] ).
cnf(c_0_2011,plain,
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1587,
[final] ).
cnf(c_0_2012,plain,
( c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1588,
[final] ).
cnf(c_0_2013,plain,
( c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X4,X1,X2),X4,X2)
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(X3,X4,X2) ),
c_0_1589,
[final] ).
cnf(c_0_2014,plain,
( c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X4,X1,X2),X4,X2)
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(X3,X4,X2) ),
c_0_1590,
[final] ).
cnf(c_0_2015,plain,
( c_in(X4,X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
c_0_1591,
[final] ).
cnf(c_0_2016,plain,
( c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
c_0_1592,
[final] ).
cnf(c_0_2017,plain,
( c_in(X4,X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
c_0_1593,
[final] ).
cnf(c_0_2018,plain,
( c_in(X4,X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
c_0_1594,
[final] ).
cnf(c_0_2019,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_1595,
[final] ).
cnf(c_0_2020,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X1,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_1596,
[final] ).
cnf(c_0_2021,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1597,
[final] ).
cnf(c_0_2022,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1598,
[final] ).
cnf(c_0_2023,plain,
( c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
c_0_1599,
[final] ).
cnf(c_0_2024,plain,
( c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
c_0_1600,
[final] ).
cnf(c_0_2025,plain,
( c_Relation_Orefl__on(X1,c_Relation_Oconverse(X2,X3,X3),X3)
| ~ c_Relation_Orefl__on(X1,X2,X3) ),
c_0_1601,
[final] ).
cnf(c_0_2026,plain,
( c_Relation_Ototal__on(X1,c_Relation_Oconverse(X2,X3,X3),X3)
| ~ c_Relation_Ototal__on(X1,X2,X3) ),
c_0_1602,
[final] ).
cnf(c_0_2027,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
c_0_1603,
[final] ).
cnf(c_0_2028,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
c_0_1604,
[final] ).
cnf(c_0_2029,plain,
( c_Wellfounded_Owf(X3,X2)
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_lessequals(X3,X1,tc_fun(tc_prod(X2,X2),tc_bool)) ),
c_0_1605,
[final] ).
cnf(c_0_2030,plain,
( c_lessequals(hAPP(X1,X5),hAPP(X2,X5),X4)
| ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
c_0_1606,
[final] ).
cnf(c_0_2031,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_1607,
[final] ).
cnf(c_0_2032,plain,
( c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1608,
[final] ).
cnf(c_0_2033,plain,
( c_in(X1,c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
| ~ c_in(X1,X2,tc_prod(X3,X3)) ),
c_0_1609,
[final] ).
cnf(c_0_2034,plain,
( c_in(X1,c_Transitive__Closure_Otrancl(X2,X3),tc_prod(X3,X3))
| ~ c_in(X1,X2,tc_prod(X3,X3)) ),
c_0_1610,
[final] ).
cnf(c_0_2035,plain,
( c_Finite__Set_Ofinite(c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X3) ),
c_0_1611,
[final] ).
cnf(c_0_2036,plain,
( c_Complete__Lattice_OSup__class_OSup(c_Equiv__Relations_Oquotient(X1,X2,X3),tc_fun(X3,tc_bool)) = X1
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
c_0_1612,
[final] ).
cnf(c_0_2037,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1613,
[final] ).
cnf(c_0_2038,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_1614,
[final] ).
cnf(c_0_2039,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_1615,
[final] ).
cnf(c_0_2040,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_1616,
[final] ).
cnf(c_0_2041,plain,
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
c_0_1617,
[final] ).
cnf(c_0_2042,plain,
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
c_0_1618,
[final] ).
cnf(c_0_2043,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Complete__Lattice_OInf__class_OInf(X2,X3),X3) = c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X1,X2,X3),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
c_0_1619,
[final] ).
cnf(c_0_2044,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Complete__Lattice_OSup__class_OSup(X2,X3),X3) = c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X1,X2,X3),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
c_0_1620,
[final] ).
cnf(c_0_2045,plain,
( c_Relation_Otrans(X1,X2)
| ~ c_Relation_Otrans(c_Relation_Oconverse(X1,X2,X2),X2) ),
c_0_1621,
[final] ).
cnf(c_0_2046,plain,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X2,X3),X3) ),
c_0_1622,
[final] ).
cnf(c_0_2047,plain,
( c_Relation_Osym(X1,X2)
| ~ c_Relation_Osym(c_Relation_Oconverse(X1,X2,X2),X2) ),
c_0_1623,
[final] ).
cnf(c_0_2048,plain,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != X2 ),
c_0_1624,
[final] ).
cnf(c_0_2049,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1625,
[final] ).
cnf(c_0_2050,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1626,
[final] ).
cnf(c_0_2051,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1627,
[final] ).
cnf(c_0_2052,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_1628,
[final] ).
cnf(c_0_2053,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
c_0_1629,
[final] ).
cnf(c_0_2054,plain,
( hBOOL(hAPP(X2,X4))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X1,X4)) ),
c_0_1630,
[final] ).
cnf(c_0_2055,plain,
( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_1631,
[final] ).
cnf(c_0_2056,plain,
( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_1632,
[final] ).
cnf(c_0_2057,plain,
( c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X1,X2),c_Wellfounded_Oacc(X1,X2),X2) ),
c_0_1633,
[final] ).
cnf(c_0_2058,plain,
( c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X1,X2),c_Wellfounded_Oacc(X1,X2),X2) ),
c_0_1634,
[final] ).
cnf(c_0_2059,plain,
( X2 = X1
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1635,
[final] ).
cnf(c_0_2060,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1636,
[final] ).
cnf(c_0_2061,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_1637,
[final] ).
cnf(c_0_2062,plain,
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X2,X3),X1,X3)
| ~ c_in(X1,X2,X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
c_0_1638,
[final] ).
cnf(c_0_2063,plain,
( c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X2,X3),X3)
| ~ c_in(X1,X2,X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
c_0_1639,
[final] ).
cnf(c_0_2064,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) = X1
| ~ class_Lattices_Olattice(X3) ),
c_0_1640,
[final] ).
cnf(c_0_2065,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = X1
| ~ class_Lattices_Olattice(X3) ),
c_0_1641,
[final] ).
cnf(c_0_2066,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1642,
[final] ).
cnf(c_0_2067,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1643,
[final] ).
cnf(c_0_2068,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_1644,
[final] ).
cnf(c_0_2069,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_1645,
[final] ).
cnf(c_0_2070,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X1,X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_1646,
[final] ).
cnf(c_0_2071,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X2,X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_1647,
[final] ).
cnf(c_0_2072,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_1648,
[final] ).
cnf(c_0_2073,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X1,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_1649,
[final] ).
cnf(c_0_2074,plain,
( c_Finite__Set_Ofinite(X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3) ),
c_0_1650,
[final] ).
cnf(c_0_2075,plain,
( c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool)) ),
c_0_1651,
[final] ).
cnf(c_0_2076,plain,
( c_lessequals(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) != X1
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_1652,
[final] ).
cnf(c_0_2077,plain,
( c_lessequals(X1,X2,X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) != X2
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1653,
[final] ).
cnf(c_0_2078,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_1654,
[final] ).
cnf(c_0_2079,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3) = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_1655,
[final] ).
cnf(c_0_2080,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1656,
[final] ).
cnf(c_0_2081,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1657,
[final] ).
cnf(c_0_2082,plain,
( X1 = X2
| c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X1,X2),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
c_0_1658,
[final] ).
cnf(c_0_2083,plain,
( c_Relation_Otrans(c_Relation_Oconverse(X1,X2,X2),X2)
| ~ c_Relation_Otrans(X1,X2) ),
c_0_1659,
[final] ).
cnf(c_0_2084,plain,
( c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X1,X2),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
c_0_1660,
[final] ).
cnf(c_0_2085,plain,
( c_Relation_Osym(c_Relation_Oconverse(X1,X2,X2),X2)
| ~ c_Relation_Osym(X1,X2) ),
c_0_1661,
[final] ).
cnf(c_0_2086,plain,
( c_Set_Oinsert(X1,X2,X3) = X2
| ~ c_in(X1,X2,X3) ),
c_0_1662,
[final] ).
cnf(c_0_2087,plain,
( c_Relation_Orefl__on(X1,X2,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
c_0_1663,
[final] ).
cnf(c_0_2088,plain,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_1664,
[final] ).
cnf(c_0_2089,plain,
( hBOOL(hAPP(X2,X1))
| ~ c_in(X1,X2,X3) ),
c_0_1665,
[final] ).
cnf(c_0_2090,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_1666,
[final] ).
cnf(c_0_2091,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_1667,
[final] ).
cnf(c_0_2092,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_1668,
[final] ).
cnf(c_0_2093,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_1669,
[final] ).
cnf(c_0_2094,plain,
( c_in(X3,c_Wellfounded_Oacc(X1,X2),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
c_0_1670,
[final] ).
cnf(c_0_2095,plain,
( c_in(X2,X1,X3)
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_1671,
[final] ).
cnf(c_0_2096,plain,
( c_Relation_Osym(X1,X2)
| c_Relation_Oconverse(X1,X2,X2) != X1 ),
c_0_1672,
[final] ).
cnf(c_0_2097,plain,
( c_Relation_Otrans(X2,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
c_0_1673,
[final] ).
cnf(c_0_2098,plain,
( c_Relation_Osym(X2,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
c_0_1674,
[final] ).
cnf(c_0_2099,plain,
( X1 = X2
| ~ c_fequal(X1,X2,X3) ),
c_0_1675,
[final] ).
cnf(c_0_2100,plain,
( c_Relation_Oconverse(X1,X2,X2) = X1
| ~ c_Relation_Osym(X1,X2) ),
c_0_1676,
[final] ).
cnf(c_0_2101,plain,
( c_Relation_Osym(c_Transitive__Closure_Ortrancl(X1,X2),X2)
| ~ c_Relation_Osym(X1,X2) ),
c_0_1677,
[final] ).
cnf(c_0_2102,plain,
( c_Relation_Osym(c_Transitive__Closure_Otrancl(X1,X2),X2)
| ~ c_Relation_Osym(X1,X2) ),
c_0_1678,
[final] ).
cnf(c_0_2103,plain,
( c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X1,X2),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
c_0_1679,
[final] ).
cnf(c_0_2104,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X2) = X1
| ~ class_Lattices_Oupper__semilattice(X2) ),
c_0_1680,
[final] ).
cnf(c_0_2105,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X1,X2) = X1
| ~ class_Lattices_Olower__semilattice(X2) ),
c_0_1681,
[final] ).
cnf(c_0_2106,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
c_0_1682,
[final] ).
cnf(c_0_2107,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
c_0_1683,
[final] ).
cnf(c_0_2108,plain,
( class_Finite__Set_Ofinite_Ofinite(tc_prod(X1,X2))
| ~ class_Finite__Set_Ofinite_Ofinite(X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
c_0_1684,
[final] ).
cnf(c_0_2109,plain,
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2))
| ~ class_Finite__Set_Ofinite_Ofinite(X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
c_0_1685,
[final] ).
cnf(c_0_2110,plain,
( c_Transitive__Closure_Otrancl(X1,X2) = X1
| ~ c_Relation_Otrans(X1,X2) ),
c_0_1686,
[final] ).
cnf(c_0_2111,plain,
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
c_0_1687,
[final] ).
cnf(c_0_2112,plain,
( class_Lattices_Oupper__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
c_0_1688,
[final] ).
cnf(c_0_2113,plain,
( class_Lattices_Olower__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
c_0_1689,
[final] ).
cnf(c_0_2114,plain,
( class_Lattices_Odistrib__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
c_0_1690,
[final] ).
cnf(c_0_2115,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
c_0_1691,
[final] ).
cnf(c_0_2116,plain,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
c_0_1692,
[final] ).
cnf(c_0_2117,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
c_0_1693,
[final] ).
cnf(c_0_2118,plain,
( class_HOL_Oord(tc_fun(X2,X1))
| ~ class_HOL_Oord(X1) ),
c_0_1694,
[final] ).
cnf(c_0_2119,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
c_0_1695,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_1696_0,axiom,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X1,X2,X5,X6,X3,X4,X7),X3,X7),X5,tc_prod(X3,X7))
| ~ c_in(c_Pair(X1,X2,X3,X4),c_Relation_Orel__comp(X5,X6,X3,X7,X4),tc_prod(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1696]) ).
cnf(c_0_1696_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X4),c_Relation_Orel__comp(X5,X6,X3,X7,X4),tc_prod(X3,X4))
| c_in(c_Pair(X1,c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X1,X2,X5,X6,X3,X4,X7),X3,X7),X5,tc_prod(X3,X7)) ),
inference(literals_permutation,[status(thm)],[c_0_1696]) ).
cnf(c_0_1697_0,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X1,X2,X5,X6,X3,X4,X7),X2,X7,X4),X6,tc_prod(X7,X4))
| ~ c_in(c_Pair(X1,X2,X3,X4),c_Relation_Orel__comp(X5,X6,X3,X7,X4),tc_prod(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1697]) ).
cnf(c_0_1697_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X4),c_Relation_Orel__comp(X5,X6,X3,X7,X4),tc_prod(X3,X4))
| c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X1,X2,X5,X6,X3,X4,X7),X2,X7,X4),X6,tc_prod(X7,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1697]) ).
cnf(c_0_1698_0,axiom,
( c_Recdef_Ocut(X1,X2,X3,X4,X5) = c_Recdef_Ocut(X6,X2,X3,X4,X5)
| hAPP(X1,c_List_Osko__Recdef__Xcuts__eq__1__1(X1,X6,X2,X3,X4,X5)) != hAPP(X6,c_List_Osko__Recdef__Xcuts__eq__1__1(X1,X6,X2,X3,X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1698]) ).
cnf(c_0_1698_1,axiom,
( hAPP(X1,c_List_Osko__Recdef__Xcuts__eq__1__1(X1,X6,X2,X3,X4,X5)) != hAPP(X6,c_List_Osko__Recdef__Xcuts__eq__1__1(X1,X6,X2,X3,X4,X5))
| c_Recdef_Ocut(X1,X2,X3,X4,X5) = c_Recdef_Ocut(X6,X2,X3,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1698]) ).
cnf(c_0_1699_0,axiom,
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,X1,X2,X2,X2),c_Relation_Orel__comp(X3,X1,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1699]) ).
cnf(c_0_1699_1,axiom,
( ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,X1,X2,X2,X2),c_Relation_Orel__comp(X3,X1,X2,X2,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1699]) ).
cnf(c_0_1700_0,axiom,
( c_in(c_Pair(c_List_Osko__Recdef__Xcuts__eq__1__1(X1,X2,X3,X4,X5,X6),X4,X5,X5),X3,tc_prod(X5,X5))
| c_Recdef_Ocut(X1,X3,X4,X5,X6) = c_Recdef_Ocut(X2,X3,X4,X5,X6) ),
inference(literals_permutation,[status(thm)],[c_0_1700]) ).
cnf(c_0_1700_1,axiom,
( c_Recdef_Ocut(X1,X3,X4,X5,X6) = c_Recdef_Ocut(X2,X3,X4,X5,X6)
| c_in(c_Pair(c_List_Osko__Recdef__Xcuts__eq__1__1(X1,X2,X3,X4,X5,X6),X4,X5,X5),X3,tc_prod(X5,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1700]) ).
cnf(c_0_1701_0,axiom,
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,X1,X3,X3,X3),c_Relation_Orel__comp(X2,X1,X3,X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)),X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1701]) ).
cnf(c_0_1701_1,axiom,
( ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,X1,X3,X3,X3),c_Relation_Orel__comp(X2,X1,X3,X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)),X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1701]) ).
cnf(c_0_1702_0,axiom,
( c_lessequals(c_Product__Type_OSigma(X1,X4,X3,X6),c_Product__Type_OSigma(X2,X5,X3,X6),tc_fun(tc_prod(X3,X6),tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(hAPP(X4,c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(X1,X4,X5,X3,X6)),hAPP(X5,c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(X1,X4,X5,X3,X6)),tc_fun(X6,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1702]) ).
cnf(c_0_1702_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Product__Type_OSigma(X1,X4,X3,X6),c_Product__Type_OSigma(X2,X5,X3,X6),tc_fun(tc_prod(X3,X6),tc_bool))
| ~ c_lessequals(hAPP(X4,c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(X1,X4,X5,X3,X6)),hAPP(X5,c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(X1,X4,X5,X3,X6)),tc_fun(X6,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1702]) ).
cnf(c_0_1702_2,axiom,
( ~ c_lessequals(hAPP(X4,c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(X1,X4,X5,X3,X6)),hAPP(X5,c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(X1,X4,X5,X3,X6)),tc_fun(X6,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Product__Type_OSigma(X1,X4,X3,X6),c_Product__Type_OSigma(X2,X5,X3,X6),tc_fun(tc_prod(X3,X6),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1702]) ).
cnf(c_0_1703_0,axiom,
( c_in(X1,c_FuncSet_OPi(X2,X3,X4,X5),tc_fun(X4,X5))
| ~ c_in(hAPP(X1,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X2,X3,X1,X4,X5)),hAPP(X3,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X2,X3,X1,X4,X5)),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1703]) ).
cnf(c_0_1703_1,axiom,
( ~ c_in(hAPP(X1,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X2,X3,X1,X4,X5)),hAPP(X3,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X2,X3,X1,X4,X5)),X5)
| c_in(X1,c_FuncSet_OPi(X2,X3,X4,X5),tc_fun(X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1703]) ).
cnf(c_0_1704_0,axiom,
( c_in(X1,c_FuncSet_OPi(X2,X3,X4,X5),tc_fun(X4,X5))
| ~ c_in(hAPP(X1,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X2,X3,X1,X4,X5)),hAPP(X3,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X2,X3,X1,X4,X5)),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1704]) ).
cnf(c_0_1704_1,axiom,
( ~ c_in(hAPP(X1,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X2,X3,X1,X4,X5)),hAPP(X3,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X2,X3,X1,X4,X5)),X5)
| c_in(X1,c_FuncSet_OPi(X2,X3,X4,X5),tc_fun(X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1704]) ).
cnf(c_0_1705_0,axiom,
( c_in(X1,c_FuncSet_OPi(X2,c_COMBK(X3,tc_fun(X5,tc_bool),X4),X4,X5),tc_fun(X4,X5))
| ~ c_in(hAPP(X1,c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X2,X3,X1,X4,X5)),X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1705]) ).
cnf(c_0_1705_1,axiom,
( ~ c_in(hAPP(X1,c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X2,X3,X1,X4,X5)),X3,X5)
| c_in(X1,c_FuncSet_OPi(X2,c_COMBK(X3,tc_fun(X5,tc_bool),X4),X4,X5),tc_fun(X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1705]) ).
cnf(c_0_1706_0,axiom,
( c_lessequals(c_Relation_Orel__comp(X1,X6,X5,X4,X8),c_Product__Type_OSigma(X2,c_COMBK(X7,tc_fun(X8,tc_bool),X5),X5,X8),tc_fun(tc_prod(X5,X8),tc_bool))
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X3,tc_fun(X4,tc_bool),X5),X5,X4),tc_fun(tc_prod(X5,X4),tc_bool))
| ~ c_lessequals(X6,c_Product__Type_OSigma(X3,c_COMBK(X7,tc_fun(X8,tc_bool),X4),X4,X8),tc_fun(tc_prod(X4,X8),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1706]) ).
cnf(c_0_1706_1,axiom,
( ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X3,tc_fun(X4,tc_bool),X5),X5,X4),tc_fun(tc_prod(X5,X4),tc_bool))
| c_lessequals(c_Relation_Orel__comp(X1,X6,X5,X4,X8),c_Product__Type_OSigma(X2,c_COMBK(X7,tc_fun(X8,tc_bool),X5),X5,X8),tc_fun(tc_prod(X5,X8),tc_bool))
| ~ c_lessequals(X6,c_Product__Type_OSigma(X3,c_COMBK(X7,tc_fun(X8,tc_bool),X4),X4,X8),tc_fun(tc_prod(X4,X8),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1706]) ).
cnf(c_0_1706_2,axiom,
( ~ c_lessequals(X6,c_Product__Type_OSigma(X3,c_COMBK(X7,tc_fun(X8,tc_bool),X4),X4,X8),tc_fun(tc_prod(X4,X8),tc_bool))
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X3,tc_fun(X4,tc_bool),X5),X5,X4),tc_fun(tc_prod(X5,X4),tc_bool))
| c_lessequals(c_Relation_Orel__comp(X1,X6,X5,X4,X8),c_Product__Type_OSigma(X2,c_COMBK(X7,tc_fun(X8,tc_bool),X5),X5,X8),tc_fun(tc_prod(X5,X8),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1706]) ).
cnf(c_0_1707_0,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X3,X1,X2,X4,X5),X1,X4,X5),X2,tc_prod(X4,X5))
| ~ c_in(X1,c_Relation_OImage(X2,X3,X4,X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1707]) ).
cnf(c_0_1707_1,axiom,
( ~ c_in(X1,c_Relation_OImage(X2,X3,X4,X5),X5)
| c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X3,X1,X2,X4,X5),X1,X4,X5),X2,tc_prod(X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1707]) ).
cnf(c_0_1708_0,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X3,X1,X2,X4,X5),X1,X4,X5),X2,tc_prod(X4,X5))
| ~ c_in(X1,c_Relation_OImage(X2,X3,X4,X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1708]) ).
cnf(c_0_1708_1,axiom,
( ~ c_in(X1,c_Relation_OImage(X2,X3,X4,X5),X5)
| c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X3,X1,X2,X4,X5),X1,X4,X5),X2,tc_prod(X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1708]) ).
cnf(c_0_1709_0,axiom,
( c_lessequals(c_Relation_Orel__comp(X1,X5,X3,X4,X7),c_Relation_Orel__comp(X2,X6,X3,X4,X7),tc_fun(tc_prod(X3,X7),tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool))
| ~ c_lessequals(X5,X6,tc_fun(tc_prod(X4,X7),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1709]) ).
cnf(c_0_1709_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool))
| c_lessequals(c_Relation_Orel__comp(X1,X5,X3,X4,X7),c_Relation_Orel__comp(X2,X6,X3,X4,X7),tc_fun(tc_prod(X3,X7),tc_bool))
| ~ c_lessequals(X5,X6,tc_fun(tc_prod(X4,X7),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1709]) ).
cnf(c_0_1709_2,axiom,
( ~ c_lessequals(X5,X6,tc_fun(tc_prod(X4,X7),tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool))
| c_lessequals(c_Relation_Orel__comp(X1,X5,X3,X4,X7),c_Relation_Orel__comp(X2,X6,X3,X4,X7),tc_fun(tc_prod(X3,X7),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1709]) ).
cnf(c_0_1710_0,axiom,
( c_lessequals(c_Transitive__Closure_Ortrancl(X3,X1),X2,tc_fun(tc_prod(X1,X1),tc_bool))
| ~ c_lessequals(c_Relation_OId(X1),X2,tc_fun(tc_prod(X1,X1),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Ortrancl(X3,X1),X2,tc_fun(tc_prod(X1,X1),tc_bool)),X3,X1,X1,X1),X2,tc_fun(tc_prod(X1,X1),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1710]) ).
cnf(c_0_1710_1,axiom,
( ~ c_lessequals(c_Relation_OId(X1),X2,tc_fun(tc_prod(X1,X1),tc_bool))
| c_lessequals(c_Transitive__Closure_Ortrancl(X3,X1),X2,tc_fun(tc_prod(X1,X1),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Ortrancl(X3,X1),X2,tc_fun(tc_prod(X1,X1),tc_bool)),X3,X1,X1,X1),X2,tc_fun(tc_prod(X1,X1),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1710]) ).
cnf(c_0_1710_2,axiom,
( ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Ortrancl(X3,X1),X2,tc_fun(tc_prod(X1,X1),tc_bool)),X3,X1,X1,X1),X2,tc_fun(tc_prod(X1,X1),tc_bool))
| ~ c_lessequals(c_Relation_OId(X1),X2,tc_fun(tc_prod(X1,X1),tc_bool))
| c_lessequals(c_Transitive__Closure_Ortrancl(X3,X1),X2,tc_fun(tc_prod(X1,X1),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1710]) ).
cnf(c_0_1711_0,axiom,
( c_lessequals(c_Transitive__Closure_Otrancl(X1,X3),X2,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Otrancl(X1,X3),X2,tc_fun(tc_prod(X3,X3),tc_bool)),X1,X3,X3,X3),X2,tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1711]) ).
cnf(c_0_1711_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool))
| c_lessequals(c_Transitive__Closure_Otrancl(X1,X3),X2,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Otrancl(X1,X3),X2,tc_fun(tc_prod(X3,X3),tc_bool)),X1,X3,X3,X3),X2,tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1711]) ).
cnf(c_0_1711_2,axiom,
( ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Otrancl(X1,X3),X2,tc_fun(tc_prod(X3,X3),tc_bool)),X1,X3,X3,X3),X2,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool))
| c_lessequals(c_Transitive__Closure_Otrancl(X1,X3),X2,tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1711]) ).
cnf(c_0_1712_0,axiom,
( c_in(c_Pair(X1,X6,X3,X7),c_Relation_Orel__comp(X5,X8,X3,X4,X7),tc_prod(X3,X7))
| ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
| ~ c_in(c_Pair(X2,X6,X4,X7),X8,tc_prod(X4,X7)) ),
inference(literals_permutation,[status(thm)],[c_0_1712]) ).
cnf(c_0_1712_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
| c_in(c_Pair(X1,X6,X3,X7),c_Relation_Orel__comp(X5,X8,X3,X4,X7),tc_prod(X3,X7))
| ~ c_in(c_Pair(X2,X6,X4,X7),X8,tc_prod(X4,X7)) ),
inference(literals_permutation,[status(thm)],[c_0_1712]) ).
cnf(c_0_1712_2,axiom,
( ~ c_in(c_Pair(X2,X6,X4,X7),X8,tc_prod(X4,X7))
| ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
| c_in(c_Pair(X1,X6,X3,X7),c_Relation_Orel__comp(X5,X8,X3,X4,X7),tc_prod(X3,X7)) ),
inference(literals_permutation,[status(thm)],[c_0_1712]) ).
cnf(c_0_1713_0,axiom,
( hAPP(X5,X1) = hAPP(X6,X1)
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| c_Recdef_Ocut(X5,X4,X2,X3,X7) != c_Recdef_Ocut(X6,X4,X2,X3,X7) ),
inference(literals_permutation,[status(thm)],[c_0_1713]) ).
cnf(c_0_1713_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| hAPP(X5,X1) = hAPP(X6,X1)
| c_Recdef_Ocut(X5,X4,X2,X3,X7) != c_Recdef_Ocut(X6,X4,X2,X3,X7) ),
inference(literals_permutation,[status(thm)],[c_0_1713]) ).
cnf(c_0_1713_2,axiom,
( c_Recdef_Ocut(X5,X4,X2,X3,X7) != c_Recdef_Ocut(X6,X4,X2,X3,X7)
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| hAPP(X5,X1) = hAPP(X6,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1713]) ).
cnf(c_0_1714_0,axiom,
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_Wellfounded_Owf(X3,X2)
| ~ c_lessequals(c_Relation_Orel__comp(X1,X3,X2,X2,X2),X1,tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1714]) ).
cnf(c_0_1714_1,axiom,
( ~ c_Wellfounded_Owf(X1,X2)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Wellfounded_Owf(X3,X2)
| ~ c_lessequals(c_Relation_Orel__comp(X1,X3,X2,X2,X2),X1,tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1714]) ).
cnf(c_0_1714_2,axiom,
( ~ c_Wellfounded_Owf(X3,X2)
| ~ c_Wellfounded_Owf(X1,X2)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_lessequals(c_Relation_Orel__comp(X1,X3,X2,X2,X2),X1,tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1714]) ).
cnf(c_0_1714_3,axiom,
( ~ c_lessequals(c_Relation_Orel__comp(X1,X3,X2,X2,X2),X1,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_Wellfounded_Owf(X3,X2)
| ~ c_Wellfounded_Owf(X1,X2)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1714]) ).
cnf(c_0_1715_0,axiom,
( c_Wellfounded_Owf(X1,X2)
| ~ c_Wellfounded_Owf(c_Relation_Orel__comp(X1,X1,X2,X2,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1715]) ).
cnf(c_0_1715_1,axiom,
( ~ c_Wellfounded_Owf(c_Relation_Orel__comp(X1,X1,X2,X2,X2),X2)
| c_Wellfounded_Owf(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1715]) ).
cnf(c_0_1716_0,axiom,
( c_in(c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(X1,X4,X5,X3,X6),X1,X3)
| c_lessequals(c_Product__Type_OSigma(X1,X4,X3,X6),c_Product__Type_OSigma(X2,X5,X3,X6),tc_fun(tc_prod(X3,X6),tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1716]) ).
cnf(c_0_1716_1,axiom,
( c_lessequals(c_Product__Type_OSigma(X1,X4,X3,X6),c_Product__Type_OSigma(X2,X5,X3,X6),tc_fun(tc_prod(X3,X6),tc_bool))
| c_in(c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(X1,X4,X5,X3,X6),X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1716]) ).
cnf(c_0_1716_2,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Product__Type_OSigma(X1,X4,X3,X6),c_Product__Type_OSigma(X2,X5,X3,X6),tc_fun(tc_prod(X3,X6),tc_bool))
| c_in(c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1(X1,X4,X5,X3,X6),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1716]) ).
cnf(c_0_1717_0,axiom,
( X1 = X2
| X4 = X5
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1717]) ).
cnf(c_0_1717_1,axiom,
( X4 = X5
| X1 = X2
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1717]) ).
cnf(c_0_1717_2,axiom,
( c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X5
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1717]) ).
cnf(c_0_1717_3,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X5
| X1 = X2
| ~ c_in(c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1717]) ).
cnf(c_0_1717_4,axiom,
( ~ c_in(c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X5
| X1 = X2
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1717]) ).
cnf(c_0_1717_5,axiom,
( ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X5
| X1 = X2
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1717]) ).
cnf(c_0_1717_6,axiom,
( ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X5
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1717]) ).
cnf(c_0_1718_0,axiom,
( X1 = X2
| X4 = X5
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1718]) ).
cnf(c_0_1718_1,axiom,
( X4 = X5
| X1 = X2
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1718]) ).
cnf(c_0_1718_2,axiom,
( c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X5
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1718]) ).
cnf(c_0_1718_3,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X5
| X1 = X2
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1718]) ).
cnf(c_0_1718_4,axiom,
( ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X5
| X1 = X2
| ~ c_in(c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1718]) ).
cnf(c_0_1718_5,axiom,
( ~ c_in(c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X5
| X1 = X2
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1718]) ).
cnf(c_0_1718_6,axiom,
( ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X5
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1718]) ).
cnf(c_0_1719_0,axiom,
( c_in(c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X1,X2,X3,X4,X5),X1,X4)
| c_in(X3,c_FuncSet_OPi(X1,c_COMBK(X2,tc_fun(X5,tc_bool),X4),X4,X5),tc_fun(X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1719]) ).
cnf(c_0_1719_1,axiom,
( c_in(X3,c_FuncSet_OPi(X1,c_COMBK(X2,tc_fun(X5,tc_bool),X4),X4,X5),tc_fun(X4,X5))
| c_in(c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(X1,X2,X3,X4,X5),X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1719]) ).
cnf(c_0_1720_0,axiom,
( hAPP(c_Recdef_Ocut(X5,X4,X2,X3,X6),X1) = hAPP(X5,X1)
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1720]) ).
cnf(c_0_1720_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| hAPP(c_Recdef_Ocut(X5,X4,X2,X3,X6),X1) = hAPP(X5,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1720]) ).
cnf(c_0_1721_0,axiom,
( hAPP(c_Recdef_Ocut(X5,X4,X2,X3,X6),X1) = hAPP(X5,X1)
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1721]) ).
cnf(c_0_1721_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| hAPP(c_Recdef_Ocut(X5,X4,X2,X3,X6),X1) = hAPP(X5,X1) ),
inference(literals_permutation,[status(thm)],[c_0_1721]) ).
cnf(c_0_1722_0,axiom,
( c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X3,X1,X2,X4,X5),X3,X4)
| ~ c_in(X1,c_Relation_OImage(X2,X3,X4,X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1722]) ).
cnf(c_0_1722_1,axiom,
( ~ c_in(X1,c_Relation_OImage(X2,X3,X4,X5),X5)
| c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X3,X1,X2,X4,X5),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1722]) ).
cnf(c_0_1723_0,axiom,
( c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X3,X1,X2,X4,X5),X3,X4)
| ~ c_in(X1,c_Relation_OImage(X2,X3,X4,X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1723]) ).
cnf(c_0_1723_1,axiom,
( ~ c_in(X1,c_Relation_OImage(X2,X3,X4,X5),X5)
| c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X3,X1,X2,X4,X5),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1723]) ).
cnf(c_0_1724_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X4,X1,X2,X3),X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1724]) ).
cnf(c_0_1724_1,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X4,X1,X2,X3),X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1724]) ).
cnf(c_0_1724_2,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X4,X1,X2,X3),X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1724]) ).
cnf(c_0_1725_0,axiom,
( c_Relation_Orefl__on(X2,X1,X3)
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1(X2,X1,X3),c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1(X2,X1,X3),X3,X3),X1,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1725]) ).
cnf(c_0_1725_1,axiom,
( ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| c_Relation_Orefl__on(X2,X1,X3)
| ~ c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1(X2,X1,X3),c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1(X2,X1,X3),X3,X3),X1,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1725]) ).
cnf(c_0_1725_2,axiom,
( ~ c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1(X2,X1,X3),c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1(X2,X1,X3),X3,X3),X1,tc_prod(X3,X3))
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| c_Relation_Orefl__on(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1725]) ).
cnf(c_0_1726_0,axiom,
( c_Relation_Orefl__on(X2,X1,X3)
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1(X2,X1,X3),c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1(X2,X1,X3),X3,X3),X1,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1726]) ).
cnf(c_0_1726_1,axiom,
( ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| c_Relation_Orefl__on(X2,X1,X3)
| ~ c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1(X2,X1,X3),c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1(X2,X1,X3),X3,X3),X1,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1726]) ).
cnf(c_0_1726_2,axiom,
( ~ c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1(X2,X1,X3),c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1(X2,X1,X3),X3,X3),X1,tc_prod(X3,X3))
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| c_Relation_Orefl__on(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1726]) ).
cnf(c_0_1727_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X4,X1,X2,X3),X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1727]) ).
cnf(c_0_1727_1,axiom,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X4,X1,X2,X3),X3,X3),X4,tc_prod(X3,X3))
| c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1727]) ).
cnf(c_0_1727_2,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X4,X1,X2,X3),X3,X3),X4,tc_prod(X3,X3))
| c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1727]) ).
cnf(c_0_1728_0,axiom,
( c_in(c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X1,X2,X3,X4,X5),X1,X4)
| c_in(X3,c_FuncSet_OPi(X1,X2,X4,X5),tc_fun(X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1728]) ).
cnf(c_0_1728_1,axiom,
( c_in(X3,c_FuncSet_OPi(X1,X2,X4,X5),tc_fun(X4,X5))
| c_in(c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X1,X2,X3,X4,X5),X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1728]) ).
cnf(c_0_1729_0,axiom,
( c_in(c_FuncSet_Osko__FuncSet__XPi__I__1__1(X1,X2,X3,X4,X5),X1,X4)
| c_in(X3,c_FuncSet_OPi(X1,X2,X4,X5),tc_fun(X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1729]) ).
cnf(c_0_1729_1,axiom,
( c_in(X3,c_FuncSet_OPi(X1,X2,X4,X5),tc_fun(X4,X5))
| c_in(c_FuncSet_Osko__FuncSet__XPi__I__1__1(X1,X2,X3,X4,X5),X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1729]) ).
cnf(c_0_1730_0,axiom,
( c_lessequals(X4,X6,tc_fun(X5,tc_bool))
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(c_Product__Type_OSigma(X4,c_COMBK(X2,tc_fun(X3,tc_bool),X5),X5,X3),c_Product__Type_OSigma(X6,c_COMBK(X2,tc_fun(X3,tc_bool),X5),X5,X3),tc_fun(tc_prod(X5,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1730]) ).
cnf(c_0_1730_1,axiom,
( ~ c_in(X1,X2,X3)
| c_lessequals(X4,X6,tc_fun(X5,tc_bool))
| ~ c_lessequals(c_Product__Type_OSigma(X4,c_COMBK(X2,tc_fun(X3,tc_bool),X5),X5,X3),c_Product__Type_OSigma(X6,c_COMBK(X2,tc_fun(X3,tc_bool),X5),X5,X3),tc_fun(tc_prod(X5,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1730]) ).
cnf(c_0_1730_2,axiom,
( ~ c_lessequals(c_Product__Type_OSigma(X4,c_COMBK(X2,tc_fun(X3,tc_bool),X5),X5,X3),c_Product__Type_OSigma(X6,c_COMBK(X2,tc_fun(X3,tc_bool),X5),X5,X3),tc_fun(tc_prod(X5,X3),tc_bool))
| ~ c_in(X1,X2,X3)
| c_lessequals(X4,X6,tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1730]) ).
cnf(c_0_1731_0,axiom,
( c_lessequals(X2,c_Relation_Orel__comp(c_Relation_Oconverse(X2,X3,X3),X2,X3,X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Relation_Orefl__on(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1731]) ).
cnf(c_0_1731_1,axiom,
( ~ c_Relation_Orefl__on(X1,X2,X3)
| c_lessequals(X2,c_Relation_Orel__comp(c_Relation_Oconverse(X2,X3,X3),X2,X3,X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1731]) ).
cnf(c_0_1732_0,axiom,
( c_lessequals(c_Relation_Orel__comp(c_Relation_Oconverse(X1,X2,X2),X1,X2,X2,X2),X1,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_Relation_Osym(X1,X2)
| ~ c_Relation_Otrans(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1732]) ).
cnf(c_0_1732_1,axiom,
( ~ c_Relation_Osym(X1,X2)
| c_lessequals(c_Relation_Orel__comp(c_Relation_Oconverse(X1,X2,X2),X1,X2,X2,X2),X1,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_Relation_Otrans(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1732]) ).
cnf(c_0_1732_2,axiom,
( ~ c_Relation_Otrans(X1,X2)
| ~ c_Relation_Osym(X1,X2)
| c_lessequals(c_Relation_Orel__comp(c_Relation_Oconverse(X1,X2,X2),X1,X2,X2,X2),X1,tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1732]) ).
cnf(c_0_1733_0,axiom,
( ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)),X3)
| ~ c_in(c_Pair(X2,X1,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1733]) ).
cnf(c_0_1733_1,axiom,
( ~ c_in(c_Pair(X2,X1,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1733]) ).
cnf(c_0_1734_0,axiom,
( X1 = X2
| X4 = X5
| X4 = X1
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1734]) ).
cnf(c_0_1734_1,axiom,
( X4 = X5
| X1 = X2
| X4 = X1
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1734]) ).
cnf(c_0_1734_2,axiom,
( X4 = X1
| X4 = X5
| X1 = X2
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1734]) ).
cnf(c_0_1734_3,axiom,
( c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X1
| X4 = X5
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1734]) ).
cnf(c_0_1734_4,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X1
| X4 = X5
| X1 = X2
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1734]) ).
cnf(c_0_1734_5,axiom,
( ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X1
| X4 = X5
| X1 = X2
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1734]) ).
cnf(c_0_1734_6,axiom,
( ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X1
| X4 = X5
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1734]) ).
cnf(c_0_1735_0,axiom,
( X1 = X2
| X4 = X5
| X5 = X1
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1735]) ).
cnf(c_0_1735_1,axiom,
( X4 = X5
| X1 = X2
| X5 = X1
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1735]) ).
cnf(c_0_1735_2,axiom,
( X5 = X1
| X4 = X5
| X1 = X2
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1735]) ).
cnf(c_0_1735_3,axiom,
( c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X1
| X4 = X5
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1735]) ).
cnf(c_0_1735_4,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X1
| X4 = X5
| X1 = X2
| ~ c_in(c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1735]) ).
cnf(c_0_1735_5,axiom,
( ~ c_in(c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X1
| X4 = X5
| X1 = X2
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1735]) ).
cnf(c_0_1735_6,axiom,
( ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X1
| X4 = X5
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1735]) ).
cnf(c_0_1736_0,axiom,
( X1 = X2
| X4 = X5
| X5 = X2
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1736]) ).
cnf(c_0_1736_1,axiom,
( X4 = X5
| X1 = X2
| X5 = X2
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1736]) ).
cnf(c_0_1736_2,axiom,
( X5 = X2
| X4 = X5
| X1 = X2
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1736]) ).
cnf(c_0_1736_3,axiom,
( c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X2
| X4 = X5
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1736]) ).
cnf(c_0_1736_4,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X2
| X4 = X5
| X1 = X2
| ~ c_in(c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1736]) ).
cnf(c_0_1736_5,axiom,
( ~ c_in(c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X2
| X4 = X5
| X1 = X2
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1736]) ).
cnf(c_0_1736_6,axiom,
( ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X2
| X4 = X5
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1736]) ).
cnf(c_0_1737_0,axiom,
( X1 = X2
| X4 = X5
| X4 = X2
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1737]) ).
cnf(c_0_1737_1,axiom,
( X4 = X5
| X1 = X2
| X4 = X2
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1737]) ).
cnf(c_0_1737_2,axiom,
( X4 = X2
| X4 = X5
| X1 = X2
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1737]) ).
cnf(c_0_1737_3,axiom,
( c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X2
| X4 = X5
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1737]) ).
cnf(c_0_1737_4,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X2
| X4 = X5
| X1 = X2
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1737]) ).
cnf(c_0_1737_5,axiom,
( ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X2
| X4 = X5
| X1 = X2
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1737]) ).
cnf(c_0_1737_6,axiom,
( ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X2
| X4 = X5
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1737]) ).
cnf(c_0_1738_0,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1738]) ).
cnf(c_0_1738_1,axiom,
( X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1738]) ).
cnf(c_0_1738_2,axiom,
( X1 = X2
| X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1738]) ).
cnf(c_0_1738_3,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1738]) ).
cnf(c_0_1738_4,axiom,
( ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1738]) ).
cnf(c_0_1738_5,axiom,
( ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1738]) ).
cnf(c_0_1739_0,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X2
| X1 = X2
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1739]) ).
cnf(c_0_1739_1,axiom,
( X4 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1739]) ).
cnf(c_0_1739_2,axiom,
( X1 = X2
| X4 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1739]) ).
cnf(c_0_1739_3,axiom,
( ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X4 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1739]) ).
cnf(c_0_1739_4,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X4 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1739]) ).
cnf(c_0_1739_5,axiom,
( ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X4 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1739]) ).
cnf(c_0_1740_0,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X2
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1740]) ).
cnf(c_0_1740_1,axiom,
( X4 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1740]) ).
cnf(c_0_1740_2,axiom,
( X1 = X2
| X4 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1740]) ).
cnf(c_0_1740_3,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| X4 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1740]) ).
cnf(c_0_1740_4,axiom,
( ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| X4 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1740]) ).
cnf(c_0_1740_5,axiom,
( ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| X4 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1740]) ).
cnf(c_0_1741_0,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| X1 = X2
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1741]) ).
cnf(c_0_1741_1,axiom,
( X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1741]) ).
cnf(c_0_1741_2,axiom,
( X1 = X2
| X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1741]) ).
cnf(c_0_1741_3,axiom,
( ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1741]) ).
cnf(c_0_1741_4,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1741]) ).
cnf(c_0_1741_5,axiom,
( ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1741]) ).
cnf(c_0_1742_0,axiom,
( c_lessequals(c_Relation_Orel__comp(X1,X1,X2,X2,X2),X1,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_Relation_Otrans(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1742]) ).
cnf(c_0_1742_1,axiom,
( ~ c_Relation_Otrans(X1,X2)
| c_lessequals(c_Relation_Orel__comp(X1,X1,X2,X2,X2),X1,tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1742]) ).
cnf(c_0_1743_0,axiom,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X4,X1,X2,X3),X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1743]) ).
cnf(c_0_1743_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X4,X1,X2,X3),X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1743]) ).
cnf(c_0_1744_0,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X4,X1,X2,X3),X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1744]) ).
cnf(c_0_1744_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X4,X1,X2,X3),X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1744]) ).
cnf(c_0_1745_0,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X4,X1,X2,X3),X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1745]) ).
cnf(c_0_1745_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X4,X1,X2,X3),X2,X3,X3),X4,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1745]) ).
cnf(c_0_1746_0,axiom,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X4,X1,X2,X3),X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1746]) ).
cnf(c_0_1746_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X4,X1,X2,X3),X3,X3),X4,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1746]) ).
cnf(c_0_1747_0,axiom,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1747]) ).
cnf(c_0_1747_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1747]) ).
cnf(c_0_1747_2,axiom,
( ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1747]) ).
cnf(c_0_1748_0,axiom,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1748]) ).
cnf(c_0_1748_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1748]) ).
cnf(c_0_1748_2,axiom,
( ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1748]) ).
cnf(c_0_1749_0,axiom,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1749]) ).
cnf(c_0_1749_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1749]) ).
cnf(c_0_1749_2,axiom,
( ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1749]) ).
cnf(c_0_1750_0,axiom,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1750]) ).
cnf(c_0_1750_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1750]) ).
cnf(c_0_1750_2,axiom,
( ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1750]) ).
cnf(c_0_1751_0,axiom,
( X1 = X2
| c_in(X1,X5,X3)
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_lessequals(X4,c_Product__Type_OSigma(X5,c_COMBK(X5,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1751]) ).
cnf(c_0_1751_1,axiom,
( c_in(X1,X5,X3)
| X1 = X2
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_lessequals(X4,c_Product__Type_OSigma(X5,c_COMBK(X5,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1751]) ).
cnf(c_0_1751_2,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| c_in(X1,X5,X3)
| X1 = X2
| ~ c_lessequals(X4,c_Product__Type_OSigma(X5,c_COMBK(X5,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1751]) ).
cnf(c_0_1751_3,axiom,
( ~ c_lessequals(X4,c_Product__Type_OSigma(X5,c_COMBK(X5,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| c_in(X1,X5,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1751]) ).
cnf(c_0_1752_0,axiom,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),X4,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1752]) ).
cnf(c_0_1752_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),X4,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1752]) ).
cnf(c_0_1752_2,axiom,
( ~ c_in(c_Pair(X2,X5,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1752]) ).
cnf(c_0_1753_0,axiom,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1753]) ).
cnf(c_0_1753_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1753]) ).
cnf(c_0_1753_2,axiom,
( ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1753]) ).
cnf(c_0_1754_0,axiom,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),X4,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1754]) ).
cnf(c_0_1754_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),X4,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1754]) ).
cnf(c_0_1754_2,axiom,
( ~ c_in(c_Pair(X2,X5,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1754]) ).
cnf(c_0_1755_0,axiom,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1755]) ).
cnf(c_0_1755_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1755]) ).
cnf(c_0_1755_2,axiom,
( ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1755]) ).
cnf(c_0_1756_0,axiom,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1756]) ).
cnf(c_0_1756_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1756]) ).
cnf(c_0_1756_2,axiom,
( ~ c_in(c_Pair(X2,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1756]) ).
cnf(c_0_1757_0,axiom,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),X4,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1757]) ).
cnf(c_0_1757_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),X4,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1757]) ).
cnf(c_0_1757_2,axiom,
( ~ c_in(c_Pair(X2,X5,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1757]) ).
cnf(c_0_1758_0,axiom,
( c_Wellfounded_Owf(c_Relation_Orel__comp(X1,X1,X2,X2,X2),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1758]) ).
cnf(c_0_1758_1,axiom,
( ~ c_Wellfounded_Owf(X1,X2)
| c_Wellfounded_Owf(c_Relation_Orel__comp(X1,X1,X2,X2,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1758]) ).
cnf(c_0_1759_0,axiom,
( c_lessequals(c_Transitive__Closure_Otrancl(X1,X3),c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1759]) ).
cnf(c_0_1759_1,axiom,
( ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| c_lessequals(c_Transitive__Closure_Otrancl(X1,X3),c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1759]) ).
cnf(c_0_1760_0,axiom,
( c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),X4,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1760]) ).
cnf(c_0_1760_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X2,X5,X3,X3),X4,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1760]) ).
cnf(c_0_1760_2,axiom,
( ~ c_in(c_Pair(X2,X5,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| c_in(c_Pair(X1,X5,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1760]) ).
cnf(c_0_1761_0,axiom,
( c_in(c_Pair(X3,X5,X2,X2),X1,tc_prod(X2,X2))
| ~ c_Relation_Otrans(X1,X2)
| ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X5,X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1761]) ).
cnf(c_0_1761_1,axiom,
( ~ c_Relation_Otrans(X1,X2)
| c_in(c_Pair(X3,X5,X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X5,X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1761]) ).
cnf(c_0_1761_2,axiom,
( ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2))
| ~ c_Relation_Otrans(X1,X2)
| c_in(c_Pair(X3,X5,X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X5,X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1761]) ).
cnf(c_0_1761_3,axiom,
( ~ c_in(c_Pair(X4,X5,X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2))
| ~ c_Relation_Otrans(X1,X2)
| c_in(c_Pair(X3,X5,X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1761]) ).
cnf(c_0_1762_0,axiom,
( c_in(c_Pair(X3,X5,X2,X2),X1,tc_prod(X2,X2))
| ~ c_Relation_Otrans(X1,X2)
| ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X5,X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1762]) ).
cnf(c_0_1762_1,axiom,
( ~ c_Relation_Otrans(X1,X2)
| c_in(c_Pair(X3,X5,X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X5,X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1762]) ).
cnf(c_0_1762_2,axiom,
( ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2))
| ~ c_Relation_Otrans(X1,X2)
| c_in(c_Pair(X3,X5,X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X5,X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1762]) ).
cnf(c_0_1762_3,axiom,
( ~ c_in(c_Pair(X4,X5,X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2))
| ~ c_Relation_Otrans(X1,X2)
| c_in(c_Pair(X3,X5,X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1762]) ).
cnf(c_0_1763_0,axiom,
( c_in(c_Pair(hAPP(X5,X1),hAPP(X5,X2),X6,X6),X4,tc_prod(X6,X6))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_Oinv__image(X4,X5,X6,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1763]) ).
cnf(c_0_1763_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_Oinv__image(X4,X5,X6,X3),tc_prod(X3,X3))
| c_in(c_Pair(hAPP(X5,X1),hAPP(X5,X2),X6,X6),X4,tc_prod(X6,X6)) ),
inference(literals_permutation,[status(thm)],[c_0_1763]) ).
cnf(c_0_1764_0,axiom,
( c_Equiv__Relations_Oequiv(c_Relation_ODomain(X1,X2,X2),X1,X2)
| c_Relation_Orel__comp(c_Relation_Oconverse(X1,X2,X2),X1,X2,X2,X2) != X1 ),
inference(literals_permutation,[status(thm)],[c_0_1764]) ).
cnf(c_0_1764_1,axiom,
( c_Relation_Orel__comp(c_Relation_Oconverse(X1,X2,X2),X1,X2,X2,X2) != X1
| c_Equiv__Relations_Oequiv(c_Relation_ODomain(X1,X2,X2),X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1764]) ).
cnf(c_0_1765_0,axiom,
( c_in(c_Pair(X2,X3,X6,X6),c_Relation_Oinv__image(X5,X1,X4,X6),tc_prod(X6,X6))
| ~ c_in(c_Pair(hAPP(X1,X2),hAPP(X1,X3),X4,X4),X5,tc_prod(X4,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1765]) ).
cnf(c_0_1765_1,axiom,
( ~ c_in(c_Pair(hAPP(X1,X2),hAPP(X1,X3),X4,X4),X5,tc_prod(X4,X4))
| c_in(c_Pair(X2,X3,X6,X6),c_Relation_Oinv__image(X5,X1,X4,X6),tc_prod(X6,X6)) ),
inference(literals_permutation,[status(thm)],[c_0_1765]) ).
cnf(c_0_1766_0,axiom,
( c_lessequals(c_Relation_OImage(X1,X6,X5,X4),X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X3,tc_fun(X4,tc_bool),X5),X5,X4),tc_fun(tc_prod(X5,X4),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1766]) ).
cnf(c_0_1766_1,axiom,
( ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X3,tc_fun(X4,tc_bool),X5),X5,X4),tc_fun(tc_prod(X5,X4),tc_bool))
| c_lessequals(c_Relation_OImage(X1,X6,X5,X4),X3,tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1766]) ).
cnf(c_0_1767_0,axiom,
( c_in(c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1(X2,X3,X1,X4),X3,X4)
| c_Wellfounded_Owf(X1,X4)
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X3,tc_fun(X4,tc_bool),X4),X4,X4),tc_fun(tc_prod(X4,X4),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1767]) ).
cnf(c_0_1767_1,axiom,
( c_Wellfounded_Owf(X1,X4)
| c_in(c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1(X2,X3,X1,X4),X3,X4)
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X3,tc_fun(X4,tc_bool),X4),X4,X4),tc_fun(tc_prod(X4,X4),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1767]) ).
cnf(c_0_1767_2,axiom,
( ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X3,tc_fun(X4,tc_bool),X4),X4,X4),tc_fun(tc_prod(X4,X4),tc_bool))
| c_Wellfounded_Owf(X1,X4)
| c_in(c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1(X2,X3,X1,X4),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1767]) ).
cnf(c_0_1768_0,axiom,
( c_in(c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1(X2,X3,X1,X4),X2,X4)
| c_Wellfounded_Owf(X1,X4)
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X3,tc_fun(X4,tc_bool),X4),X4,X4),tc_fun(tc_prod(X4,X4),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1768]) ).
cnf(c_0_1768_1,axiom,
( c_Wellfounded_Owf(X1,X4)
| c_in(c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1(X2,X3,X1,X4),X2,X4)
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X3,tc_fun(X4,tc_bool),X4),X4,X4),tc_fun(tc_prod(X4,X4),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1768]) ).
cnf(c_0_1768_2,axiom,
( ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X3,tc_fun(X4,tc_bool),X4),X4,X4),tc_fun(tc_prod(X4,X4),tc_bool))
| c_Wellfounded_Owf(X1,X4)
| c_in(c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1(X2,X3,X1,X4),X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1768]) ).
cnf(c_0_1769_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X4,X3),X3,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X4,X3,X3),X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1769]) ).
cnf(c_0_1769_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X4,X3,X3),X3),tc_prod(X3,X3))
| c_in(c_Pair(X1,X2,X3,X3),c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X4,X3),X3,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1769]) ).
cnf(c_0_1770_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X4,X3,X3),X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X4,X3),X3,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1770]) ).
cnf(c_0_1770_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X4,X3),X3,X3),tc_prod(X3,X3))
| c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X4,X3,X3),X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1770]) ).
cnf(c_0_1771_0,axiom,
( c_lessequals(c_Set_Oimage(X1,X2,X5,X4),X3,tc_fun(X4,tc_bool))
| ~ c_in(X1,c_FuncSet_OPi(X2,c_COMBK(X3,tc_fun(X4,tc_bool),X5),X5,X4),tc_fun(X5,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1771]) ).
cnf(c_0_1771_1,axiom,
( ~ c_in(X1,c_FuncSet_OPi(X2,c_COMBK(X3,tc_fun(X4,tc_bool),X5),X5,X4),tc_fun(X5,X4))
| c_lessequals(c_Set_Oimage(X1,X2,X5,X4),X3,tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1771]) ).
cnf(c_0_1772_0,axiom,
( X2 = X3
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1772]) ).
cnf(c_0_1772_1,axiom,
( ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X2 = X3
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1772]) ).
cnf(c_0_1772_2,axiom,
( ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X2 = X3
| ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1772]) ).
cnf(c_0_1772_3,axiom,
( ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1772]) ).
cnf(c_0_1773_0,axiom,
( ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1773]) ).
cnf(c_0_1773_1,axiom,
( ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1773]) ).
cnf(c_0_1773_2,axiom,
( ~ c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1773]) ).
cnf(c_0_1774_0,axiom,
( c_lessequals(c_Product__Type_OSigma(X4,c_COMBK(X2,tc_fun(X3,tc_bool),X6),X6,X3),c_Product__Type_OSigma(X5,c_COMBK(X2,tc_fun(X3,tc_bool),X6),X6,X3),tc_fun(tc_prod(X6,X3),tc_bool))
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X4,X5,tc_fun(X6,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1774]) ).
cnf(c_0_1774_1,axiom,
( ~ c_in(X1,X2,X3)
| c_lessequals(c_Product__Type_OSigma(X4,c_COMBK(X2,tc_fun(X3,tc_bool),X6),X6,X3),c_Product__Type_OSigma(X5,c_COMBK(X2,tc_fun(X3,tc_bool),X6),X6,X3),tc_fun(tc_prod(X6,X3),tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X6,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1774]) ).
cnf(c_0_1774_2,axiom,
( ~ c_lessequals(X4,X5,tc_fun(X6,tc_bool))
| ~ c_in(X1,X2,X3)
| c_lessequals(c_Product__Type_OSigma(X4,c_COMBK(X2,tc_fun(X3,tc_bool),X6),X6,X3),c_Product__Type_OSigma(X5,c_COMBK(X2,tc_fun(X3,tc_bool),X6),X6,X3),tc_fun(tc_prod(X6,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1774]) ).
cnf(c_0_1775_0,axiom,
( c_in(c_Pair(X2,X1,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X4,X3,X3),X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1775]) ).
cnf(c_0_1775_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X4,X3,X3),X3),tc_prod(X3,X3))
| c_in(c_Pair(X2,X1,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1775]) ).
cnf(c_0_1776_0,axiom,
( c_Wellfounded_Owf(X4,X3)
| ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1776]) ).
cnf(c_0_1776_1,axiom,
( ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)),X3)
| c_Wellfounded_Owf(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1776]) ).
cnf(c_0_1777_0,axiom,
( ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X3,X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1777]) ).
cnf(c_0_1777_1,axiom,
( ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_Pair(X4,X3,X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1777]) ).
cnf(c_0_1777_2,axiom,
( ~ c_in(c_Pair(X4,X3,X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1777]) ).
cnf(c_0_1778_0,axiom,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X1,X2,X3,X4),X3,X4),X2,tc_prod(X3,X4))
| ~ c_in(X1,c_Relation_ODomain(X2,X3,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1778]) ).
cnf(c_0_1778_1,axiom,
( ~ c_in(X1,c_Relation_ODomain(X2,X3,X4),X3)
| c_in(c_Pair(X1,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X1,X2,X3,X4),X3,X4),X2,tc_prod(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1778]) ).
cnf(c_0_1779_0,axiom,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X1,X2,X3,X4),X3,X4),X2,tc_prod(X3,X4))
| ~ c_in(X1,c_Relation_ODomain(X2,X3,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1779]) ).
cnf(c_0_1779_1,axiom,
( ~ c_in(X1,c_Relation_ODomain(X2,X3,X4),X3)
| c_in(c_Pair(X1,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X1,X2,X3,X4),X3,X4),X2,tc_prod(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1779]) ).
cnf(c_0_1780_0,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X1,X2,X4,X3),X1,X3,X4),X2,tc_prod(X3,X4))
| ~ c_in(X1,c_Relation_ORange(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1780]) ).
cnf(c_0_1780_1,axiom,
( ~ c_in(X1,c_Relation_ORange(X2,X3,X4),X4)
| c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X1,X2,X4,X3),X1,X3,X4),X2,tc_prod(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1780]) ).
cnf(c_0_1781_0,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X1,X2,X4,X3),X1,X3,X4),X2,tc_prod(X3,X4))
| ~ c_in(X1,c_Relation_ORange(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1781]) ).
cnf(c_0_1781_1,axiom,
( ~ c_in(X1,c_Relation_ORange(X2,X3,X4),X4)
| c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X1,X2,X4,X3),X1,X3,X4),X2,tc_prod(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1781]) ).
cnf(c_0_1782_0,axiom,
( X1 = X2
| X4 = X2
| X5 = X2
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1782]) ).
cnf(c_0_1782_1,axiom,
( X4 = X2
| X1 = X2
| X5 = X2
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1782]) ).
cnf(c_0_1782_2,axiom,
( X5 = X2
| X4 = X2
| X1 = X2
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1782]) ).
cnf(c_0_1782_3,axiom,
( c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X2
| X4 = X2
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1782]) ).
cnf(c_0_1782_4,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X2
| X4 = X2
| X1 = X2
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1782]) ).
cnf(c_0_1782_5,axiom,
( ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X2
| X4 = X2
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1782]) ).
cnf(c_0_1783_0,axiom,
( X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X4
| X1 = X4
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X2,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1783]) ).
cnf(c_0_1783_1,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X2 = X4
| X1 = X4
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X2,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1783]) ).
cnf(c_0_1783_2,axiom,
( X2 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X1 = X4
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X2,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1783]) ).
cnf(c_0_1783_3,axiom,
( X1 = X4
| X2 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X2,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1783]) ).
cnf(c_0_1783_4,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X4
| X2 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X2,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1783]) ).
cnf(c_0_1783_5,axiom,
( ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X2,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X4
| X2 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1783]) ).
cnf(c_0_1784_0,axiom,
( X1 = X2
| X5 = X1
| X4 = X1
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1784]) ).
cnf(c_0_1784_1,axiom,
( X5 = X1
| X1 = X2
| X4 = X1
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1784]) ).
cnf(c_0_1784_2,axiom,
( X4 = X1
| X5 = X1
| X1 = X2
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1784]) ).
cnf(c_0_1784_3,axiom,
( c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X1
| X5 = X1
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1784]) ).
cnf(c_0_1784_4,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X1
| X5 = X1
| X1 = X2
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1784]) ).
cnf(c_0_1784_5,axiom,
( ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X1
| X5 = X1
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1784]) ).
cnf(c_0_1785_0,axiom,
( X1 = X2
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X2
| X1 = X4
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1785]) ).
cnf(c_0_1785_1,axiom,
( c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X4 = X2
| X1 = X4
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1785]) ).
cnf(c_0_1785_2,axiom,
( X4 = X2
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X1 = X4
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1785]) ).
cnf(c_0_1785_3,axiom,
( X1 = X4
| X4 = X2
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1785]) ).
cnf(c_0_1785_4,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X4
| X4 = X2
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1785]) ).
cnf(c_0_1785_5,axiom,
( ~ c_in(c_Pair(X4,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X4
| X4 = X2
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1785]) ).
cnf(c_0_1786_0,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1786]) ).
cnf(c_0_1786_1,axiom,
( X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1786]) ).
cnf(c_0_1786_2,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1786]) ).
cnf(c_0_1786_3,axiom,
( ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1786]) ).
cnf(c_0_1787_0,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1787]) ).
cnf(c_0_1787_1,axiom,
( X4 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1787]) ).
cnf(c_0_1787_2,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X4 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1787]) ).
cnf(c_0_1787_3,axiom,
( ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X4 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1787]) ).
cnf(c_0_1788_0,axiom,
( c_Finite__Set_Ofinite(X4,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,c_Product__Type_OSigma(X1,c_COMBK(X1,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_in(X4,c_Equiv__Relations_Oquotient(X1,X3,X2),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1788]) ).
cnf(c_0_1788_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X4,X2)
| ~ c_lessequals(X3,c_Product__Type_OSigma(X1,c_COMBK(X1,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_in(X4,c_Equiv__Relations_Oquotient(X1,X3,X2),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1788]) ).
cnf(c_0_1788_2,axiom,
( ~ c_lessequals(X3,c_Product__Type_OSigma(X1,c_COMBK(X1,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X4,X2)
| ~ c_in(X4,c_Equiv__Relations_Oquotient(X1,X3,X2),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1788]) ).
cnf(c_0_1788_3,axiom,
( ~ c_in(X4,c_Equiv__Relations_Oquotient(X1,X3,X2),tc_fun(X2,tc_bool))
| ~ c_lessequals(X3,c_Product__Type_OSigma(X1,c_COMBK(X1,tc_fun(X2,tc_bool),X2),X2,X2),tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1788]) ).
cnf(c_0_1789_0,axiom,
( c_in(c_Pair(X3,X4,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X4,X3,X2,X2),X1,tc_prod(X2,X2)),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1789]) ).
cnf(c_0_1789_1,axiom,
( c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X4,X3,X2,X2),X1,tc_prod(X2,X2)),X2)
| c_in(c_Pair(X3,X4,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1789]) ).
cnf(c_0_1789_2,axiom,
( ~ c_Wellfounded_Owf(X1,X2)
| c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X4,X3,X2,X2),X1,tc_prod(X2,X2)),X2)
| c_in(c_Pair(X3,X4,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1789]) ).
cnf(c_0_1790_0,axiom,
( c_in(X2,hAPP(X6,X1),X4)
| ~ c_in(c_Pair(X1,X2,X3,X4),c_Product__Type_OSigma(X5,X6,X3,X4),tc_prod(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1790]) ).
cnf(c_0_1790_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X4),c_Product__Type_OSigma(X5,X6,X3,X4),tc_prod(X3,X4))
| c_in(X2,hAPP(X6,X1),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1790]) ).
cnf(c_0_1791_0,axiom,
( c_in(c_Pair(X2,X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X4,X3,X3),X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1791]) ).
cnf(c_0_1791_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| c_in(c_Pair(X2,X1,X3,X3),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X4,X3,X3),X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1791]) ).
cnf(c_0_1792_0,axiom,
( X4 = X5
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(X4,c_Equiv__Relations_Oquotient(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_in(X5,c_Equiv__Relations_Oquotient(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_in(X6,X4,X3)
| ~ c_in(X7,X5,X3)
| ~ c_in(c_Pair(X6,X7,X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1792]) ).
cnf(c_0_1792_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| X4 = X5
| ~ c_in(X4,c_Equiv__Relations_Oquotient(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_in(X5,c_Equiv__Relations_Oquotient(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_in(X6,X4,X3)
| ~ c_in(X7,X5,X3)
| ~ c_in(c_Pair(X6,X7,X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1792]) ).
cnf(c_0_1792_2,axiom,
( ~ c_in(X4,c_Equiv__Relations_Oquotient(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| X4 = X5
| ~ c_in(X5,c_Equiv__Relations_Oquotient(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_in(X6,X4,X3)
| ~ c_in(X7,X5,X3)
| ~ c_in(c_Pair(X6,X7,X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1792]) ).
cnf(c_0_1792_3,axiom,
( ~ c_in(X5,c_Equiv__Relations_Oquotient(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_in(X4,c_Equiv__Relations_Oquotient(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| X4 = X5
| ~ c_in(X6,X4,X3)
| ~ c_in(X7,X5,X3)
| ~ c_in(c_Pair(X6,X7,X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1792]) ).
cnf(c_0_1792_4,axiom,
( ~ c_in(X6,X4,X3)
| ~ c_in(X5,c_Equiv__Relations_Oquotient(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_in(X4,c_Equiv__Relations_Oquotient(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| X4 = X5
| ~ c_in(X7,X5,X3)
| ~ c_in(c_Pair(X6,X7,X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1792]) ).
cnf(c_0_1792_5,axiom,
( ~ c_in(X7,X5,X3)
| ~ c_in(X6,X4,X3)
| ~ c_in(X5,c_Equiv__Relations_Oquotient(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_in(X4,c_Equiv__Relations_Oquotient(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| X4 = X5
| ~ c_in(c_Pair(X6,X7,X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1792]) ).
cnf(c_0_1792_6,axiom,
( ~ c_in(c_Pair(X6,X7,X3,X3),X2,tc_prod(X3,X3))
| ~ c_in(X7,X5,X3)
| ~ c_in(X6,X4,X3)
| ~ c_in(X5,c_Equiv__Relations_Oquotient(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_in(X4,c_Equiv__Relations_Oquotient(X1,X2,X3),tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| X4 = X5 ),
inference(literals_permutation,[status(thm)],[c_0_1792]) ).
cnf(c_0_1793_0,axiom,
( X1 = X2
| X4 = X5
| X4 = X2
| X5 = X2
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1793]) ).
cnf(c_0_1793_1,axiom,
( X4 = X5
| X1 = X2
| X4 = X2
| X5 = X2
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1793]) ).
cnf(c_0_1793_2,axiom,
( X4 = X2
| X4 = X5
| X1 = X2
| X5 = X2
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1793]) ).
cnf(c_0_1793_3,axiom,
( X5 = X2
| X4 = X2
| X4 = X5
| X1 = X2
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1793]) ).
cnf(c_0_1793_4,axiom,
( c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X2
| X4 = X2
| X4 = X5
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1793]) ).
cnf(c_0_1793_5,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X2
| X4 = X2
| X4 = X5
| X1 = X2
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1793]) ).
cnf(c_0_1793_6,axiom,
( ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X5 = X2
| X4 = X2
| X4 = X5
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1793]) ).
cnf(c_0_1794_0,axiom,
( X1 = X2
| X4 = X5
| X5 = X1
| X4 = X1
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1794]) ).
cnf(c_0_1794_1,axiom,
( X4 = X5
| X1 = X2
| X5 = X1
| X4 = X1
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1794]) ).
cnf(c_0_1794_2,axiom,
( X5 = X1
| X4 = X5
| X1 = X2
| X4 = X1
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1794]) ).
cnf(c_0_1794_3,axiom,
( X4 = X1
| X5 = X1
| X4 = X5
| X1 = X2
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1794]) ).
cnf(c_0_1794_4,axiom,
( c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X1
| X5 = X1
| X4 = X5
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1794]) ).
cnf(c_0_1794_5,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X1
| X5 = X1
| X4 = X5
| X1 = X2
| ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1794]) ).
cnf(c_0_1794_6,axiom,
( ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X1
| X5 = X1
| X4 = X5
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1794]) ).
cnf(c_0_1795_0,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X2
| X1 = X2
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1795]) ).
cnf(c_0_1795_1,axiom,
( X4 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1795]) ).
cnf(c_0_1795_2,axiom,
( X1 = X2
| X4 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1795]) ).
cnf(c_0_1795_3,axiom,
( X1 = X2
| X1 = X2
| X4 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1795]) ).
cnf(c_0_1795_4,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| X1 = X2
| X4 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1795]) ).
cnf(c_0_1795_5,axiom,
( ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| X1 = X2
| X4 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1795]) ).
cnf(c_0_1796_0,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| X1 = X2
| X1 = X4
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1796]) ).
cnf(c_0_1796_1,axiom,
( X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X1 = X4
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1796]) ).
cnf(c_0_1796_2,axiom,
( X1 = X2
| X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1796]) ).
cnf(c_0_1796_3,axiom,
( X1 = X4
| X1 = X2
| X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1796]) ).
cnf(c_0_1796_4,axiom,
( ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| X1 = X2
| X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1796]) ).
cnf(c_0_1796_5,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| X1 = X2
| X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1796]) ).
cnf(c_0_1797_0,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| X1 = X2
| X2 = X1
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1797]) ).
cnf(c_0_1797_1,axiom,
( X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X2 = X1
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1797]) ).
cnf(c_0_1797_2,axiom,
( X1 = X2
| X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X1
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1797]) ).
cnf(c_0_1797_3,axiom,
( X2 = X1
| X1 = X2
| X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1797]) ).
cnf(c_0_1797_4,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X2 = X1
| X1 = X2
| X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1797]) ).
cnf(c_0_1797_5,axiom,
( ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X2 = X1
| X1 = X2
| X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1797]) ).
cnf(c_0_1798_0,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X2
| X1 = X2
| X2 = X4
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1798]) ).
cnf(c_0_1798_1,axiom,
( X4 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X2 = X4
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1798]) ).
cnf(c_0_1798_2,axiom,
( X1 = X2
| X4 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X4
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1798]) ).
cnf(c_0_1798_3,axiom,
( X2 = X4
| X1 = X2
| X4 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1798]) ).
cnf(c_0_1798_4,axiom,
( ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X4
| X1 = X2
| X4 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1798]) ).
cnf(c_0_1798_5,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X4
| X1 = X2
| X4 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1798]) ).
cnf(c_0_1799_0,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1799]) ).
cnf(c_0_1799_1,axiom,
( X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1799]) ).
cnf(c_0_1799_2,axiom,
( X1 = X2
| X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1799]) ).
cnf(c_0_1799_3,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1799]) ).
cnf(c_0_1799_4,axiom,
( ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1799]) ).
cnf(c_0_1800_0,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X1
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1800]) ).
cnf(c_0_1800_1,axiom,
( X4 = X1
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1800]) ).
cnf(c_0_1800_2,axiom,
( X1 = X2
| X4 = X1
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1800]) ).
cnf(c_0_1800_3,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| X4 = X1
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1800]) ).
cnf(c_0_1800_4,axiom,
( ~ c_in(c_Pair(X4,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| X4 = X1
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X4,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1800]) ).
cnf(c_0_1801_0,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1801]) ).
cnf(c_0_1801_1,axiom,
( X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1801]) ).
cnf(c_0_1801_2,axiom,
( X1 = X2
| X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1801]) ).
cnf(c_0_1801_3,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1801]) ).
cnf(c_0_1801_4,axiom,
( ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1801]) ).
cnf(c_0_1802_0,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X2,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X4
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1802]) ).
cnf(c_0_1802_1,axiom,
( X2 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X2,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1802]) ).
cnf(c_0_1802_2,axiom,
( X1 = X2
| X2 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X2,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1802]) ).
cnf(c_0_1802_3,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| X2 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X2,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1802]) ).
cnf(c_0_1802_4,axiom,
( ~ c_in(c_Pair(X1,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| X2 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X2,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1802]) ).
cnf(c_0_1803_0,axiom,
( c_in(X1,X5,X3)
| ~ c_in(c_Pair(X1,X2,X3,X4),c_Product__Type_OSigma(X5,X6,X3,X4),tc_prod(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1803]) ).
cnf(c_0_1803_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X4),c_Product__Type_OSigma(X5,X6,X3,X4),tc_prod(X3,X4))
| c_in(X1,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1803]) ).
cnf(c_0_1804_0,axiom,
( c_in(c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1(X2,X1,X3),X2,X3)
| c_Relation_Orefl__on(X2,X1,X3)
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1804]) ).
cnf(c_0_1804_1,axiom,
( c_Relation_Orefl__on(X2,X1,X3)
| c_in(c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1(X2,X1,X3),X2,X3)
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1804]) ).
cnf(c_0_1804_2,axiom,
( ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| c_Relation_Orefl__on(X2,X1,X3)
| c_in(c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1(X2,X1,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1804]) ).
cnf(c_0_1805_0,axiom,
( c_in(c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1(X2,X1,X3),X2,X3)
| c_Relation_Orefl__on(X2,X1,X3)
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1805]) ).
cnf(c_0_1805_1,axiom,
( c_Relation_Orefl__on(X2,X1,X3)
| c_in(c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1(X2,X1,X3),X2,X3)
| ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1805]) ).
cnf(c_0_1805_2,axiom,
( ~ c_lessequals(X1,c_Product__Type_OSigma(X2,c_COMBK(X2,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| c_Relation_Orefl__on(X2,X1,X3)
| c_in(c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1(X2,X1,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1805]) ).
cnf(c_0_1806_0,axiom,
( c_in(c_Pair(X2,X1,X4,X3),X5,tc_prod(X4,X3))
| ~ c_in(c_Pair(X1,X2,X3,X4),c_Relation_Oconverse(X5,X4,X3),tc_prod(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1806]) ).
cnf(c_0_1806_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X4),c_Relation_Oconverse(X5,X4,X3),tc_prod(X3,X4))
| c_in(c_Pair(X2,X1,X4,X3),X5,tc_prod(X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1806]) ).
cnf(c_0_1807_0,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X1,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X1,X2),X2,X2),c_Transitive__Closure_Otrancl(X1,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X3,X3,X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1807]) ).
cnf(c_0_1807_1,axiom,
( ~ c_in(c_Pair(X3,X3,X2,X2),X1,tc_prod(X2,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X1,X2),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X1,X2),X2,X2),c_Transitive__Closure_Otrancl(X1,X2),tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1807]) ).
cnf(c_0_1808_0,axiom,
( c_in(c_Pair(X2,X1,X4,X3),c_Relation_Oconverse(X5,X3,X4),tc_prod(X4,X3))
| ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1808]) ).
cnf(c_0_1808_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
| c_in(c_Pair(X2,X1,X4,X3),c_Relation_Oconverse(X5,X3,X4),tc_prod(X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1808]) ).
cnf(c_0_1809_0,axiom,
( c_in(c_Pair(X2,X1,X4,X3),c_Relation_Oconverse(X5,X3,X4),tc_prod(X4,X3))
| ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1809]) ).
cnf(c_0_1809_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
| c_in(c_Pair(X2,X1,X4,X3),c_Relation_Oconverse(X5,X3,X4),tc_prod(X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1809]) ).
cnf(c_0_1810_0,axiom,
( c_in(hAPP(X1,X6),X3,X4)
| ~ c_in(X1,c_FuncSet_OPi(X2,c_COMBK(X3,tc_fun(X4,tc_bool),X5),X5,X4),tc_fun(X5,X4))
| ~ c_in(X6,X2,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1810]) ).
cnf(c_0_1810_1,axiom,
( ~ c_in(X1,c_FuncSet_OPi(X2,c_COMBK(X3,tc_fun(X4,tc_bool),X5),X5,X4),tc_fun(X5,X4))
| c_in(hAPP(X1,X6),X3,X4)
| ~ c_in(X6,X2,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1810]) ).
cnf(c_0_1810_2,axiom,
( ~ c_in(X6,X2,X5)
| ~ c_in(X1,c_FuncSet_OPi(X2,c_COMBK(X3,tc_fun(X4,tc_bool),X5),X5,X4),tc_fun(X5,X4))
| c_in(hAPP(X1,X6),X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1810]) ).
cnf(c_0_1811_0,axiom,
( X1 = X2
| c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1811]) ).
cnf(c_0_1811_1,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| X1 = X2
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1811]) ).
cnf(c_0_1811_2,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1811]) ).
cnf(c_0_1812_0,axiom,
( X1 = X2
| c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1812]) ).
cnf(c_0_1812_1,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| X1 = X2
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1812]) ).
cnf(c_0_1812_2,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1812]) ).
cnf(c_0_1813_0,axiom,
( X1 = X2
| c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1813]) ).
cnf(c_0_1813_1,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| X1 = X2
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1813]) ).
cnf(c_0_1813_2,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1813]) ).
cnf(c_0_1814_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1814]) ).
cnf(c_0_1814_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1814]) ).
cnf(c_0_1815_0,axiom,
( c_in(X4,c_Relation_OImage(X6,X2,X3,X5),X5)
| ~ c_in(X1,X2,X3)
| ~ c_in(c_Pair(X1,X4,X3,X5),X6,tc_prod(X3,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1815]) ).
cnf(c_0_1815_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(X4,c_Relation_OImage(X6,X2,X3,X5),X5)
| ~ c_in(c_Pair(X1,X4,X3,X5),X6,tc_prod(X3,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1815]) ).
cnf(c_0_1815_2,axiom,
( ~ c_in(c_Pair(X1,X4,X3,X5),X6,tc_prod(X3,X5))
| ~ c_in(X1,X2,X3)
| c_in(X4,c_Relation_OImage(X6,X2,X3,X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1815]) ).
cnf(c_0_1816_0,axiom,
( c_in(X4,c_Relation_OImage(X6,X2,X3,X5),X5)
| ~ c_in(X1,X2,X3)
| ~ c_in(c_Pair(X1,X4,X3,X5),X6,tc_prod(X3,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1816]) ).
cnf(c_0_1816_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(X4,c_Relation_OImage(X6,X2,X3,X5),X5)
| ~ c_in(c_Pair(X1,X4,X3,X5),X6,tc_prod(X3,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_1816]) ).
cnf(c_0_1816_2,axiom,
( ~ c_in(c_Pair(X1,X4,X3,X5),X6,tc_prod(X3,X5))
| ~ c_in(X1,X2,X3)
| c_in(X4,c_Relation_OImage(X6,X2,X3,X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1816]) ).
cnf(c_0_1817_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1817]) ).
cnf(c_0_1817_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1817]) ).
cnf(c_0_1818_0,axiom,
( c_in(c_Pair(X4,X3,X2,X2),X1,tc_prod(X2,X2))
| ~ c_Relation_Osym(X1,X2)
| ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1818]) ).
cnf(c_0_1818_1,axiom,
( ~ c_Relation_Osym(X1,X2)
| c_in(c_Pair(X4,X3,X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1818]) ).
cnf(c_0_1818_2,axiom,
( ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2))
| ~ c_Relation_Osym(X1,X2)
| c_in(c_Pair(X4,X3,X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1818]) ).
cnf(c_0_1819_0,axiom,
( c_in(c_Pair(X4,X3,X2,X2),X1,tc_prod(X2,X2))
| ~ c_Relation_Osym(X1,X2)
| ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1819]) ).
cnf(c_0_1819_1,axiom,
( ~ c_Relation_Osym(X1,X2)
| c_in(c_Pair(X4,X3,X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1819]) ).
cnf(c_0_1819_2,axiom,
( ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2))
| ~ c_Relation_Osym(X1,X2)
| c_in(c_Pair(X4,X3,X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1819]) ).
cnf(c_0_1820_0,axiom,
( X2 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X3,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1820]) ).
cnf(c_0_1820_1,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X4
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X3,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1820]) ).
cnf(c_0_1820_2,axiom,
( ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X3,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_1820]) ).
cnf(c_0_1821_0,axiom,
( X1 = X4
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X3,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1821]) ).
cnf(c_0_1821_1,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X3,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1821]) ).
cnf(c_0_1821_2,axiom,
( ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X3,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_1821]) ).
cnf(c_0_1822_0,axiom,
( X1 = X2
| X1 = X3
| c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1822]) ).
cnf(c_0_1822_1,axiom,
( X1 = X3
| X1 = X2
| c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1822]) ).
cnf(c_0_1822_2,axiom,
( c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X3
| X1 = X2
| ~ c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1822]) ).
cnf(c_0_1822_3,axiom,
( ~ c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X3
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1822]) ).
cnf(c_0_1823_0,axiom,
( X1 = X2
| X3 = X2
| c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1823]) ).
cnf(c_0_1823_1,axiom,
( X3 = X2
| X1 = X2
| c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1823]) ).
cnf(c_0_1823_2,axiom,
( c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X2
| X1 = X2
| ~ c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1823]) ).
cnf(c_0_1823_3,axiom,
( ~ c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X1,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X2
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1823]) ).
cnf(c_0_1824_0,axiom,
( X1 = X2
| X3 = X1
| c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1824]) ).
cnf(c_0_1824_1,axiom,
( X3 = X1
| X1 = X2
| c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1824]) ).
cnf(c_0_1824_2,axiom,
( c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X1
| X1 = X2
| ~ c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1824]) ).
cnf(c_0_1824_3,axiom,
( ~ c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X1
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1824]) ).
cnf(c_0_1825_0,axiom,
( X1 = X2
| X3 = X2
| c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1825]) ).
cnf(c_0_1825_1,axiom,
( X3 = X2
| X1 = X2
| c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1825]) ).
cnf(c_0_1825_2,axiom,
( c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X2
| X1 = X2
| ~ c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1825]) ).
cnf(c_0_1825_3,axiom,
( ~ c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X4,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X3 = X2
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1825]) ).
cnf(c_0_1826_0,axiom,
( ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(X3,X4,X2)
| ~ c_in(c_Pair(X5,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(X5,X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1826]) ).
cnf(c_0_1826_1,axiom,
( ~ c_in(X3,X4,X2)
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_Pair(X5,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(X5,X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1826]) ).
cnf(c_0_1826_2,axiom,
( ~ c_in(c_Pair(X5,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(X3,X4,X2)
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(X5,X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1826]) ).
cnf(c_0_1826_3,axiom,
( ~ c_in(X5,X4,X2)
| ~ c_in(c_Pair(X5,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(X3,X4,X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1826]) ).
cnf(c_0_1827_0,axiom,
( ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(X3,X4,X2)
| ~ c_in(c_Pair(X5,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(X5,X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1827]) ).
cnf(c_0_1827_1,axiom,
( ~ c_in(X3,X4,X2)
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_Pair(X5,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(X5,X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1827]) ).
cnf(c_0_1827_2,axiom,
( ~ c_in(c_Pair(X5,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(X3,X4,X2)
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(X5,X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1827]) ).
cnf(c_0_1827_3,axiom,
( ~ c_in(X5,X4,X2)
| ~ c_in(c_Pair(X5,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(X3,X4,X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1827]) ).
cnf(c_0_1828_0,axiom,
( hBOOL(hAPP(X5,X4))
| hBOOL(hAPP(X5,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_Pair(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X5,X2,X3),X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1828]) ).
cnf(c_0_1828_1,axiom,
( hBOOL(hAPP(X5,X1))
| hBOOL(hAPP(X5,X4))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_Pair(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X5,X2,X3),X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1828]) ).
cnf(c_0_1828_2,axiom,
( ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| hBOOL(hAPP(X5,X1))
| hBOOL(hAPP(X5,X4))
| ~ c_in(c_Pair(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X5,X2,X3),X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1828]) ).
cnf(c_0_1828_3,axiom,
( ~ c_in(c_Pair(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X5,X2,X3),X3,X3),X2,tc_prod(X3,X3))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| hBOOL(hAPP(X5,X1))
| hBOOL(hAPP(X5,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1828]) ).
cnf(c_0_1829_0,axiom,
( hBOOL(hAPP(X5,X4))
| hBOOL(hAPP(X5,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_Pair(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X5,X2,X3),X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1829]) ).
cnf(c_0_1829_1,axiom,
( hBOOL(hAPP(X5,X1))
| hBOOL(hAPP(X5,X4))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_Pair(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X5,X2,X3),X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1829]) ).
cnf(c_0_1829_2,axiom,
( ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| hBOOL(hAPP(X5,X1))
| hBOOL(hAPP(X5,X4))
| ~ c_in(c_Pair(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X5,X2,X3),X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1829]) ).
cnf(c_0_1829_3,axiom,
( ~ c_in(c_Pair(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X5,X2,X3),X3,X3),X2,tc_prod(X3,X3))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| hBOOL(hAPP(X5,X1))
| hBOOL(hAPP(X5,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1829]) ).
cnf(c_0_1830_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X3)
| ~ c_in(X6,c_Equiv__Relations_Oquotient(X5,X4,X3),tc_fun(X3,tc_bool))
| ~ c_in(X6,c_Equiv__Relations_Oquotient(X5,X4,X3),tc_fun(X3,tc_bool))
| ~ c_in(X1,X6,X3)
| ~ c_in(X2,X6,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1830]) ).
cnf(c_0_1830_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X5,X4,X3)
| c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(X6,c_Equiv__Relations_Oquotient(X5,X4,X3),tc_fun(X3,tc_bool))
| ~ c_in(X6,c_Equiv__Relations_Oquotient(X5,X4,X3),tc_fun(X3,tc_bool))
| ~ c_in(X1,X6,X3)
| ~ c_in(X2,X6,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1830]) ).
cnf(c_0_1830_2,axiom,
( ~ c_in(X6,c_Equiv__Relations_Oquotient(X5,X4,X3),tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X3)
| c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(X6,c_Equiv__Relations_Oquotient(X5,X4,X3),tc_fun(X3,tc_bool))
| ~ c_in(X1,X6,X3)
| ~ c_in(X2,X6,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1830]) ).
cnf(c_0_1830_3,axiom,
( ~ c_in(X6,c_Equiv__Relations_Oquotient(X5,X4,X3),tc_fun(X3,tc_bool))
| ~ c_in(X6,c_Equiv__Relations_Oquotient(X5,X4,X3),tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X3)
| c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(X1,X6,X3)
| ~ c_in(X2,X6,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1830]) ).
cnf(c_0_1830_4,axiom,
( ~ c_in(X1,X6,X3)
| ~ c_in(X6,c_Equiv__Relations_Oquotient(X5,X4,X3),tc_fun(X3,tc_bool))
| ~ c_in(X6,c_Equiv__Relations_Oquotient(X5,X4,X3),tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X3)
| c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(X2,X6,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1830]) ).
cnf(c_0_1830_5,axiom,
( ~ c_in(X2,X6,X3)
| ~ c_in(X1,X6,X3)
| ~ c_in(X6,c_Equiv__Relations_Oquotient(X5,X4,X3),tc_fun(X3,tc_bool))
| ~ c_in(X6,c_Equiv__Relations_Oquotient(X5,X4,X3),tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X3)
| c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1830]) ).
cnf(c_0_1831_0,axiom,
( X4 = X5
| c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3))
| c_in(c_Pair(X5,X4,X3,X3),X2,tc_prod(X3,X3))
| ~ c_Relation_Ototal__on(X1,X2,X3)
| ~ c_in(X4,X1,X3)
| ~ c_in(X5,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1831]) ).
cnf(c_0_1831_1,axiom,
( c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3))
| X4 = X5
| c_in(c_Pair(X5,X4,X3,X3),X2,tc_prod(X3,X3))
| ~ c_Relation_Ototal__on(X1,X2,X3)
| ~ c_in(X4,X1,X3)
| ~ c_in(X5,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1831]) ).
cnf(c_0_1831_2,axiom,
( c_in(c_Pair(X5,X4,X3,X3),X2,tc_prod(X3,X3))
| c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3))
| X4 = X5
| ~ c_Relation_Ototal__on(X1,X2,X3)
| ~ c_in(X4,X1,X3)
| ~ c_in(X5,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1831]) ).
cnf(c_0_1831_3,axiom,
( ~ c_Relation_Ototal__on(X1,X2,X3)
| c_in(c_Pair(X5,X4,X3,X3),X2,tc_prod(X3,X3))
| c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3))
| X4 = X5
| ~ c_in(X4,X1,X3)
| ~ c_in(X5,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1831]) ).
cnf(c_0_1831_4,axiom,
( ~ c_in(X4,X1,X3)
| ~ c_Relation_Ototal__on(X1,X2,X3)
| c_in(c_Pair(X5,X4,X3,X3),X2,tc_prod(X3,X3))
| c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3))
| X4 = X5
| ~ c_in(X5,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1831]) ).
cnf(c_0_1831_5,axiom,
( ~ c_in(X5,X1,X3)
| ~ c_in(X4,X1,X3)
| ~ c_Relation_Ototal__on(X1,X2,X3)
| c_in(c_Pair(X5,X4,X3,X3),X2,tc_prod(X3,X3))
| c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3))
| X4 = X5 ),
inference(literals_permutation,[status(thm)],[c_0_1831]) ).
cnf(c_0_1832_0,axiom,
( c_Relation_Orel__comp(c_Relation_Oconverse(X2,X3,X3),X2,X3,X3,X3) = X2
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1832]) ).
cnf(c_0_1832_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Relation_Orel__comp(c_Relation_Oconverse(X2,X3,X3),X2,X3,X3,X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1832]) ).
cnf(c_0_1833_0,axiom,
( c_lessequals(c_Relation_OImage(X1,X5,X3,X4),c_Relation_OImage(X2,X6,X3,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool))
| ~ c_lessequals(X5,X6,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1833]) ).
cnf(c_0_1833_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool))
| c_lessequals(c_Relation_OImage(X1,X5,X3,X4),c_Relation_OImage(X2,X6,X3,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X5,X6,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1833]) ).
cnf(c_0_1833_2,axiom,
( ~ c_lessequals(X5,X6,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool))
| c_lessequals(c_Relation_OImage(X1,X5,X3,X4),c_Relation_OImage(X2,X6,X3,X4),tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1833]) ).
cnf(c_0_1834_0,axiom,
( X1 = X2
| ~ c_in(X3,X4,X5)
| c_Product__Type_OSigma(X1,c_COMBK(X4,tc_fun(X5,tc_bool),X6),X6,X5) != c_Product__Type_OSigma(X2,c_COMBK(X4,tc_fun(X5,tc_bool),X6),X6,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1834]) ).
cnf(c_0_1834_1,axiom,
( ~ c_in(X3,X4,X5)
| X1 = X2
| c_Product__Type_OSigma(X1,c_COMBK(X4,tc_fun(X5,tc_bool),X6),X6,X5) != c_Product__Type_OSigma(X2,c_COMBK(X4,tc_fun(X5,tc_bool),X6),X6,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1834]) ).
cnf(c_0_1834_2,axiom,
( c_Product__Type_OSigma(X1,c_COMBK(X4,tc_fun(X5,tc_bool),X6),X6,X5) != c_Product__Type_OSigma(X2,c_COMBK(X4,tc_fun(X5,tc_bool),X6),X6,X5)
| ~ c_in(X3,X4,X5)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1834]) ).
cnf(c_0_1835_0,axiom,
( X2 = X3
| c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1835]) ).
cnf(c_0_1835_1,axiom,
( c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1835]) ).
cnf(c_0_1835_2,axiom,
( c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1835]) ).
cnf(c_0_1835_3,axiom,
( ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Pair(X3,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3 ),
inference(literals_permutation,[status(thm)],[c_0_1835]) ).
cnf(c_0_1836_0,axiom,
( c_in(c_Pair(X1,X4,X3,X6),c_Product__Type_OSigma(X2,X5,X3,X6),tc_prod(X3,X6))
| ~ c_in(X1,X2,X3)
| ~ c_in(X4,hAPP(X5,X1),X6) ),
inference(literals_permutation,[status(thm)],[c_0_1836]) ).
cnf(c_0_1836_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(c_Pair(X1,X4,X3,X6),c_Product__Type_OSigma(X2,X5,X3,X6),tc_prod(X3,X6))
| ~ c_in(X4,hAPP(X5,X1),X6) ),
inference(literals_permutation,[status(thm)],[c_0_1836]) ).
cnf(c_0_1836_2,axiom,
( ~ c_in(X4,hAPP(X5,X1),X6)
| ~ c_in(X1,X2,X3)
| c_in(c_Pair(X1,X4,X3,X6),c_Product__Type_OSigma(X2,X5,X3,X6),tc_prod(X3,X6)) ),
inference(literals_permutation,[status(thm)],[c_0_1836]) ).
cnf(c_0_1837_0,axiom,
( c_in(c_Pair(X1,X4,X3,X6),c_Product__Type_OSigma(X2,X5,X3,X6),tc_prod(X3,X6))
| ~ c_in(X1,X2,X3)
| ~ c_in(X4,hAPP(X5,X1),X6) ),
inference(literals_permutation,[status(thm)],[c_0_1837]) ).
cnf(c_0_1837_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(c_Pair(X1,X4,X3,X6),c_Product__Type_OSigma(X2,X5,X3,X6),tc_prod(X3,X6))
| ~ c_in(X4,hAPP(X5,X1),X6) ),
inference(literals_permutation,[status(thm)],[c_0_1837]) ).
cnf(c_0_1837_2,axiom,
( ~ c_in(X4,hAPP(X5,X1),X6)
| ~ c_in(X1,X2,X3)
| c_in(c_Pair(X1,X4,X3,X6),c_Product__Type_OSigma(X2,X5,X3,X6),tc_prod(X3,X6)) ),
inference(literals_permutation,[status(thm)],[c_0_1837]) ).
cnf(c_0_1838_0,axiom,
( X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1838]) ).
cnf(c_0_1838_1,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| ~ c_in(c_Pair(X4,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1838]) ).
cnf(c_0_1838_2,axiom,
( ~ c_in(c_Pair(X4,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1838]) ).
cnf(c_0_1839_0,axiom,
( X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(X4,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1839]) ).
cnf(c_0_1839_1,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| ~ c_in(c_Pair(X4,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1839]) ).
cnf(c_0_1839_2,axiom,
( ~ c_in(c_Pair(X4,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1839]) ).
cnf(c_0_1840_0,axiom,
( c_in(X3,c_Wellfounded_Oacc(X2,t_a),t_a)
| hBOOL(hAPP(X4,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X4,X2),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
inference(literals_permutation,[status(thm)],[c_0_1840]) ).
cnf(c_0_1840_1,axiom,
( hBOOL(hAPP(X4,X1))
| c_in(X3,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X4,X2),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
inference(literals_permutation,[status(thm)],[c_0_1840]) ).
cnf(c_0_1840_2,axiom,
( ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| hBOOL(hAPP(X4,X1))
| c_in(X3,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X4,X2),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
inference(literals_permutation,[status(thm)],[c_0_1840]) ).
cnf(c_0_1840_3,axiom,
( ~ c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X4,X2),t_a,t_a),X2,tc_prod(t_a,t_a))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| hBOOL(hAPP(X4,X1))
| c_in(X3,c_Wellfounded_Oacc(X2,t_a),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_1840]) ).
cnf(c_0_1841_0,axiom,
( c_in(X3,c_Wellfounded_Oacc(X2,t_a),t_a)
| hBOOL(hAPP(X4,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X4,X2),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
inference(literals_permutation,[status(thm)],[c_0_1841]) ).
cnf(c_0_1841_1,axiom,
( hBOOL(hAPP(X4,X1))
| c_in(X3,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X4,X2),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
inference(literals_permutation,[status(thm)],[c_0_1841]) ).
cnf(c_0_1841_2,axiom,
( ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| hBOOL(hAPP(X4,X1))
| c_in(X3,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X4,X2),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
inference(literals_permutation,[status(thm)],[c_0_1841]) ).
cnf(c_0_1841_3,axiom,
( ~ c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X4,X2),t_a,t_a),X2,tc_prod(t_a,t_a))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| hBOOL(hAPP(X4,X1))
| c_in(X3,c_Wellfounded_Oacc(X2,t_a),t_a) ),
inference(literals_permutation,[status(thm)],[c_0_1841]) ).
cnf(c_0_1842_0,axiom,
( c_lessequals(c_Set_Oimage(X4,X1,X3,X5),c_Set_Oimage(X4,X2,X3,X5),tc_fun(X5,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1842]) ).
cnf(c_0_1842_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Set_Oimage(X4,X1,X3,X5),c_Set_Oimage(X4,X2,X3,X5),tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1842]) ).
cnf(c_0_1843_0,axiom,
( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1843]) ).
cnf(c_0_1843_1,axiom,
( ~ c_lessequals(X2,X5,tc_fun(X3,tc_bool))
| c_lessequals(c_Set_Oimage(X1,X2,X3,X4),c_Set_Oimage(X1,X5,X3,X4),tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1843]) ).
cnf(c_0_1844_0,axiom,
( c_in(X4,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_Pair(X4,X1,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1844]) ).
cnf(c_0_1844_1,axiom,
( ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| c_in(X4,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_Pair(X4,X1,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1844]) ).
cnf(c_0_1844_2,axiom,
( ~ c_in(c_Pair(X4,X1,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| c_in(X4,c_Wellfounded_Oacc(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1844]) ).
cnf(c_0_1845_0,axiom,
( c_in(X1,c_Wellfounded_Oacc(X4,X3),X3)
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(X2,c_Wellfounded_Oacc(X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1845]) ).
cnf(c_0_1845_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| c_in(X1,c_Wellfounded_Oacc(X4,X3),X3)
| ~ c_in(X2,c_Wellfounded_Oacc(X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1845]) ).
cnf(c_0_1845_2,axiom,
( ~ c_in(X2,c_Wellfounded_Oacc(X4,X3),X3)
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| c_in(X1,c_Wellfounded_Oacc(X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1845]) ).
cnf(c_0_1846_0,axiom,
( hBOOL(hAPP(X4,X3))
| hBOOL(hAPP(X4,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X4,X2),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
inference(literals_permutation,[status(thm)],[c_0_1846]) ).
cnf(c_0_1846_1,axiom,
( hBOOL(hAPP(X4,X1))
| hBOOL(hAPP(X4,X3))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X4,X2),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
inference(literals_permutation,[status(thm)],[c_0_1846]) ).
cnf(c_0_1846_2,axiom,
( ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| hBOOL(hAPP(X4,X1))
| hBOOL(hAPP(X4,X3))
| ~ c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X4,X2),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
inference(literals_permutation,[status(thm)],[c_0_1846]) ).
cnf(c_0_1846_3,axiom,
( ~ c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X4,X2),t_a,t_a),X2,tc_prod(t_a,t_a))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| hBOOL(hAPP(X4,X1))
| hBOOL(hAPP(X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1846]) ).
cnf(c_0_1847_0,axiom,
( hBOOL(hAPP(X4,X3))
| hBOOL(hAPP(X4,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X4,X2),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
inference(literals_permutation,[status(thm)],[c_0_1847]) ).
cnf(c_0_1847_1,axiom,
( hBOOL(hAPP(X4,X1))
| hBOOL(hAPP(X4,X3))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X4,X2),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
inference(literals_permutation,[status(thm)],[c_0_1847]) ).
cnf(c_0_1847_2,axiom,
( ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| hBOOL(hAPP(X4,X1))
| hBOOL(hAPP(X4,X3))
| ~ c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X4,X2),t_a,t_a),X2,tc_prod(t_a,t_a)) ),
inference(literals_permutation,[status(thm)],[c_0_1847]) ).
cnf(c_0_1847_3,axiom,
( ~ c_in(c_Pair(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X4,X2),t_a,t_a),X2,tc_prod(t_a,t_a))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| hBOOL(hAPP(X4,X1))
| hBOOL(hAPP(X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1847]) ).
cnf(c_0_1848_0,axiom,
( c_in(X4,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_Pair(X4,X1,X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1848]) ).
cnf(c_0_1848_1,axiom,
( ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| c_in(X4,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_Pair(X4,X1,X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1848]) ).
cnf(c_0_1848_2,axiom,
( ~ c_in(c_Pair(X4,X1,X3,X3),X2,tc_prod(X3,X3))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| c_in(X4,c_Wellfounded_Oacc(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1848]) ).
cnf(c_0_1849_0,axiom,
( c_in(X4,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_Pair(X4,X1,X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1849]) ).
cnf(c_0_1849_1,axiom,
( ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| c_in(X4,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_Pair(X4,X1,X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1849]) ).
cnf(c_0_1849_2,axiom,
( ~ c_in(c_Pair(X4,X1,X3,X3),X2,tc_prod(X3,X3))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| c_in(X4,c_Wellfounded_Oacc(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1849]) ).
cnf(c_0_1850_0,axiom,
( c_in(X1,c_Relation_ODomain(X2,X3,X3),X3)
| X1 = X4
| ~ c_in(c_Pair(X1,X4,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1850]) ).
cnf(c_0_1850_1,axiom,
( X1 = X4
| c_in(X1,c_Relation_ODomain(X2,X3,X3),X3)
| ~ c_in(c_Pair(X1,X4,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1850]) ).
cnf(c_0_1850_2,axiom,
( ~ c_in(c_Pair(X1,X4,X3,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
| X1 = X4
| c_in(X1,c_Relation_ODomain(X2,X3,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1850]) ).
cnf(c_0_1851_0,axiom,
( c_in(hAPP(X1,X6),hAPP(X3,X6),X5)
| ~ c_in(X1,c_FuncSet_OPi(X2,X3,X4,X5),tc_fun(X4,X5))
| ~ c_in(X6,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1851]) ).
cnf(c_0_1851_1,axiom,
( ~ c_in(X1,c_FuncSet_OPi(X2,X3,X4,X5),tc_fun(X4,X5))
| c_in(hAPP(X1,X6),hAPP(X3,X6),X5)
| ~ c_in(X6,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1851]) ).
cnf(c_0_1851_2,axiom,
( ~ c_in(X6,X2,X4)
| ~ c_in(X1,c_FuncSet_OPi(X2,X3,X4,X5),tc_fun(X4,X5))
| c_in(hAPP(X1,X6),hAPP(X3,X6),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1851]) ).
cnf(c_0_1852_0,axiom,
( c_in(hAPP(X1,X6),hAPP(X3,X6),X5)
| ~ c_in(X1,c_FuncSet_OPi(X2,X3,X4,X5),tc_fun(X4,X5))
| ~ c_in(X6,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1852]) ).
cnf(c_0_1852_1,axiom,
( ~ c_in(X1,c_FuncSet_OPi(X2,X3,X4,X5),tc_fun(X4,X5))
| c_in(hAPP(X1,X6),hAPP(X3,X6),X5)
| ~ c_in(X6,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1852]) ).
cnf(c_0_1852_2,axiom,
( ~ c_in(X6,X2,X4)
| ~ c_in(X1,c_FuncSet_OPi(X2,X3,X4,X5),tc_fun(X4,X5))
| c_in(hAPP(X1,X6),hAPP(X3,X6),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1852]) ).
cnf(c_0_1853_0,axiom,
( c_Nitpick_Orefl_H(X1,X2)
| ~ c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X1,X2),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X1,X2),X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1853]) ).
cnf(c_0_1853_1,axiom,
( ~ c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X1,X2),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X1,X2),X2,X2),X1,tc_prod(X2,X2))
| c_Nitpick_Orefl_H(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1853]) ).
cnf(c_0_1854_0,axiom,
( c_in(hAPP(X1,X6),X5,X4)
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ c_in(X6,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1854]) ).
cnf(c_0_1854_1,axiom,
( ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| c_in(hAPP(X1,X6),X5,X4)
| ~ c_in(X6,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1854]) ).
cnf(c_0_1854_2,axiom,
( ~ c_in(X6,X2,X3)
| ~ c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| c_in(hAPP(X1,X6),X5,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1854]) ).
cnf(c_0_1855_0,axiom,
( c_in(X2,c_Relation_ORange(X5,X3,X4),X4)
| ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1855]) ).
cnf(c_0_1855_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
| c_in(X2,c_Relation_ORange(X5,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1855]) ).
cnf(c_0_1856_0,axiom,
( c_in(X2,c_Relation_ORange(X5,X3,X4),X4)
| ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1856]) ).
cnf(c_0_1856_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
| c_in(X2,c_Relation_ORange(X5,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1856]) ).
cnf(c_0_1857_0,axiom,
( c_in(X1,c_Relation_ODomain(X5,X3,X4),X3)
| ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1857]) ).
cnf(c_0_1857_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
| c_in(X1,c_Relation_ODomain(X5,X3,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1857]) ).
cnf(c_0_1858_0,axiom,
( c_in(X1,c_Relation_ODomain(X5,X3,X4),X3)
| ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1858]) ).
cnf(c_0_1858_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
| c_in(X1,c_Relation_ODomain(X5,X3,X4),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1858]) ).
cnf(c_0_1859_0,axiom,
( v_thesis____
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1859]) ).
cnf(c_0_1859_1,axiom,
( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_thesis____
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1859]) ).
cnf(c_0_1859_2,axiom,
( ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_thesis____ ),
inference(literals_permutation,[status(thm)],[c_0_1859]) ).
cnf(c_0_1860_0,axiom,
( c_in(X5,X1,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1860]) ).
cnf(c_0_1860_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_in(X5,X1,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1860]) ).
cnf(c_0_1860_2,axiom,
( ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_in(X5,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1860]) ).
cnf(c_0_1861_0,axiom,
( c_in(X4,X1,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1861]) ).
cnf(c_0_1861_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_in(X4,X1,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1861]) ).
cnf(c_0_1861_2,axiom,
( ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1861]) ).
cnf(c_0_1862_0,axiom,
( c_in(X5,X1,X3)
| ~ c_Relation_Orefl__on(X1,X2,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1862]) ).
cnf(c_0_1862_1,axiom,
( ~ c_Relation_Orefl__on(X1,X2,X3)
| c_in(X5,X1,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1862]) ).
cnf(c_0_1862_2,axiom,
( ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3))
| ~ c_Relation_Orefl__on(X1,X2,X3)
| c_in(X5,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1862]) ).
cnf(c_0_1863_0,axiom,
( c_in(X4,X1,X3)
| ~ c_Relation_Orefl__on(X1,X2,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1863]) ).
cnf(c_0_1863_1,axiom,
( ~ c_Relation_Orefl__on(X1,X2,X3)
| c_in(X4,X1,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1863]) ).
cnf(c_0_1863_2,axiom,
( ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3))
| ~ c_Relation_Orefl__on(X1,X2,X3)
| c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1863]) ).
cnf(c_0_1864_0,axiom,
( c_lessequals(X2,c_Product__Type_OSigma(X1,c_COMBK(X1,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1864]) ).
cnf(c_0_1864_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_lessequals(X2,c_Product__Type_OSigma(X1,c_COMBK(X1,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1864]) ).
cnf(c_0_1865_0,axiom,
( c_lessequals(X2,c_Product__Type_OSigma(X1,c_COMBK(X1,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Relation_Orefl__on(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1865]) ).
cnf(c_0_1865_1,axiom,
( ~ c_Relation_Orefl__on(X1,X2,X3)
| c_lessequals(X2,c_Product__Type_OSigma(X1,c_COMBK(X1,tc_fun(X3,tc_bool),X3),X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1865]) ).
cnf(c_0_1866_0,axiom,
( c_in(X1,X4,X3)
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId__on(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1866]) ).
cnf(c_0_1866_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId__on(X4,X3),tc_prod(X3,X3))
| c_in(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1866]) ).
cnf(c_0_1867_0,axiom,
( X1 = X2
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId__on(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1867]) ).
cnf(c_0_1867_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId__on(X4,X3),tc_prod(X3,X3))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1867]) ).
cnf(c_0_1868_0,axiom,
( c_Finite__Set_Ofinite(X3,X5)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,c_Set_Oimage(X4,X1,X2,X5),tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1868]) ).
cnf(c_0_1868_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X3,X5)
| ~ c_lessequals(X3,c_Set_Oimage(X4,X1,X2,X5),tc_fun(X5,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1868]) ).
cnf(c_0_1868_2,axiom,
( ~ c_lessequals(X3,c_Set_Oimage(X4,X1,X2,X5),tc_fun(X5,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1868]) ).
cnf(c_0_1869_0,axiom,
( ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_Pair(X3,X3,X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1869]) ).
cnf(c_0_1869_1,axiom,
( ~ c_in(c_Pair(X3,X3,X2,X2),X1,tc_prod(X2,X2))
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1869]) ).
cnf(c_0_1870_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X3),c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1870]) ).
cnf(c_0_1870_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X3),c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1870]) ).
cnf(c_0_1871_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X4),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4),X4)
| ~ class_Lattices_Olattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1871]) ).
cnf(c_0_1871_1,axiom,
( ~ class_Lattices_Olattice(X4)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X4),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1871]) ).
cnf(c_0_1872_0,axiom,
( X1 = X2
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId(X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1872]) ).
cnf(c_0_1872_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId(X3),tc_prod(X3,X3))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1872]) ).
cnf(c_0_1873_0,axiom,
( c_Set_Oinsert(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5) = c_Set_Oimage(X4,X2,X3,X5)
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1873]) ).
cnf(c_0_1873_1,axiom,
( ~ c_in(X1,X2,X3)
| c_Set_Oinsert(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5) = c_Set_Oimage(X4,X2,X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1873]) ).
cnf(c_0_1874_0,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X1,X2,X3),X2,X3,X3),X1,tc_prod(X3,X3))
| c_in(X2,c_Wellfounded_Oacc(X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1874]) ).
cnf(c_0_1874_1,axiom,
( c_in(X2,c_Wellfounded_Oacc(X1,X3),X3)
| c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X1,X2,X3),X2,X3,X3),X1,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1874]) ).
cnf(c_0_1875_0,axiom,
( c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X2,X1,X3),X1,X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1875]) ).
cnf(c_0_1875_1,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X2,X1,X3),X1,X3,X3),X2,tc_prod(X3,X3))
| c_in(X1,c_Wellfounded_Oacc(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1875]) ).
cnf(c_0_1876_0,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X1 = X2
| X2 = X1
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1876]) ).
cnf(c_0_1876_1,axiom,
( X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X2 = X1
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1876]) ).
cnf(c_0_1876_2,axiom,
( X1 = X2
| X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X1
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1876]) ).
cnf(c_0_1876_3,axiom,
( X2 = X1
| X1 = X2
| X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1876]) ).
cnf(c_0_1876_4,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X2 = X1
| X1 = X2
| X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1876]) ).
cnf(c_0_1877_0,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X1 = X2
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1877]) ).
cnf(c_0_1877_1,axiom,
( X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1877]) ).
cnf(c_0_1877_2,axiom,
( X1 = X2
| X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1877]) ).
cnf(c_0_1877_3,axiom,
( X1 = X2
| X1 = X2
| X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1877]) ).
cnf(c_0_1877_4,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| X1 = X2
| X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1877]) ).
cnf(c_0_1878_0,axiom,
( c_in(c_List_Osko__Equiv__Relations__XquotientE__1__1(X2,X1,X3,X4),X2,X4)
| ~ c_in(X1,c_Equiv__Relations_Oquotient(X2,X3,X4),tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1878]) ).
cnf(c_0_1878_1,axiom,
( ~ c_in(X1,c_Equiv__Relations_Oquotient(X2,X3,X4),tc_fun(X4,tc_bool))
| c_in(c_List_Osko__Equiv__Relations__XquotientE__1__1(X2,X1,X3,X4),X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1878]) ).
cnf(c_0_1879_0,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1879]) ).
cnf(c_0_1879_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1879]) ).
cnf(c_0_1880_0,axiom,
( c_in(X1,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3),tc_prod(X3,X3))
| ~ c_in(X1,c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1880]) ).
cnf(c_0_1880_1,axiom,
( ~ c_in(X1,c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
| c_in(X1,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1880]) ).
cnf(c_0_1881_0,axiom,
( c_in(X1,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(tc_prod(X3,X3),tc_bool)),X3),tc_prod(X3,X3))
| ~ c_in(X1,c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1881]) ).
cnf(c_0_1881_1,axiom,
( ~ c_in(X1,c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
| c_in(X1,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(tc_prod(X3,X3),tc_bool)),X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1881]) ).
cnf(c_0_1882_0,axiom,
( X1 = X2
| c_Pair(X3,X1,X4,X5) != c_Pair(X6,X2,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1882]) ).
cnf(c_0_1882_1,axiom,
( c_Pair(X3,X1,X4,X5) != c_Pair(X6,X2,X4,X5)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1882]) ).
cnf(c_0_1883_0,axiom,
( X1 = X2
| c_Pair(X1,X3,X4,X5) != c_Pair(X2,X6,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_1883]) ).
cnf(c_0_1883_1,axiom,
( c_Pair(X1,X3,X4,X5) != c_Pair(X2,X6,X4,X5)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1883]) ).
cnf(c_0_1884_0,axiom,
( c_in(c_Pair(X1,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| c_in(X1,c_Relation_ODomain(X3,X2,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1884]) ).
cnf(c_0_1884_1,axiom,
( c_in(X1,c_Relation_ODomain(X3,X2,X2),X2)
| c_in(c_Pair(X1,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1884]) ).
cnf(c_0_1885_0,axiom,
( c_in(c_Pair(X4,X4,X3,X3),X2,tc_prod(X3,X3))
| ~ c_Relation_Orefl__on(X1,X2,X3)
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1885]) ).
cnf(c_0_1885_1,axiom,
( ~ c_Relation_Orefl__on(X1,X2,X3)
| c_in(c_Pair(X4,X4,X3,X3),X2,tc_prod(X3,X3))
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1885]) ).
cnf(c_0_1885_2,axiom,
( ~ c_in(X4,X1,X3)
| ~ c_Relation_Orefl__on(X1,X2,X3)
| c_in(c_Pair(X4,X4,X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1885]) ).
cnf(c_0_1886_0,axiom,
( c_in(c_Pair(X4,X4,X3,X3),X2,tc_prod(X3,X3))
| ~ c_Relation_Orefl__on(X1,X2,X3)
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1886]) ).
cnf(c_0_1886_1,axiom,
( ~ c_Relation_Orefl__on(X1,X2,X3)
| c_in(c_Pair(X4,X4,X3,X3),X2,tc_prod(X3,X3))
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1886]) ).
cnf(c_0_1886_2,axiom,
( ~ c_in(X4,X1,X3)
| ~ c_Relation_Orefl__on(X1,X2,X3)
| c_in(c_Pair(X4,X4,X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1886]) ).
cnf(c_0_1887_0,axiom,
( c_in(c_Pair(X1,X1,X3,X3),c_Relation_OId__on(X2,X3),tc_prod(X3,X3))
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1887]) ).
cnf(c_0_1887_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(c_Pair(X1,X1,X3,X3),c_Relation_OId__on(X2,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1887]) ).
cnf(c_0_1888_0,axiom,
( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
| ~ c_in(X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1888]) ).
cnf(c_0_1888_1,axiom,
( ~ c_in(X2,X3,X4)
| c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1888]) ).
cnf(c_0_1889_0,axiom,
( c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5)
| ~ c_in(X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1889]) ).
cnf(c_0_1889_1,axiom,
( ~ c_in(X2,X3,X4)
| c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1889]) ).
cnf(c_0_1890_0,axiom,
( c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1890]) ).
cnf(c_0_1890_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1890]) ).
cnf(c_0_1891_0,axiom,
( c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5)
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1891]) ).
cnf(c_0_1891_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_1891]) ).
cnf(c_0_1892_0,axiom,
( c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Relation_Orefl__on(X1,X2,X3)
| ~ c_Relation_Orefl__on(X4,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1892]) ).
cnf(c_0_1892_1,axiom,
( ~ c_Relation_Orefl__on(X1,X2,X3)
| c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Relation_Orefl__on(X4,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1892]) ).
cnf(c_0_1892_2,axiom,
( ~ c_Relation_Orefl__on(X4,X5,X3)
| ~ c_Relation_Orefl__on(X1,X2,X3)
| c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(tc_prod(X3,X3),tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1892]) ).
cnf(c_0_1893_0,axiom,
( c_Relation_Orefl__on(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Relation_Orefl__on(X1,X2,X3)
| ~ c_Relation_Orefl__on(X4,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1893]) ).
cnf(c_0_1893_1,axiom,
( ~ c_Relation_Orefl__on(X1,X2,X3)
| c_Relation_Orefl__on(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Relation_Orefl__on(X4,X5,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1893]) ).
cnf(c_0_1893_2,axiom,
( ~ c_Relation_Orefl__on(X4,X5,X3)
| ~ c_Relation_Orefl__on(X1,X2,X3)
| c_Relation_Orefl__on(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(tc_prod(X3,X3),tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1893]) ).
cnf(c_0_1894_0,axiom,
( c_Pair(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X2,X1,X3),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X2,X1,X3),X3,X3) = X1
| ~ c_in(X1,c_Relation_OId__on(X2,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1894]) ).
cnf(c_0_1894_1,axiom,
( ~ c_in(X1,c_Relation_OId__on(X2,X3),tc_prod(X3,X3))
| c_Pair(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X2,X1,X3),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X2,X1,X3),X3,X3) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1894]) ).
cnf(c_0_1895_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1895]) ).
cnf(c_0_1895_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1895]) ).
cnf(c_0_1895_2,axiom,
( ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1895]) ).
cnf(c_0_1896_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1896]) ).
cnf(c_0_1896_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1896]) ).
cnf(c_0_1896_2,axiom,
( ~ c_lessequals(X4,X5,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X5,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1896]) ).
cnf(c_0_1897_0,axiom,
( c_in(c_Pair(X3,X3,X2,X2),X1,tc_prod(X2,X2))
| ~ c_Nitpick_Orefl_H(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1897]) ).
cnf(c_0_1897_1,axiom,
( ~ c_Nitpick_Orefl_H(X1,X2)
| c_in(c_Pair(X3,X3,X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1897]) ).
cnf(c_0_1898_0,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X3,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X1
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1898]) ).
cnf(c_0_1898_1,axiom,
( X2 = X1
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X3,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1898]) ).
cnf(c_0_1898_2,axiom,
( X1 = X2
| X2 = X1
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X3,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1898]) ).
cnf(c_0_1899_0,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X3,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1899]) ).
cnf(c_0_1899_1,axiom,
( X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X3,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1899]) ).
cnf(c_0_1899_2,axiom,
( X1 = X2
| X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X3,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1899]) ).
cnf(c_0_1900_0,axiom,
( X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_1900]) ).
cnf(c_0_1900_1,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1900]) ).
cnf(c_0_1901_0,axiom,
( hBOOL(hAPP(X1,X4))
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1901]) ).
cnf(c_0_1901_1,axiom,
( hBOOL(hAPP(X2,X4))
| hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1901]) ).
cnf(c_0_1901_2,axiom,
( ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4))
| hBOOL(hAPP(X2,X4))
| hBOOL(hAPP(X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1901]) ).
cnf(c_0_1902_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1902]) ).
cnf(c_0_1902_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1902]) ).
cnf(c_0_1903_0,axiom,
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1903]) ).
cnf(c_0_1903_1,axiom,
( ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4))
| hBOOL(hAPP(X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1903]) ).
cnf(c_0_1904_0,axiom,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1904]) ).
cnf(c_0_1904_1,axiom,
( ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4))
| hBOOL(hAPP(X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1904]) ).
cnf(c_0_1905_0,axiom,
( hBOOL(hAPP(X4,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X4,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1905]) ).
cnf(c_0_1905_1,axiom,
( ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| hBOOL(hAPP(X4,X1))
| ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X4,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1905]) ).
cnf(c_0_1905_2,axiom,
( ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X4,X2,X3)))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| hBOOL(hAPP(X4,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1905]) ).
cnf(c_0_1906_0,axiom,
( hBOOL(hAPP(X4,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X4,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1906]) ).
cnf(c_0_1906_1,axiom,
( ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| hBOOL(hAPP(X4,X1))
| ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X4,X2,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_1906]) ).
cnf(c_0_1906_2,axiom,
( ~ hBOOL(hAPP(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X4,X2,X3)))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| hBOOL(hAPP(X4,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_1906]) ).
cnf(c_0_1907_0,axiom,
( c_Relation_Otrans(c_Relation_Oinv__image(X1,X3,X2,X4),X4)
| ~ c_Relation_Otrans(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1907]) ).
cnf(c_0_1907_1,axiom,
( ~ c_Relation_Otrans(X1,X2)
| c_Relation_Otrans(c_Relation_Oinv__image(X1,X3,X2,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1907]) ).
cnf(c_0_1908_0,axiom,
( c_Finite__Set_Ofinite(c_Set_Oimage(X3,X1,X2,X4),X4)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1908]) ).
cnf(c_0_1908_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_Set_Oimage(X3,X1,X2,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1908]) ).
cnf(c_0_1909_0,axiom,
( c_Wellfounded_Owf(c_Relation_Oinv__image(X1,X3,X2,X4),X4)
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1909]) ).
cnf(c_0_1909_1,axiom,
( ~ c_Wellfounded_Owf(X1,X2)
| c_Wellfounded_Owf(c_Relation_Oinv__image(X1,X3,X2,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1909]) ).
cnf(c_0_1910_0,axiom,
( c_Relation_Osym(c_Relation_Oinv__image(X1,X3,X2,X4),X4)
| ~ c_Relation_Osym(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1910]) ).
cnf(c_0_1910_1,axiom,
( ~ c_Relation_Osym(X1,X2)
| c_Relation_Osym(c_Relation_Oinv__image(X1,X3,X2,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1910]) ).
cnf(c_0_1911_0,axiom,
( c_lessequals(c_Relation_ODomain(X1,X3,X4),c_Relation_ODomain(X2,X3,X4),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1911]) ).
cnf(c_0_1911_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool))
| c_lessequals(c_Relation_ODomain(X1,X3,X4),c_Relation_ODomain(X2,X3,X4),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1911]) ).
cnf(c_0_1912_0,axiom,
( c_in(X1,c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_in(X1,c_Transitive__Closure_Otrancl(X2,X3),tc_prod(X3,X3))
| ~ c_lessequals(X2,X4,tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1912]) ).
cnf(c_0_1912_1,axiom,
( ~ c_in(X1,c_Transitive__Closure_Otrancl(X2,X3),tc_prod(X3,X3))
| c_in(X1,c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3))
| ~ c_lessequals(X2,X4,tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1912]) ).
cnf(c_0_1912_2,axiom,
( ~ c_lessequals(X2,X4,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_in(X1,c_Transitive__Closure_Otrancl(X2,X3),tc_prod(X3,X3))
| c_in(X1,c_Transitive__Closure_Otrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1912]) ).
cnf(c_0_1913_0,axiom,
( c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),X3) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1913]) ).
cnf(c_0_1913_1,axiom,
( ~ c_in(X1,X2,X3)
| c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),X3) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1913]) ).
cnf(c_0_1914_0,axiom,
( c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1914]) ).
cnf(c_0_1914_1,axiom,
( ~ c_in(X1,X2,X3)
| c_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1914]) ).
cnf(c_0_1915_0,axiom,
( c_Transitive__Closure_Ortrancl(X2,X3) = c_Transitive__Closure_Ortrancl(X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(X2,c_Transitive__Closure_Ortrancl(X1,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1915]) ).
cnf(c_0_1915_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool))
| c_Transitive__Closure_Ortrancl(X2,X3) = c_Transitive__Closure_Ortrancl(X1,X3)
| ~ c_lessequals(X2,c_Transitive__Closure_Ortrancl(X1,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1915]) ).
cnf(c_0_1915_2,axiom,
( ~ c_lessequals(X2,c_Transitive__Closure_Ortrancl(X1,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool))
| c_Transitive__Closure_Ortrancl(X2,X3) = c_Transitive__Closure_Ortrancl(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1915]) ).
cnf(c_0_1916_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1916]) ).
cnf(c_0_1916_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1916]) ).
cnf(c_0_1916_2,axiom,
( ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1916]) ).
cnf(c_0_1917_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1917]) ).
cnf(c_0_1917_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1917]) ).
cnf(c_0_1917_2,axiom,
( ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1917]) ).
cnf(c_0_1918_0,axiom,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1918]) ).
cnf(c_0_1918_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1918]) ).
cnf(c_0_1918_2,axiom,
( ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1918]) ).
cnf(c_0_1919_0,axiom,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1919]) ).
cnf(c_0_1919_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1919]) ).
cnf(c_0_1919_2,axiom,
( ~ c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1919]) ).
cnf(c_0_1920_0,axiom,
( c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Relation_Oconverse(X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1920]) ).
cnf(c_0_1920_1,axiom,
( ~ c_in(c_Relation_Oconverse(X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1920]) ).
cnf(c_0_1921_0,axiom,
( c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1921]) ).
cnf(c_0_1921_1,axiom,
( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1921]) ).
cnf(c_0_1922_0,axiom,
( c_lessequals(X1,X2,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1922]) ).
cnf(c_0_1922_1,axiom,
( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| c_lessequals(X1,X2,tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1922]) ).
cnf(c_0_1923_0,axiom,
( c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1923]) ).
cnf(c_0_1923_1,axiom,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1923]) ).
cnf(c_0_1924_0,axiom,
( c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1924]) ).
cnf(c_0_1924_1,axiom,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool))
| c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1924]) ).
cnf(c_0_1925_0,axiom,
( c_Pair(c_ATP__Linkup_Osko__Relation__XIdE__1__1(X1,X2),c_ATP__Linkup_Osko__Relation__XIdE__1__1(X1,X2),X2,X2) = X1
| ~ c_in(X1,c_Relation_OId(X2),tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1925]) ).
cnf(c_0_1925_1,axiom,
( ~ c_in(X1,c_Relation_OId(X2),tc_prod(X2,X2))
| c_Pair(c_ATP__Linkup_Osko__Relation__XIdE__1__1(X1,X2),c_ATP__Linkup_Osko__Relation__XIdE__1__1(X1,X2),X2,X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_1925]) ).
cnf(c_0_1926_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Odistrib__lattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1926]) ).
cnf(c_0_1926_1,axiom,
( ~ class_Lattices_Odistrib__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1926]) ).
cnf(c_0_1927_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X4),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4)
| ~ class_Lattices_Odistrib__lattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1927]) ).
cnf(c_0_1927_1,axiom,
( ~ class_Lattices_Odistrib__lattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X4),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1927]) ).
cnf(c_0_1928_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3)
| ~ class_Lattices_Odistrib__lattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1928]) ).
cnf(c_0_1928_1,axiom,
( ~ class_Lattices_Odistrib__lattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1928]) ).
cnf(c_0_1929_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X4),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Odistrib__lattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1929]) ).
cnf(c_0_1929_1,axiom,
( ~ class_Lattices_Odistrib__lattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X4),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1929]) ).
cnf(c_0_1930_0,axiom,
( c_in(X1,X2,X4)
| c_in(X1,X3,X4)
| ~ c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1930]) ).
cnf(c_0_1930_1,axiom,
( c_in(X1,X3,X4)
| c_in(X1,X2,X4)
| ~ c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1930]) ).
cnf(c_0_1930_2,axiom,
( ~ c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4)
| c_in(X1,X3,X4)
| c_in(X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1930]) ).
cnf(c_0_1931_0,axiom,
( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1931]) ).
cnf(c_0_1931_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1931]) ).
cnf(c_0_1931_2,axiom,
( ~ hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1931]) ).
cnf(c_0_1932_0,axiom,
( c_lessequals(c_Transitive__Closure_Ortrancl(X1,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(X1,c_Transitive__Closure_Ortrancl(X2,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1932]) ).
cnf(c_0_1932_1,axiom,
( ~ c_lessequals(X1,c_Transitive__Closure_Ortrancl(X2,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| c_lessequals(c_Transitive__Closure_Ortrancl(X1,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1932]) ).
cnf(c_0_1933_0,axiom,
( c_in(X2,X1,X4)
| c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1933]) ).
cnf(c_0_1933_1,axiom,
( c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| c_in(X2,X1,X4)
| ~ c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1933]) ).
cnf(c_0_1933_2,axiom,
( ~ c_lessequals(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool))
| c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| c_in(X2,X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1933]) ).
cnf(c_0_1934_0,axiom,
( c_in(X1,X2,X3)
| c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1934]) ).
cnf(c_0_1934_1,axiom,
( c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| c_in(X1,X2,X3)
| ~ c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1934]) ).
cnf(c_0_1934_2,axiom,
( ~ c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1934]) ).
cnf(c_0_1935_0,axiom,
( X1 = X4
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1935]) ).
cnf(c_0_1935_1,axiom,
( hBOOL(hAPP(X2,X4))
| X1 = X4
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_1935]) ).
cnf(c_0_1935_2,axiom,
( ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4))
| hBOOL(hAPP(X2,X4))
| X1 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_1935]) ).
cnf(c_0_1936_0,axiom,
( c_lessequals(c_Set_Oinsert(X4,X1,X3),c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1936]) ).
cnf(c_0_1936_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Set_Oinsert(X4,X1,X3),c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1936]) ).
cnf(c_0_1937_0,axiom,
( X1 = X2
| c_in(c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1937]) ).
cnf(c_0_1937_1,axiom,
( c_in(c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1937]) ).
cnf(c_0_1937_2,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1937]) ).
cnf(c_0_1938_0,axiom,
( X1 = X2
| c_in(c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1938]) ).
cnf(c_0_1938_1,axiom,
( c_in(c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1938]) ).
cnf(c_0_1938_2,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Arrow__Order__Mirabelle_Oabove(X3,X1,X2),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1938]) ).
cnf(c_0_1939_0,axiom,
( c_in(c_Relation_Oconverse(X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1939]) ).
cnf(c_0_1939_1,axiom,
( ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Relation_Oconverse(X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1939]) ).
cnf(c_0_1940_0,axiom,
( c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1940]) ).
cnf(c_0_1940_1,axiom,
( ~ c_in(X1,X2,X3)
| c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1940]) ).
cnf(c_0_1940_2,axiom,
( ~ c_lessequals(X4,X2,tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,X3)
| c_lessequals(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1940]) ).
cnf(c_0_1941_0,axiom,
( c_lessequals(c_Transitive__Closure_Ortrancl(X1,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1941]) ).
cnf(c_0_1941_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool))
| c_lessequals(c_Transitive__Closure_Ortrancl(X1,X3),c_Transitive__Closure_Ortrancl(X2,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1941]) ).
cnf(c_0_1942_0,axiom,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1942]) ).
cnf(c_0_1942_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,tc_bool)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1942]) ).
cnf(c_0_1943_0,axiom,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1943]) ).
cnf(c_0_1943_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_1943]) ).
cnf(c_0_1944_0,axiom,
( c_in(c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X1,X2,X3),X2,tc_fun(X3,tc_bool))
| ~ c_in(X1,c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1944]) ).
cnf(c_0_1944_1,axiom,
( ~ c_in(X1,c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X3,tc_bool)),X3)
| c_in(c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X1,X2,X3),X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1944]) ).
cnf(c_0_1945_0,axiom,
( c_in(X1,X3,X4)
| ~ c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1945]) ).
cnf(c_0_1945_1,axiom,
( ~ c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4)
| c_in(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1945]) ).
cnf(c_0_1946_0,axiom,
( c_in(X1,X2,X4)
| ~ c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1946]) ).
cnf(c_0_1946_1,axiom,
( ~ c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4)
| c_in(X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1946]) ).
cnf(c_0_1947_0,axiom,
( c_in(X1,c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1947]) ).
cnf(c_0_1947_1,axiom,
( ~ c_in(X1,c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X1,X2,X3),X3)
| c_in(X1,c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1947]) ).
cnf(c_0_1948_0,axiom,
( c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3)
| ~ c_in(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1948]) ).
cnf(c_0_1948_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1948]) ).
cnf(c_0_1948_2,axiom,
( ~ c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3)
| c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1948]) ).
cnf(c_0_1949_0,axiom,
( c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3)
| ~ c_in(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1949]) ).
cnf(c_0_1949_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1949]) ).
cnf(c_0_1949_2,axiom,
( ~ c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3)
| c_in(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1949]) ).
cnf(c_0_1950_0,axiom,
( c_in(X1,X4,X3)
| ~ c_in(X1,c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1950]) ).
cnf(c_0_1950_1,axiom,
( ~ c_in(X1,c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X3,tc_bool)),X3)
| c_in(X1,X4,X3)
| ~ c_in(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1950]) ).
cnf(c_0_1950_2,axiom,
( ~ c_in(X4,X2,tc_fun(X3,tc_bool))
| ~ c_in(X1,c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X3,tc_bool)),X3)
| c_in(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1950]) ).
cnf(c_0_1951_0,axiom,
( c_in(X2,c_Wellfounded_Oacc(X1,X3),X3)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X1,X2,X3),c_Wellfounded_Oacc(X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1951]) ).
cnf(c_0_1951_1,axiom,
( ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X1,X2,X3),c_Wellfounded_Oacc(X1,X3),X3)
| c_in(X2,c_Wellfounded_Oacc(X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1951]) ).
cnf(c_0_1952_0,axiom,
( c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X2,X1,X3),c_Wellfounded_Oacc(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1952]) ).
cnf(c_0_1952_1,axiom,
( ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X2,X1,X3),c_Wellfounded_Oacc(X2,X3),X3)
| c_in(X1,c_Wellfounded_Oacc(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1952]) ).
cnf(c_0_1953_0,axiom,
( c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1953]) ).
cnf(c_0_1953_1,axiom,
( ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool))
| c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1953]) ).
cnf(c_0_1954_0,axiom,
( c_Wellfounded_Owf(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X1,X2),X2,X2),X2)
| ~ c_Wellfounded_Owf(c_Relation_Oconverse(X1,X2,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1954]) ).
cnf(c_0_1954_1,axiom,
( ~ c_Wellfounded_Owf(c_Relation_Oconverse(X1,X2,X2),X2)
| c_Wellfounded_Owf(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X1,X2),X2,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1954]) ).
cnf(c_0_1955_0,axiom,
( c_in(X1,X2,X3)
| c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1955]) ).
cnf(c_0_1955_1,axiom,
( c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| c_in(X1,X2,X3)
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1955]) ).
cnf(c_0_1955_2,axiom,
( ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1955]) ).
cnf(c_0_1956_0,axiom,
( c_in(X1,X2,X3)
| c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1956]) ).
cnf(c_0_1956_1,axiom,
( c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| c_in(X1,X2,X3)
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1956]) ).
cnf(c_0_1956_2,axiom,
( ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| c_lessequals(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool))
| c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1956]) ).
cnf(c_0_1957_0,axiom,
( c_in(X1,c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X1,X2,X3),X3)
| ~ c_in(X1,c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1957]) ).
cnf(c_0_1957_1,axiom,
( ~ c_in(X1,c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X3,tc_bool)),X3)
| c_in(X1,c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1957]) ).
cnf(c_0_1958_0,axiom,
( c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X4,X2,X3),c_Wellfounded_Oacc(X2,X3),X3)
| hBOOL(hAPP(X4,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1958]) ).
cnf(c_0_1958_1,axiom,
( hBOOL(hAPP(X4,X1))
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X4,X2,X3),c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1958]) ).
cnf(c_0_1958_2,axiom,
( ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| hBOOL(hAPP(X4,X1))
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X4,X2,X3),c_Wellfounded_Oacc(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1958]) ).
cnf(c_0_1959_0,axiom,
( c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X4,X2,X3),c_Wellfounded_Oacc(X2,X3),X3)
| hBOOL(hAPP(X4,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1959]) ).
cnf(c_0_1959_1,axiom,
( hBOOL(hAPP(X4,X1))
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X4,X2,X3),c_Wellfounded_Oacc(X2,X3),X3)
| ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1959]) ).
cnf(c_0_1959_2,axiom,
( ~ c_in(X1,c_Wellfounded_Oacc(X2,X3),X3)
| hBOOL(hAPP(X4,X1))
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X4,X2,X3),c_Wellfounded_Oacc(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1959]) ).
cnf(c_0_1960_0,axiom,
( c_in(X1,X4,X3)
| ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1960]) ).
cnf(c_0_1960_1,axiom,
( ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool))
| c_in(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1960]) ).
cnf(c_0_1961_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1961]) ).
cnf(c_0_1961_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1961]) ).
cnf(c_0_1961_2,axiom,
( ~ c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1961]) ).
cnf(c_0_1961_3,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1961]) ).
cnf(c_0_1962_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1962]) ).
cnf(c_0_1962_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1962]) ).
cnf(c_0_1962_2,axiom,
( ~ c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1962]) ).
cnf(c_0_1962_3,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1962]) ).
cnf(c_0_1963_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1963]) ).
cnf(c_0_1963_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ c_lessequals(X4,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1963]) ).
cnf(c_0_1963_2,axiom,
( ~ c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1963]) ).
cnf(c_0_1963_3,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1963]) ).
cnf(c_0_1964_0,axiom,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1964]) ).
cnf(c_0_1964_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1964]) ).
cnf(c_0_1964_2,axiom,
( ~ c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1964]) ).
cnf(c_0_1964_3,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1964]) ).
cnf(c_0_1965_0,axiom,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1965]) ).
cnf(c_0_1965_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1965]) ).
cnf(c_0_1965_2,axiom,
( ~ c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1965]) ).
cnf(c_0_1965_3,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1965]) ).
cnf(c_0_1966_0,axiom,
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1966]) ).
cnf(c_0_1966_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ c_lessequals(X1,X4,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1966]) ).
cnf(c_0_1966_2,axiom,
( ~ c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1966]) ).
cnf(c_0_1966_3,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1966]) ).
cnf(c_0_1967_0,axiom,
( c_in(X4,c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1967]) ).
cnf(c_0_1967_1,axiom,
( ~ c_in(X1,X2,tc_fun(X3,tc_bool))
| c_in(X4,c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1967]) ).
cnf(c_0_1967_2,axiom,
( ~ c_in(X4,X1,X3)
| ~ c_in(X1,X2,tc_fun(X3,tc_bool))
| c_in(X4,c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1967]) ).
cnf(c_0_1968_0,axiom,
( c_lessequals(c_Relation_OField(X1,X3),c_Relation_OField(X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1968]) ).
cnf(c_0_1968_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool))
| c_lessequals(c_Relation_OField(X1,X3),c_Relation_OField(X2,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1968]) ).
cnf(c_0_1969_0,axiom,
( c_lessequals(c_Wellfounded_Oacc(X2,X3),c_Wellfounded_Oacc(X1,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1969]) ).
cnf(c_0_1969_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool))
| c_lessequals(c_Wellfounded_Oacc(X2,X3),c_Wellfounded_Oacc(X1,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1969]) ).
cnf(c_0_1970_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1970]) ).
cnf(c_0_1970_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1970]) ).
cnf(c_0_1971_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4)
| ~ class_Lattices_Oupper__semilattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1971]) ).
cnf(c_0_1971_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1971]) ).
cnf(c_0_1972_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4)
| ~ class_Lattices_Olattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1972]) ).
cnf(c_0_1972_1,axiom,
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1972]) ).
cnf(c_0_1973_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1973]) ).
cnf(c_0_1973_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1973]) ).
cnf(c_0_1974_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1974]) ).
cnf(c_0_1974_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1974]) ).
cnf(c_0_1975_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4)
| ~ class_Lattices_Olattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1975]) ).
cnf(c_0_1975_1,axiom,
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1975]) ).
cnf(c_0_1976_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1976]) ).
cnf(c_0_1976_1,axiom,
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1976]) ).
cnf(c_0_1977_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1977]) ).
cnf(c_0_1977_1,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X4,X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1977]) ).
cnf(c_0_1978_0,axiom,
( c_in(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X2,X1,X3),X2,X3)
| ~ c_in(X1,c_Relation_OId__on(X2,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_1978]) ).
cnf(c_0_1978_1,axiom,
( ~ c_in(X1,c_Relation_OId__on(X2,X3),tc_prod(X3,X3))
| c_in(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X2,X1,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1978]) ).
cnf(c_0_1979_0,axiom,
( c_in(c_Arrow__Order__Mirabelle_Omktop(X1,X2),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1979]) ).
cnf(c_0_1979_1,axiom,
( ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Arrow__Order__Mirabelle_Omktop(X1,X2),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1979]) ).
cnf(c_0_1980_0,axiom,
( c_in(c_Arrow__Order__Mirabelle_Omkbot(X1,X2),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1980]) ).
cnf(c_0_1980_1,axiom,
( ~ c_in(X1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Arrow__Order__Mirabelle_Omkbot(X1,X2),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1980]) ).
cnf(c_0_1981_0,axiom,
( c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1981]) ).
cnf(c_0_1981_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1981]) ).
cnf(c_0_1981_2,axiom,
( ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1981]) ).
cnf(c_0_1982_0,axiom,
( c_in(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1982]) ).
cnf(c_0_1982_1,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,c_Set_Oinsert(X1,X4,X3),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool))
| c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1982]) ).
cnf(c_0_1983_0,axiom,
( c_in(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1983]) ).
cnf(c_0_1983_1,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X4,X3),X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool))
| c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1983]) ).
cnf(c_0_1984_0,axiom,
( c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Osym(X1,X2)
| ~ c_Relation_Osym(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1984]) ).
cnf(c_0_1984_1,axiom,
( ~ c_Relation_Osym(X1,X2)
| c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Osym(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1984]) ).
cnf(c_0_1984_2,axiom,
( ~ c_Relation_Osym(X3,X2)
| ~ c_Relation_Osym(X1,X2)
| c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1984]) ).
cnf(c_0_1985_0,axiom,
( c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Osym(X1,X2)
| ~ c_Relation_Osym(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1985]) ).
cnf(c_0_1985_1,axiom,
( ~ c_Relation_Osym(X1,X2)
| c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Osym(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1985]) ).
cnf(c_0_1985_2,axiom,
( ~ c_Relation_Osym(X3,X2)
| ~ c_Relation_Osym(X1,X2)
| c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1985]) ).
cnf(c_0_1986_0,axiom,
( c_Relation_Otrans(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Otrans(X1,X2)
| ~ c_Relation_Otrans(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1986]) ).
cnf(c_0_1986_1,axiom,
( ~ c_Relation_Otrans(X1,X2)
| c_Relation_Otrans(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Otrans(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_1986]) ).
cnf(c_0_1986_2,axiom,
( ~ c_Relation_Otrans(X3,X2)
| ~ c_Relation_Otrans(X1,X2)
| c_Relation_Otrans(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_1986]) ).
cnf(c_0_1987_0,axiom,
( c_lessequals(X1,X2,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1987]) ).
cnf(c_0_1987_1,axiom,
( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| c_lessequals(X1,X2,X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1987]) ).
cnf(c_0_1987_2,axiom,
( ~ class_Lattices_Olower__semilattice(X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| c_lessequals(X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1987]) ).
cnf(c_0_1988_0,axiom,
( c_lessequals(X1,X3,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1988]) ).
cnf(c_0_1988_1,axiom,
( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| c_lessequals(X1,X3,X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1988]) ).
cnf(c_0_1988_2,axiom,
( ~ class_Lattices_Olower__semilattice(X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| c_lessequals(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1988]) ).
cnf(c_0_1989_0,axiom,
( c_lessequals(X1,X2,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1989]) ).
cnf(c_0_1989_1,axiom,
( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| c_lessequals(X1,X2,X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1989]) ).
cnf(c_0_1989_2,axiom,
( ~ class_Lattices_Olower__semilattice(X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| c_lessequals(X1,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1989]) ).
cnf(c_0_1990_0,axiom,
( c_lessequals(X1,X3,X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1990]) ).
cnf(c_0_1990_1,axiom,
( ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| c_lessequals(X1,X3,X4)
| ~ class_Lattices_Olower__semilattice(X4) ),
inference(literals_permutation,[status(thm)],[c_0_1990]) ).
cnf(c_0_1990_2,axiom,
( ~ class_Lattices_Olower__semilattice(X4)
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X4),X4)
| c_lessequals(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_1990]) ).
cnf(c_0_1991_0,axiom,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1991]) ).
cnf(c_0_1991_1,axiom,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| c_lessequals(X2,X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1991]) ).
cnf(c_0_1991_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| c_lessequals(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1991]) ).
cnf(c_0_1992_0,axiom,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1992_1,axiom,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| c_lessequals(X1,X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1992_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| c_lessequals(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1992]) ).
cnf(c_0_1993_0,axiom,
( c_lessequals(X2,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1993_1,axiom,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| c_lessequals(X2,X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1993_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| c_lessequals(X2,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1993]) ).
cnf(c_0_1994_0,axiom,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1994]) ).
cnf(c_0_1994_1,axiom,
( ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| c_lessequals(X1,X4,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_1994]) ).
cnf(c_0_1994_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X4,X3)
| c_lessequals(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1994]) ).
cnf(c_0_1995_0,axiom,
( X1 = X2
| c_in(X1,X3,X4)
| ~ c_in(X1,c_Set_Oinsert(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1995]) ).
cnf(c_0_1995_1,axiom,
( c_in(X1,X3,X4)
| X1 = X2
| ~ c_in(X1,c_Set_Oinsert(X2,X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_1995]) ).
cnf(c_0_1995_2,axiom,
( ~ c_in(X1,c_Set_Oinsert(X2,X3,X4),X4)
| c_in(X1,X3,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_1995]) ).
cnf(c_0_1996_0,axiom,
( c_in(c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X1,X2,X3),X2,tc_fun(X3,tc_bool))
| c_in(X1,c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1996]) ).
cnf(c_0_1996_1,axiom,
( c_in(X1,c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X3,tc_bool)),X3)
| c_in(c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X1,X2,X3),X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1996]) ).
cnf(c_0_1997_0,axiom,
( c_Relation_Orefl__on(X1,X2,X3)
| ~ c_Relation_Orefl__on(X1,c_Relation_Oconverse(X2,X3,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1997]) ).
cnf(c_0_1997_1,axiom,
( ~ c_Relation_Orefl__on(X1,c_Relation_Oconverse(X2,X3,X3),X3)
| c_Relation_Orefl__on(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1997]) ).
cnf(c_0_1998_0,axiom,
( c_Relation_Ototal__on(X1,X2,X3)
| ~ c_Relation_Ototal__on(X1,c_Relation_Oconverse(X2,X3,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_1998]) ).
cnf(c_0_1998_1,axiom,
( ~ c_Relation_Ototal__on(X1,c_Relation_Oconverse(X2,X3,X3),X3)
| c_Relation_Ototal__on(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_1998]) ).
cnf(c_0_1999_0,axiom,
( c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1999]) ).
cnf(c_0_1999_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_1999]) ).
cnf(c_0_2000_0,axiom,
( c_Relation_Otrans(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Otrans(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2000]) ).
cnf(c_0_2000_1,axiom,
( ~ c_Relation_Otrans(X1,X2)
| c_Relation_Otrans(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2000]) ).
cnf(c_0_2001_0,axiom,
( c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2001]) ).
cnf(c_0_2001_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2001]) ).
cnf(c_0_2002_0,axiom,
( c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2002]) ).
cnf(c_0_2002_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2002]) ).
cnf(c_0_2003_0,axiom,
( c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2003]) ).
cnf(c_0_2003_1,axiom,
( ~ c_Wellfounded_Owf(X1,X2)
| c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2003]) ).
cnf(c_0_2004_0,axiom,
( c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2004]) ).
cnf(c_0_2004_1,axiom,
( ~ c_Wellfounded_Owf(X1,X2)
| c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2004]) ).
cnf(c_0_2005_0,axiom,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2005]) ).
cnf(c_0_2005_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2005]) ).
cnf(c_0_2006_0,axiom,
( X1 = X2
| c_in(X3,X1,X4)
| c_in(X3,X2,X4)
| c_Set_Oinsert(X3,X1,X4) != c_Set_Oinsert(X3,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2006]) ).
cnf(c_0_2006_1,axiom,
( c_in(X3,X1,X4)
| X1 = X2
| c_in(X3,X2,X4)
| c_Set_Oinsert(X3,X1,X4) != c_Set_Oinsert(X3,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2006]) ).
cnf(c_0_2006_2,axiom,
( c_in(X3,X2,X4)
| c_in(X3,X1,X4)
| X1 = X2
| c_Set_Oinsert(X3,X1,X4) != c_Set_Oinsert(X3,X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2006]) ).
cnf(c_0_2006_3,axiom,
( c_Set_Oinsert(X3,X1,X4) != c_Set_Oinsert(X3,X2,X4)
| c_in(X3,X2,X4)
| c_in(X3,X1,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2006]) ).
cnf(c_0_2007_0,axiom,
( hBOOL(hAPP(X3,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ hBOOL(hAPP(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X3,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2007]) ).
cnf(c_0_2007_1,axiom,
( ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| hBOOL(hAPP(X3,X1))
| ~ hBOOL(hAPP(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X3,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2007]) ).
cnf(c_0_2007_2,axiom,
( ~ hBOOL(hAPP(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X3,X2)))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| hBOOL(hAPP(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2007]) ).
cnf(c_0_2008_0,axiom,
( hBOOL(hAPP(X3,X1))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| ~ hBOOL(hAPP(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X3,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2008]) ).
cnf(c_0_2008_1,axiom,
( ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| hBOOL(hAPP(X3,X1))
| ~ hBOOL(hAPP(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X3,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2008]) ).
cnf(c_0_2008_2,axiom,
( ~ hBOOL(hAPP(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X3,X2)))
| ~ c_in(X1,c_Wellfounded_Oacc(X2,t_a),t_a)
| hBOOL(hAPP(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2008]) ).
cnf(c_0_2009_0,axiom,
( c_Finite__Set_Ofinite(X1,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2009]) ).
cnf(c_0_2009_1,axiom,
( ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3)
| c_Finite__Set_Ofinite(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2009]) ).
cnf(c_0_2010_0,axiom,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2010]) ).
cnf(c_0_2010_1,axiom,
( ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3)
| c_Finite__Set_Ofinite(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2010]) ).
cnf(c_0_2011_0,axiom,
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2011]) ).
cnf(c_0_2011_1,axiom,
( ~ c_in(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2011]) ).
cnf(c_0_2012_0,axiom,
( c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2012]) ).
cnf(c_0_2012_1,axiom,
( ~ c_in(X1,X2,tc_fun(X3,tc_bool))
| c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2012]) ).
cnf(c_0_2013_0,axiom,
( c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X4,X1,X2),X4,X2)
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(X3,X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2013]) ).
cnf(c_0_2013_1,axiom,
( ~ c_Wellfounded_Owf(X1,X2)
| c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X4,X1,X2),X4,X2)
| ~ c_in(X3,X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2013]) ).
cnf(c_0_2013_2,axiom,
( ~ c_in(X3,X4,X2)
| ~ c_Wellfounded_Owf(X1,X2)
| c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X4,X1,X2),X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2013]) ).
cnf(c_0_2014_0,axiom,
( c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X4,X1,X2),X4,X2)
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(X3,X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2014]) ).
cnf(c_0_2014_1,axiom,
( ~ c_Wellfounded_Owf(X1,X2)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X4,X1,X2),X4,X2)
| ~ c_in(X3,X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2014]) ).
cnf(c_0_2014_2,axiom,
( ~ c_in(X3,X4,X2)
| ~ c_Wellfounded_Owf(X1,X2)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X4,X1,X2),X4,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2014]) ).
cnf(c_0_2015_0,axiom,
( c_in(X4,X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2015]) ).
cnf(c_0_2015_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_in(X4,X2,X3)
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2015]) ).
cnf(c_0_2015_2,axiom,
( ~ c_in(X4,X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_in(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2015]) ).
cnf(c_0_2016_0,axiom,
( c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2016]) ).
cnf(c_0_2016_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(X1,X4,X3)
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2016]) ).
cnf(c_0_2016_2,axiom,
( ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ c_in(X1,X2,X3)
| c_in(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2016]) ).
cnf(c_0_2017_0,axiom,
( c_in(X4,X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2017]) ).
cnf(c_0_2017_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_in(X4,X2,X3)
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2017]) ).
cnf(c_0_2017_2,axiom,
( ~ c_in(X4,X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_in(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2017]) ).
cnf(c_0_2018_0,axiom,
( c_in(X4,X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2018]) ).
cnf(c_0_2018_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_in(X4,X2,X3)
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2018]) ).
cnf(c_0_2018_2,axiom,
( ~ c_in(X4,X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_in(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2018]) ).
cnf(c_0_2019_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2019]) ).
cnf(c_0_2019_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2019]) ).
cnf(c_0_2019_2,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2019]) ).
cnf(c_0_2020_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X1,X3),X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2020]) ).
cnf(c_0_2020_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X1,X3),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2020]) ).
cnf(c_0_2020_2,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X1,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2020]) ).
cnf(c_0_2021_0,axiom,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2021]) ).
cnf(c_0_2021_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2021]) ).
cnf(c_0_2021_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2021]) ).
cnf(c_0_2022_0,axiom,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2022]) ).
cnf(c_0_2022_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2022]) ).
cnf(c_0_2022_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2022]) ).
cnf(c_0_2023_0,axiom,
( c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2023]) ).
cnf(c_0_2023_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(X1,c_Set_Oinsert(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2023]) ).
cnf(c_0_2024_0,axiom,
( c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2024]) ).
cnf(c_0_2024_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(X1,c_Set_Oinsert(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2024]) ).
cnf(c_0_2025_0,axiom,
( c_Relation_Orefl__on(X1,c_Relation_Oconverse(X2,X3,X3),X3)
| ~ c_Relation_Orefl__on(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2025]) ).
cnf(c_0_2025_1,axiom,
( ~ c_Relation_Orefl__on(X1,X2,X3)
| c_Relation_Orefl__on(X1,c_Relation_Oconverse(X2,X3,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2025]) ).
cnf(c_0_2026_0,axiom,
( c_Relation_Ototal__on(X1,c_Relation_Oconverse(X2,X3,X3),X3)
| ~ c_Relation_Ototal__on(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2026]) ).
cnf(c_0_2026_1,axiom,
( ~ c_Relation_Ototal__on(X1,X2,X3)
| c_Relation_Ototal__on(X1,c_Relation_Oconverse(X2,X3,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2026]) ).
cnf(c_0_2027_0,axiom,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2027]) ).
cnf(c_0_2027_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| X1 = X2
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2027]) ).
cnf(c_0_2027_2,axiom,
( ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2027]) ).
cnf(c_0_2028_0,axiom,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2028]) ).
cnf(c_0_2028_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| X1 = X2
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2028]) ).
cnf(c_0_2028_2,axiom,
( ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2028]) ).
cnf(c_0_2029_0,axiom,
( c_Wellfounded_Owf(X3,X2)
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_lessequals(X3,X1,tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2029]) ).
cnf(c_0_2029_1,axiom,
( ~ c_Wellfounded_Owf(X1,X2)
| c_Wellfounded_Owf(X3,X2)
| ~ c_lessequals(X3,X1,tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2029]) ).
cnf(c_0_2029_2,axiom,
( ~ c_lessequals(X3,X1,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_Wellfounded_Owf(X1,X2)
| c_Wellfounded_Owf(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2029]) ).
cnf(c_0_2030_0,axiom,
( c_lessequals(hAPP(X1,X5),hAPP(X2,X5),X4)
| ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2030]) ).
cnf(c_0_2030_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| c_lessequals(hAPP(X1,X5),hAPP(X2,X5),X4)
| ~ class_HOL_Oord(X4) ),
inference(literals_permutation,[status(thm)],[c_0_2030]) ).
cnf(c_0_2030_2,axiom,
( ~ class_HOL_Oord(X4)
| ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| c_lessequals(hAPP(X1,X5),hAPP(X2,X5),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2030]) ).
cnf(c_0_2031_0,axiom,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2031_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,X4,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2031_2,axiom,
( ~ c_lessequals(X2,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2031_3,axiom,
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X2,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X1,X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2031]) ).
cnf(c_0_2032_0,axiom,
( c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2032]) ).
cnf(c_0_2032_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2032]) ).
cnf(c_0_2032_2,axiom,
( ~ c_lessequals(X4,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X2,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2032]) ).
cnf(c_0_2032_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X4,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| c_lessequals(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2032]) ).
cnf(c_0_2033_0,axiom,
( c_in(X1,c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
| ~ c_in(X1,X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2033]) ).
cnf(c_0_2033_1,axiom,
( ~ c_in(X1,X2,tc_prod(X3,X3))
| c_in(X1,c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2033]) ).
cnf(c_0_2034_0,axiom,
( c_in(X1,c_Transitive__Closure_Otrancl(X2,X3),tc_prod(X3,X3))
| ~ c_in(X1,X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2034]) ).
cnf(c_0_2034_1,axiom,
( ~ c_in(X1,X2,tc_prod(X3,X3))
| c_in(X1,c_Transitive__Closure_Otrancl(X2,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2034]) ).
cnf(c_0_2035_0,axiom,
( c_Finite__Set_Ofinite(c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X3,tc_bool)),X3)
| ~ c_in(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2035]) ).
cnf(c_0_2035_1,axiom,
( ~ c_in(X1,X2,tc_fun(X3,tc_bool))
| c_Finite__Set_Ofinite(c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X3,tc_bool)),X3)
| ~ c_Finite__Set_Ofinite(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2035]) ).
cnf(c_0_2035_2,axiom,
( ~ c_Finite__Set_Ofinite(X1,X3)
| ~ c_in(X1,X2,tc_fun(X3,tc_bool))
| c_Finite__Set_Ofinite(c_Complete__Lattice_OInf__class_OInf(X2,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2035]) ).
cnf(c_0_2036_0,axiom,
( c_Complete__Lattice_OSup__class_OSup(c_Equiv__Relations_Oquotient(X1,X2,X3),tc_fun(X3,tc_bool)) = X1
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2036]) ).
cnf(c_0_2036_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Complete__Lattice_OSup__class_OSup(c_Equiv__Relations_Oquotient(X1,X2,X3),tc_fun(X3,tc_bool)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2036]) ).
cnf(c_0_2037_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2037]) ).
cnf(c_0_2037_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2037]) ).
cnf(c_0_2038_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2038]) ).
cnf(c_0_2038_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2038]) ).
cnf(c_0_2039_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2039]) ).
cnf(c_0_2039_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2039]) ).
cnf(c_0_2040_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2040]) ).
cnf(c_0_2040_1,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2040]) ).
cnf(c_0_2041_0,axiom,
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2041]) ).
cnf(c_0_2041_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2041]) ).
cnf(c_0_2041_2,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2041]) ).
cnf(c_0_2042_0,axiom,
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2042]) ).
cnf(c_0_2042_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2042]) ).
cnf(c_0_2042_2,axiom,
( ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2042]) ).
cnf(c_0_2043_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Complete__Lattice_OInf__class_OInf(X2,X3),X3) = c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X1,X2,X3),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2043]) ).
cnf(c_0_2043_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Complete__Lattice_OInf__class_OInf(X2,X3),X3) = c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2043]) ).
cnf(c_0_2044_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Complete__Lattice_OSup__class_OSup(X2,X3),X3) = c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X1,X2,X3),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2044]) ).
cnf(c_0_2044_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Complete__Lattice_OSup__class_OSup(X2,X3),X3) = c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2044]) ).
cnf(c_0_2045_0,axiom,
( c_Relation_Otrans(X1,X2)
| ~ c_Relation_Otrans(c_Relation_Oconverse(X1,X2,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2045]) ).
cnf(c_0_2045_1,axiom,
( ~ c_Relation_Otrans(c_Relation_Oconverse(X1,X2,X2),X2)
| c_Relation_Otrans(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2045]) ).
cnf(c_0_2046_0,axiom,
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2046]) ).
cnf(c_0_2046_1,axiom,
( ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X2,X3),X3)
| c_Finite__Set_Ofinite(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2046]) ).
cnf(c_0_2047_0,axiom,
( c_Relation_Osym(X1,X2)
| ~ c_Relation_Osym(c_Relation_Oconverse(X1,X2,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2047]) ).
cnf(c_0_2047_1,axiom,
( ~ c_Relation_Osym(c_Relation_Oconverse(X1,X2,X2),X2)
| c_Relation_Osym(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2047]) ).
cnf(c_0_2048_0,axiom,
( c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_2048]) ).
cnf(c_0_2048_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) != X2
| c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2048]) ).
cnf(c_0_2049_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2049]) ).
cnf(c_0_2049_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2049]) ).
cnf(c_0_2050_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)) = X1
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2050]) ).
cnf(c_0_2050_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2050]) ).
cnf(c_0_2051_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2051]) ).
cnf(c_0_2051_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2051]) ).
cnf(c_0_2052_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)) = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2052]) ).
cnf(c_0_2052_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2052]) ).
cnf(c_0_2053_0,axiom,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2053]) ).
cnf(c_0_2053_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X3,X2))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2053]) ).
cnf(c_0_2053_2,axiom,
( ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2053]) ).
cnf(c_0_2054_0,axiom,
( hBOOL(hAPP(X2,X4))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2054]) ).
cnf(c_0_2054_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(X1,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2054]) ).
cnf(c_0_2054_2,axiom,
( ~ hBOOL(hAPP(X1,X4))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| hBOOL(hAPP(X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2054]) ).
cnf(c_0_2055_0,axiom,
( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2055]) ).
cnf(c_0_2055_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2055]) ).
cnf(c_0_2056_0,axiom,
( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2056]) ).
cnf(c_0_2056_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2056]) ).
cnf(c_0_2057_0,axiom,
( c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X1,X2),c_Wellfounded_Oacc(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2057]) ).
cnf(c_0_2057_1,axiom,
( ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X1,X2),c_Wellfounded_Oacc(X1,X2),X2)
| c_Wellfounded_Owf(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2057]) ).
cnf(c_0_2058_0,axiom,
( c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X1,X2),c_Wellfounded_Oacc(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2058]) ).
cnf(c_0_2058_1,axiom,
( ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X1,X2),c_Wellfounded_Oacc(X1,X2),X2)
| c_Wellfounded_Owf(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2058]) ).
cnf(c_0_2059_0,axiom,
( X2 = X1
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2059]) ).
cnf(c_0_2059_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| X2 = X1
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2059]) ).
cnf(c_0_2059_2,axiom,
( ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X2 = X1
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2059]) ).
cnf(c_0_2059_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2059]) ).
cnf(c_0_2060_0,axiom,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2060]) ).
cnf(c_0_2060_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2060]) ).
cnf(c_0_2060_2,axiom,
( ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2060]) ).
cnf(c_0_2060_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2060]) ).
cnf(c_0_2061_0,axiom,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2061]) ).
cnf(c_0_2061_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| X1 = X2
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2061]) ).
cnf(c_0_2061_2,axiom,
( ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2061]) ).
cnf(c_0_2061_3,axiom,
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2061]) ).
cnf(c_0_2062_0,axiom,
( c_lessequals(c_Complete__Lattice_OInf__class_OInf(X2,X3),X1,X3)
| ~ c_in(X1,X2,X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2062]) ).
cnf(c_0_2062_1,axiom,
( ~ c_in(X1,X2,X3)
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X2,X3),X1,X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2062]) ).
cnf(c_0_2062_2,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ c_in(X1,X2,X3)
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X2,X3),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2062]) ).
cnf(c_0_2063_0,axiom,
( c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X2,X3),X3)
| ~ c_in(X1,X2,X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2063]) ).
cnf(c_0_2063_1,axiom,
( ~ c_in(X1,X2,X3)
| c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X2,X3),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2063]) ).
cnf(c_0_2063_2,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X3)
| ~ c_in(X1,X2,X3)
| c_lessequals(X1,c_Complete__Lattice_OSup__class_OSup(X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2063]) ).
cnf(c_0_2064_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) = X1
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2064]) ).
cnf(c_0_2064_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X3) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2064]) ).
cnf(c_0_2065_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = X1
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2065]) ).
cnf(c_0_2065_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2065]) ).
cnf(c_0_2066_0,axiom,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2066]) ).
cnf(c_0_2066_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2066]) ).
cnf(c_0_2067_0,axiom,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2067]) ).
cnf(c_0_2067_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2067]) ).
cnf(c_0_2068_0,axiom,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2068]) ).
cnf(c_0_2068_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2068]) ).
cnf(c_0_2069_0,axiom,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2069]) ).
cnf(c_0_2069_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2069]) ).
cnf(c_0_2070_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X1,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2070]) ).
cnf(c_0_2070_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2070]) ).
cnf(c_0_2071_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X2,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2071]) ).
cnf(c_0_2071_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2071]) ).
cnf(c_0_2072_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2072]) ).
cnf(c_0_2072_1,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2072]) ).
cnf(c_0_2073_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X1,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2073]) ).
cnf(c_0_2073_1,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2073]) ).
cnf(c_0_2074_0,axiom,
( c_Finite__Set_Ofinite(X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_Finite__Set_Ofinite(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2074]) ).
cnf(c_0_2074_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Finite__Set_Ofinite(X1,X3)
| ~ c_Finite__Set_Ofinite(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2074]) ).
cnf(c_0_2074_2,axiom,
( ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| c_Finite__Set_Ofinite(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2074]) ).
cnf(c_0_2075_0,axiom,
( c_Finite__Set_Ofinite(X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2075]) ).
cnf(c_0_2075_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X3,X2)
| ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2075]) ).
cnf(c_0_2075_2,axiom,
( ~ c_lessequals(X3,X1,tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2075]) ).
cnf(c_0_2076_0,axiom,
( c_lessequals(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) != X1
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2076]) ).
cnf(c_0_2076_1,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) != X1
| c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2076]) ).
cnf(c_0_2076_2,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) != X1
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2076]) ).
cnf(c_0_2077_0,axiom,
( c_lessequals(X1,X2,X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) != X2
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2077]) ).
cnf(c_0_2077_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) != X2
| c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2077]) ).
cnf(c_0_2077_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) != X2
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2077]) ).
cnf(c_0_2078_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2078]) ).
cnf(c_0_2078_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = X1
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2078]) ).
cnf(c_0_2078_2,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2078]) ).
cnf(c_0_2079_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3) = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2079]) ).
cnf(c_0_2079_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3) = X1
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2079]) ).
cnf(c_0_2079_2,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2079]) ).
cnf(c_0_2080_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2080]) ).
cnf(c_0_2080_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) = X2
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2080]) ).
cnf(c_0_2080_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2080]) ).
cnf(c_0_2081_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2081]) ).
cnf(c_0_2081_1,axiom,
( ~ c_lessequals(X1,X2,X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = X2
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2081]) ).
cnf(c_0_2081_2,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| ~ c_lessequals(X1,X2,X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2081]) ).
cnf(c_0_2082_0,axiom,
( X1 = X2
| c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X1,X2),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2082]) ).
cnf(c_0_2082_1,axiom,
( c_in(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X1,X2),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2082]) ).
cnf(c_0_2083_0,axiom,
( c_Relation_Otrans(c_Relation_Oconverse(X1,X2,X2),X2)
| ~ c_Relation_Otrans(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2083]) ).
cnf(c_0_2083_1,axiom,
( ~ c_Relation_Otrans(X1,X2)
| c_Relation_Otrans(c_Relation_Oconverse(X1,X2,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2083]) ).
cnf(c_0_2084_0,axiom,
( c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X1,X2),X2)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2084]) ).
cnf(c_0_2084_1,axiom,
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2084]) ).
cnf(c_0_2085_0,axiom,
( c_Relation_Osym(c_Relation_Oconverse(X1,X2,X2),X2)
| ~ c_Relation_Osym(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2085]) ).
cnf(c_0_2085_1,axiom,
( ~ c_Relation_Osym(X1,X2)
| c_Relation_Osym(c_Relation_Oconverse(X1,X2,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2085]) ).
cnf(c_0_2086_0,axiom,
( c_Set_Oinsert(X1,X2,X3) = X2
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2086]) ).
cnf(c_0_2086_1,axiom,
( ~ c_in(X1,X2,X3)
| c_Set_Oinsert(X1,X2,X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2086]) ).
cnf(c_0_2087_0,axiom,
( c_Relation_Orefl__on(X1,X2,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2087]) ).
cnf(c_0_2087_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Relation_Orefl__on(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2087]) ).
cnf(c_0_2088_0,axiom,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2088]) ).
cnf(c_0_2088_1,axiom,
( c_lessequals(X2,X1,X3)
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2088]) ).
cnf(c_0_2088_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X2,X1,X3)
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2088]) ).
cnf(c_0_2089_0,axiom,
( hBOOL(hAPP(X2,X1))
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2089]) ).
cnf(c_0_2089_1,axiom,
( ~ c_in(X1,X2,X3)
| hBOOL(hAPP(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2089]) ).
cnf(c_0_2090_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2090]) ).
cnf(c_0_2090_1,axiom,
( ~ class_Lattices_Olower__semilattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2090]) ).
cnf(c_0_2091_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2091]) ).
cnf(c_0_2091_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2091]) ).
cnf(c_0_2092_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2092]) ).
cnf(c_0_2092_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2092]) ).
cnf(c_0_2093_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3)
| ~ class_Lattices_Olattice(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2093]) ).
cnf(c_0_2093_1,axiom,
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2093]) ).
cnf(c_0_2094_0,axiom,
( c_in(X3,c_Wellfounded_Oacc(X1,X2),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2094]) ).
cnf(c_0_2094_1,axiom,
( ~ c_Wellfounded_Owf(X1,X2)
| c_in(X3,c_Wellfounded_Oacc(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2094]) ).
cnf(c_0_2095_0,axiom,
( c_in(X2,X1,X3)
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2095]) ).
cnf(c_0_2095_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| c_in(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2095]) ).
cnf(c_0_2096_0,axiom,
( c_Relation_Osym(X1,X2)
| c_Relation_Oconverse(X1,X2,X2) != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2096]) ).
cnf(c_0_2096_1,axiom,
( c_Relation_Oconverse(X1,X2,X2) != X1
| c_Relation_Osym(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2096]) ).
cnf(c_0_2097_0,axiom,
( c_Relation_Otrans(X2,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2097]) ).
cnf(c_0_2097_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Relation_Otrans(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2097]) ).
cnf(c_0_2098_0,axiom,
( c_Relation_Osym(X2,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2098]) ).
cnf(c_0_2098_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Relation_Osym(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2098]) ).
cnf(c_0_2099_0,axiom,
( X1 = X2
| ~ c_fequal(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2099]) ).
cnf(c_0_2099_1,axiom,
( ~ c_fequal(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2099]) ).
cnf(c_0_2100_0,axiom,
( c_Relation_Oconverse(X1,X2,X2) = X1
| ~ c_Relation_Osym(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2100]) ).
cnf(c_0_2100_1,axiom,
( ~ c_Relation_Osym(X1,X2)
| c_Relation_Oconverse(X1,X2,X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2100]) ).
cnf(c_0_2101_0,axiom,
( c_Relation_Osym(c_Transitive__Closure_Ortrancl(X1,X2),X2)
| ~ c_Relation_Osym(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2101]) ).
cnf(c_0_2101_1,axiom,
( ~ c_Relation_Osym(X1,X2)
| c_Relation_Osym(c_Transitive__Closure_Ortrancl(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2101]) ).
cnf(c_0_2102_0,axiom,
( c_Relation_Osym(c_Transitive__Closure_Otrancl(X1,X2),X2)
| ~ c_Relation_Osym(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2102]) ).
cnf(c_0_2102_1,axiom,
( ~ c_Relation_Osym(X1,X2)
| c_Relation_Osym(c_Transitive__Closure_Otrancl(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2102]) ).
cnf(c_0_2103_0,axiom,
( c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X1,X2),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2103]) ).
cnf(c_0_2103_1,axiom,
( ~ c_Wellfounded_Owf(X1,X2)
| c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2103]) ).
cnf(c_0_2104_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X2) = X1
| ~ class_Lattices_Oupper__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2104]) ).
cnf(c_0_2104_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2104]) ).
cnf(c_0_2105_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X1,X2) = X1
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2105]) ).
cnf(c_0_2105_1,axiom,
( ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X1,X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2105]) ).
cnf(c_0_2106_0,axiom,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2106]) ).
cnf(c_0_2106_1,axiom,
( ~ class_Orderings_Opreorder(X2)
| c_lessequals(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2106]) ).
cnf(c_0_2107_0,axiom,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2107]) ).
cnf(c_0_2107_1,axiom,
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2107]) ).
cnf(c_0_2108_0,axiom,
( class_Finite__Set_Ofinite_Ofinite(tc_prod(X1,X2))
| ~ class_Finite__Set_Ofinite_Ofinite(X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2108]) ).
cnf(c_0_2108_1,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(X1)
| class_Finite__Set_Ofinite_Ofinite(tc_prod(X1,X2))
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2108]) ).
cnf(c_0_2108_2,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X1)
| class_Finite__Set_Ofinite_Ofinite(tc_prod(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2108]) ).
cnf(c_0_2109_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_2109]) ).
cnf(c_0_2109_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_2109]) ).
cnf(c_0_2109_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_2109]) ).
cnf(c_0_2110_0,axiom,
( c_Transitive__Closure_Otrancl(X1,X2) = X1
| ~ c_Relation_Otrans(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2110]) ).
cnf(c_0_2110_1,axiom,
( ~ c_Relation_Otrans(X1,X2)
| c_Transitive__Closure_Otrancl(X1,X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2110]) ).
cnf(c_0_2111_0,axiom,
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2111]) ).
cnf(c_0_2111_1,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2111]) ).
cnf(c_0_2112_0,axiom,
( class_Lattices_Oupper__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2112]) ).
cnf(c_0_2112_1,axiom,
( ~ class_Lattices_Olattice(X1)
| class_Lattices_Oupper__semilattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2112]) ).
cnf(c_0_2113_0,axiom,
( class_Lattices_Olower__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2113]) ).
cnf(c_0_2113_1,axiom,
( ~ class_Lattices_Olattice(X1)
| class_Lattices_Olower__semilattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2113]) ).
cnf(c_0_2114_0,axiom,
( class_Lattices_Odistrib__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2114]) ).
cnf(c_0_2114_1,axiom,
( ~ class_Lattices_Odistrib__lattice(X1)
| class_Lattices_Odistrib__lattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2114]) ).
cnf(c_0_2115_0,axiom,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2115]) ).
cnf(c_0_2115_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2115]) ).
cnf(c_0_2116_0,axiom,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2116]) ).
cnf(c_0_2116_1,axiom,
( ~ class_Lattices_Olattice(X1)
| class_Lattices_Olattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2116]) ).
cnf(c_0_2117_0,axiom,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2117]) ).
cnf(c_0_2117_1,axiom,
( ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2117]) ).
cnf(c_0_2118_0,axiom,
( class_HOL_Oord(tc_fun(X2,X1))
| ~ class_HOL_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2118]) ).
cnf(c_0_2118_1,axiom,
( ~ class_HOL_Oord(X1)
| class_HOL_Oord(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2118]) ).
cnf(c_0_2119_0,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2119]) ).
cnf(c_0_2119_1,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(X2)
| c_Finite__Set_Ofinite(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2119]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_621,negated_conjecture,
~ v_thesis____,
file('<stdin>',cls_conjecture_0) ).
fof(c_0_1_622,negated_conjecture,
~ v_thesis____,
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_2_623,negated_conjecture,
~ v_thesis____,
c_0_1 ).
cnf(c_0_3_624,negated_conjecture,
~ v_thesis____,
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4_625,negated_conjecture,
~ v_thesis____,
c_0_3,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_1300,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox/tmp/iprover_modulo_ba6f59.p',c_0_4) ).
cnf(c_1680,negated_conjecture,
~ v_thesis____,
inference(copy,[status(esa)],[c_1300]) ).
cnf(c_1684,negated_conjecture,
~ v_thesis____,
inference(copy,[status(esa)],[c_1680]) ).
cnf(c_1685,negated_conjecture,
~ v_thesis____,
inference(copy,[status(esa)],[c_1684]) ).
cnf(c_1686,negated_conjecture,
~ v_thesis____,
inference(copy,[status(esa)],[c_1685]) ).
cnf(c_5516,negated_conjecture,
~ v_thesis____,
inference(copy,[status(esa)],[c_1686]) ).
cnf(c_538,plain,
( ~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_thesis____ ),
file('/export/starexec/sandbox/tmp/iprover_modulo_ba6f59.p',c_0_1859_0) ).
cnf(c_4064,plain,
( ~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| v_thesis____ ),
inference(copy,[status(esa)],[c_538]) ).
cnf(c_4065,plain,
( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| v_thesis____ ),
inference(rewriting,[status(thm)],[c_4064]) ).
cnf(c_5520,plain,
( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_5516,c_4065]) ).
cnf(c_5521,plain,
( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(rewriting,[status(thm)],[c_5520]) ).
cnf(c_637,plain,
( X0 = X1
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X2,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_ba6f59.p',c_0_1899_0) ).
cnf(c_4262,plain,
( X0 = X1
| c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X2,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(copy,[status(esa)],[c_637]) ).
cnf(c_4263,plain,
( c_in(c_Pair(X0,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X2,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X0 = X1 ),
inference(rewriting,[status(thm)],[c_4262]) ).
cnf(c_5668,plain,
( ~ c_in(c_Arrow__Order__Mirabelle_Omktop(X0,v_b____),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| v_a____ = v_b____ ),
inference(resolution,[status(thm)],[c_5521,c_4263]) ).
cnf(c_5669,plain,
( ~ c_in(c_Arrow__Order__Mirabelle_Omktop(X0,v_b____),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| v_a____ = v_b____ ),
inference(rewriting,[status(thm)],[c_5668]) ).
cnf(c_1179,plain,
v_a____ != v_b____,
file('/export/starexec/sandbox/tmp/iprover_modulo_ba6f59.p',c_0_616_0) ).
cnf(c_5344,plain,
v_a____ != v_b____,
inference(copy,[status(esa)],[c_1179]) ).
cnf(c_5708,plain,
~ c_in(c_Arrow__Order__Mirabelle_Omktop(X0,v_b____),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(forward_subsumption_resolution,[status(thm)],[c_5669,c_5344]) ).
cnf(c_5709,plain,
~ c_in(c_Arrow__Order__Mirabelle_Omktop(X0,v_b____),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(rewriting,[status(thm)],[c_5708]) ).
cnf(c_835,plain,
( ~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Arrow__Order__Mirabelle_Omktop(X0,X1),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_ba6f59.p',c_0_1979_0) ).
cnf(c_4658,plain,
( ~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Arrow__Order__Mirabelle_Omktop(X0,X1),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(copy,[status(esa)],[c_835]) ).
cnf(c_4659,plain,
( c_in(c_Arrow__Order__Mirabelle_Omktop(X0,X1),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(rewriting,[status(thm)],[c_4658]) ).
cnf(c_5749,plain,
~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(resolution,[status(thm)],[c_5709,c_4659]) ).
cnf(c_5750,plain,
~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(rewriting,[status(thm)],[c_5749]) ).
cnf(c_1178,plain,
c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
file('/export/starexec/sandbox/tmp/iprover_modulo_ba6f59.p',c_0_617_0) ).
cnf(c_5342,plain,
c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(copy,[status(esa)],[c_1178]) ).
cnf(c_5756,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_5750,c_5342]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SCT073-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.12 % Command : iprover_modulo %s %d
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 2 03:30:19 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % Running in mono-core mode
% 0.18/0.50 % Orienting using strategy Equiv(ClausalAll)
% 0.18/0.50 % Orientation found
% 0.18/0.50 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_8b462d.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_ba6f59.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_2addeb | grep -v "SZS"
% 0.18/0.53
% 0.18/0.53 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.18/0.53
% 0.18/0.53 %
% 0.18/0.53 % ------ iProver source info
% 0.18/0.53
% 0.18/0.53 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.18/0.53 % git: non_committed_changes: true
% 0.18/0.53 % git: last_make_outside_of_git: true
% 0.18/0.53
% 0.18/0.53 %
% 0.18/0.53 % ------ Input Options
% 0.18/0.53
% 0.18/0.53 % --out_options all
% 0.18/0.53 % --tptp_safe_out true
% 0.18/0.53 % --problem_path ""
% 0.18/0.53 % --include_path ""
% 0.18/0.53 % --clausifier .//eprover
% 0.18/0.53 % --clausifier_options --tstp-format
% 0.18/0.53 % --stdin false
% 0.18/0.53 % --dbg_backtrace false
% 0.18/0.53 % --dbg_dump_prop_clauses false
% 0.18/0.53 % --dbg_dump_prop_clauses_file -
% 0.18/0.53 % --dbg_out_stat false
% 0.18/0.53
% 0.18/0.53 % ------ General Options
% 0.18/0.53
% 0.18/0.53 % --fof false
% 0.18/0.53 % --time_out_real 150.
% 0.18/0.53 % --time_out_prep_mult 0.2
% 0.18/0.53 % --time_out_virtual -1.
% 0.18/0.53 % --schedule none
% 0.18/0.53 % --ground_splitting input
% 0.18/0.53 % --splitting_nvd 16
% 0.18/0.53 % --non_eq_to_eq false
% 0.18/0.53 % --prep_gs_sim true
% 0.18/0.53 % --prep_unflatten false
% 0.18/0.53 % --prep_res_sim true
% 0.18/0.53 % --prep_upred true
% 0.18/0.53 % --res_sim_input true
% 0.18/0.53 % --clause_weak_htbl true
% 0.18/0.53 % --gc_record_bc_elim false
% 0.18/0.53 % --symbol_type_check false
% 0.18/0.53 % --clausify_out false
% 0.18/0.53 % --large_theory_mode false
% 0.18/0.53 % --prep_sem_filter none
% 0.18/0.53 % --prep_sem_filter_out false
% 0.18/0.53 % --preprocessed_out false
% 0.18/0.53 % --sub_typing false
% 0.18/0.53 % --brand_transform false
% 0.18/0.53 % --pure_diseq_elim true
% 0.18/0.53 % --min_unsat_core false
% 0.18/0.53 % --pred_elim true
% 0.18/0.53 % --add_important_lit false
% 0.18/0.53 % --soft_assumptions false
% 0.18/0.53 % --reset_solvers false
% 0.18/0.53 % --bc_imp_inh []
% 0.18/0.53 % --conj_cone_tolerance 1.5
% 0.18/0.53 % --prolific_symb_bound 500
% 0.18/0.53 % --lt_threshold 2000
% 0.18/0.53
% 0.18/0.53 % ------ SAT Options
% 0.18/0.53
% 0.18/0.53 % --sat_mode false
% 0.18/0.53 % --sat_fm_restart_options ""
% 0.18/0.53 % --sat_gr_def false
% 0.18/0.53 % --sat_epr_types true
% 0.18/0.53 % --sat_non_cyclic_types false
% 0.18/0.53 % --sat_finite_models false
% 0.18/0.53 % --sat_fm_lemmas false
% 0.18/0.53 % --sat_fm_prep false
% 0.18/0.53 % --sat_fm_uc_incr true
% 0.18/0.53 % --sat_out_model small
% 0.18/0.53 % --sat_out_clauses false
% 0.18/0.53
% 0.18/0.53 % ------ QBF Options
% 0.18/0.53
% 0.18/0.53 % --qbf_mode false
% 0.18/0.53 % --qbf_elim_univ true
% 0.18/0.53 % --qbf_sk_in true
% 0.18/0.53 % --qbf_pred_elim true
% 0.18/0.53 % --qbf_split 32
% 0.18/0.53
% 0.18/0.53 % ------ BMC1 Options
% 0.18/0.53
% 0.18/0.53 % --bmc1_incremental false
% 0.18/0.53 % --bmc1_axioms reachable_all
% 0.18/0.53 % --bmc1_min_bound 0
% 0.18/0.53 % --bmc1_max_bound -1
% 0.18/0.53 % --bmc1_max_bound_default -1
% 0.18/0.53 % --bmc1_symbol_reachability true
% 0.18/0.53 % --bmc1_property_lemmas false
% 0.18/0.53 % --bmc1_k_induction false
% 0.18/0.53 % --bmc1_non_equiv_states false
% 0.18/0.53 % --bmc1_deadlock false
% 0.18/0.53 % --bmc1_ucm false
% 0.18/0.53 % --bmc1_add_unsat_core none
% 0.18/0.53 % --bmc1_unsat_core_children false
% 0.18/0.53 % --bmc1_unsat_core_extrapolate_axioms false
% 0.18/0.53 % --bmc1_out_stat full
% 0.18/0.53 % --bmc1_ground_init false
% 0.18/0.53 % --bmc1_pre_inst_next_state false
% 0.18/0.53 % --bmc1_pre_inst_state false
% 0.18/0.53 % --bmc1_pre_inst_reach_state false
% 0.18/0.53 % --bmc1_out_unsat_core false
% 0.18/0.53 % --bmc1_aig_witness_out false
% 0.18/0.53 % --bmc1_verbose false
% 0.18/0.53 % --bmc1_dump_clauses_tptp false
% 3.40/3.61 % --bmc1_dump_unsat_core_tptp false
% 3.40/3.61 % --bmc1_dump_file -
% 3.40/3.61 % --bmc1_ucm_expand_uc_limit 128
% 3.40/3.61 % --bmc1_ucm_n_expand_iterations 6
% 3.40/3.61 % --bmc1_ucm_extend_mode 1
% 3.40/3.61 % --bmc1_ucm_init_mode 2
% 3.40/3.61 % --bmc1_ucm_cone_mode none
% 3.40/3.61 % --bmc1_ucm_reduced_relation_type 0
% 3.40/3.61 % --bmc1_ucm_relax_model 4
% 3.40/3.61 % --bmc1_ucm_full_tr_after_sat true
% 3.40/3.61 % --bmc1_ucm_expand_neg_assumptions false
% 3.40/3.61 % --bmc1_ucm_layered_model none
% 3.40/3.61 % --bmc1_ucm_max_lemma_size 10
% 3.40/3.61
% 3.40/3.61 % ------ AIG Options
% 3.40/3.61
% 3.40/3.61 % --aig_mode false
% 3.40/3.61
% 3.40/3.61 % ------ Instantiation Options
% 3.40/3.61
% 3.40/3.61 % --instantiation_flag true
% 3.40/3.61 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 3.40/3.61 % --inst_solver_per_active 750
% 3.40/3.61 % --inst_solver_calls_frac 0.5
% 3.40/3.61 % --inst_passive_queue_type priority_queues
% 3.40/3.61 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 3.40/3.61 % --inst_passive_queues_freq [25;2]
% 3.40/3.61 % --inst_dismatching true
% 3.40/3.61 % --inst_eager_unprocessed_to_passive true
% 3.40/3.61 % --inst_prop_sim_given true
% 3.40/3.61 % --inst_prop_sim_new false
% 3.40/3.61 % --inst_orphan_elimination true
% 3.40/3.61 % --inst_learning_loop_flag true
% 3.40/3.61 % --inst_learning_start 3000
% 3.40/3.61 % --inst_learning_factor 2
% 3.40/3.61 % --inst_start_prop_sim_after_learn 3
% 3.40/3.61 % --inst_sel_renew solver
% 3.40/3.61 % --inst_lit_activity_flag true
% 3.40/3.61 % --inst_out_proof true
% 3.40/3.61
% 3.40/3.61 % ------ Resolution Options
% 3.40/3.61
% 3.40/3.61 % --resolution_flag true
% 3.40/3.61 % --res_lit_sel kbo_max
% 3.40/3.61 % --res_to_prop_solver none
% 3.40/3.61 % --res_prop_simpl_new false
% 3.40/3.61 % --res_prop_simpl_given false
% 3.40/3.61 % --res_passive_queue_type priority_queues
% 3.40/3.61 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 3.40/3.61 % --res_passive_queues_freq [15;5]
% 3.40/3.61 % --res_forward_subs full
% 3.40/3.61 % --res_backward_subs full
% 3.40/3.61 % --res_forward_subs_resolution true
% 3.40/3.61 % --res_backward_subs_resolution true
% 3.40/3.61 % --res_orphan_elimination false
% 3.40/3.61 % --res_time_limit 1000.
% 3.40/3.61 % --res_out_proof true
% 3.40/3.61 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_8b462d.s
% 3.40/3.61 % --modulo true
% 3.40/3.61
% 3.40/3.61 % ------ Combination Options
% 3.40/3.61
% 3.40/3.61 % --comb_res_mult 1000
% 3.40/3.61 % --comb_inst_mult 300
% 3.40/3.61 % ------
% 3.40/3.61
% 3.40/3.61 % ------ Parsing...% successful
% 3.40/3.61
% 3.40/3.61 % ------ 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 %
% 3.40/3.61
% 3.40/3.61 % ------ Proving...
% 3.40/3.61 % ------ Problem Properties
% 3.40/3.61
% 3.40/3.61 %
% 3.40/3.61 % EPR false
% 3.40/3.61 % Horn false
% 3.40/3.61 % Has equality true
% 3.40/3.61
% 3.40/3.61 % % ------ Input Options Time Limit: Unbounded
% 3.40/3.61
% 3.40/3.61
% 3.40/3.61 Compiling...
% 3.40/3.61 Loading plugin: done.
% 3.40/3.61 Compiling...
% 3.40/3.61 Loading plugin: done.
% 3.40/3.61 Compiling...
% 3.40/3.61 Loading plugin: done.
% 3.40/3.61 Compiling...
% 3.40/3.61 Loading plugin: done.
% 3.40/3.61 Compiling...
% 3.40/3.61 Loading plugin: done.
% 3.40/3.61 Compiling...
% 3.40/3.61 Loading plugin: done.
% 3.40/3.61 Compiling...
% 3.40/3.61 Loading plugin: done.
% 3.40/3.61 Compiling...
% 3.40/3.61 Loading plugin: done.
% 3.40/3.61 Compiling...
% 3.40/3.61 Loading plugin: done.
% 3.40/3.61 Compiling...
% 3.40/3.61 Loading plugin: done.
% 3.40/3.61 Compiling...
% 3.40/3.61 Loading plugin: done.
% 3.40/3.61 Compiling...
% 3.40/3.61 Loading plugin: done.
% 3.40/3.61 Compiling...
% 3.40/3.61 Loading plugin: done.
% 3.40/3.61 Compiling...
% 3.40/3.61 Loading plugin: done.
% 3.40/3.61 Compiling...
% 3.40/3.61 Loading plugin: done.
% 3.40/3.61 Compiling...
% 3.40/3.61 Loading plugin: done.
% 3.40/3.61 Compiling...
% 3.40/3.61 Loading plugin: done.
% 3.40/3.61 Compiling...
% 3.40/3.61 Loading plugin: done.
% 3.40/3.61 Compiling...
% 3.40/3.61 Loading plugin: done.
% 3.40/3.61 Compiling...
% 3.40/3.61 Loading plugin: done.
% 3.40/3.61 % % ------ Current options:
% 3.40/3.61
% 3.40/3.61 % ------ Input Options
% 3.40/3.61
% 3.40/3.61 % --out_options all
% 3.40/3.61 % --tptp_safe_out true
% 3.40/3.61 % --problem_path ""
% 3.40/3.61 % --include_path ""
% 3.40/3.61 % --clausifier .//eprover
% 3.40/3.61 % --clausifier_options --tstp-format
% 3.40/3.61 % --stdin false
% 3.40/3.61 % --dbg_backtrace false
% 3.40/3.61 % --dbg_dump_prop_clauses false
% 3.40/3.61 % --dbg_dump_prop_clauses_file -
% 3.40/3.61 % --dbg_out_stat false
% 3.40/3.61
% 3.40/3.61 % ------ General Options
% 3.40/3.61
% 3.40/3.61 % --fof false
% 3.40/3.61 % --time_out_real 150.
% 3.40/3.61 % --time_out_prep_mult 0.2
% 3.40/3.61 % --time_out_virtual -1.
% 3.40/3.61 % --schedule none
% 3.40/3.61 % --ground_splitting input
% 3.40/3.61 % --splitting_nvd 16
% 3.40/3.61 % --non_eq_to_eq false
% 3.40/3.61 % --prep_gs_sim true
% 3.40/3.61 % --prep_unflatten false
% 3.40/3.61 % --prep_res_sim true
% 3.40/3.61 % --prep_upred true
% 3.40/3.61 % --res_sim_input true
% 3.40/3.61 % --clause_weak_htbl true
% 3.40/3.61 % --gc_record_bc_elim false
% 3.40/3.61 % --symbol_type_check false
% 3.40/3.61 % --clausify_out false
% 3.40/3.61 % --large_theory_mode false
% 3.40/3.61 % --prep_sem_filter none
% 3.40/3.61 % --prep_sem_filter_out false
% 3.40/3.61 % --preprocessed_out false
% 3.40/3.61 % --sub_typing false
% 3.40/3.61 % --brand_transform false
% 3.40/3.61 % --pure_diseq_elim true
% 3.40/3.61 % --min_unsat_core false
% 3.40/3.61 % --pred_elim true
% 3.40/3.61 % --add_important_lit false
% 3.40/3.61 % --soft_assumptions false
% 3.40/3.61 % --reset_solvers false
% 3.40/3.61 % --bc_imp_inh []
% 3.40/3.61 % --conj_cone_tolerance 1.5
% 3.40/3.61 % --prolific_symb_bound 500
% 3.40/3.61 % --lt_threshold 2000
% 3.40/3.61
% 3.40/3.61 % ------ SAT Options
% 3.40/3.61
% 3.40/3.61 % --sat_mode false
% 3.40/3.61 % --sat_fm_restart_options ""
% 3.40/3.61 % --sat_gr_def false
% 3.40/3.61 % --sat_epr_types true
% 3.40/3.61 % --sat_non_cyclic_types false
% 3.40/3.61 % --sat_finite_models false
% 3.40/3.61 % --sat_fm_lemmas false
% 3.40/3.61 % --sat_fm_prep false
% 3.40/3.61 % --sat_fm_uc_incr true
% 3.40/3.61 % --sat_out_model small
% 3.40/3.61 % --sat_out_clauses false
% 3.40/3.61
% 3.40/3.61 % ------ QBF Options
% 3.40/3.61
% 3.40/3.61 % --qbf_mode false
% 3.40/3.61 % --qbf_elim_univ true
% 3.40/3.61 % --qbf_sk_in true
% 3.40/3.61 % --qbf_pred_elim true
% 3.40/3.61 % --qbf_split 32
% 3.40/3.61
% 3.40/3.61 % ------ BMC1 Options
% 3.40/3.61
% 3.40/3.61 % --bmc1_incremental false
% 3.40/3.61 % --bmc1_axioms reachable_all
% 3.40/3.61 % --bmc1_min_bound 0
% 3.40/3.61 % --bmc1_max_bound -1
% 3.40/3.61 % --bmc1_max_bound_default -1
% 3.40/3.61 % --bmc1_symbol_reachability true
% 3.40/3.61 % --bmc1_property_lemmas false
% 3.40/3.61 % --bmc1_k_induction false
% 3.40/3.61 % --bmc1_non_equiv_states false
% 3.40/3.61 % --bmc1_deadlock false
% 3.40/3.61 % --bmc1_ucm false
% 3.40/3.61 % --bmc1_add_unsat_core none
% 3.40/3.61 % --bmc1_unsat_core_children false
% 3.40/3.61 % --bmc1_unsat_core_extrapolate_axioms false
% 3.40/3.61 % --bmc1_out_stat full
% 3.40/3.61 % --bmc1_ground_init false
% 3.40/3.61 % --bmc1_pre_inst_next_state false
% 3.40/3.61 % --bmc1_pre_inst_state false
% 3.40/3.61 % --bmc1_pre_inst_reach_state false
% 3.40/3.61 % --bmc1_out_unsat_core false
% 3.40/3.61 % --bmc1_aig_witness_out false
% 3.40/3.61 % --bmc1_verbose false
% 3.40/3.61 % --bmc1_dump_clauses_tptp false
% 3.40/3.61 % --bmc1_dump_unsat_core_tptp false
% 3.40/3.61 % --bmc1_dump_file -
% 3.40/3.61 % --bmc1_ucm_expand_uc_limit 128
% 3.40/3.61 % --bmc1_ucm_n_expand_iterations 6
% 3.40/3.61 % --bmc1_ucm_extend_mode 1
% 3.40/3.61 % --bmc1_ucm_init_mode 2
% 3.40/3.61 % --bmc1_ucm_cone_mode none
% 3.40/3.61 % --bmc1_ucm_reduced_relation_type 0
% 3.40/3.61 % --bmc1_ucm_relax_model 4
% 3.40/3.61 % --bmc1_ucm_full_tr_after_sat true
% 3.40/3.61 % --bmc1_ucm_expand_neg_assumptions false
% 3.40/3.61 % --bmc1_ucm_layered_model none
% 3.40/3.63 % --bmc1_ucm_max_lemma_size 10
% 3.40/3.63
% 3.40/3.63 % ------ AIG Options
% 3.40/3.63
% 3.40/3.63 % --aig_mode false
% 3.40/3.63
% 3.40/3.63 % ------ Instantiation Options
% 3.40/3.63
% 3.40/3.63 % --instantiation_flag true
% 3.40/3.63 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 3.40/3.63 % --inst_solver_per_active 750
% 3.40/3.63 % --inst_solver_calls_frac 0.5
% 3.40/3.63 % --inst_passive_queue_type priority_queues
% 3.40/3.63 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 3.40/3.63 % --inst_passive_queues_freq [25;2]
% 3.40/3.63 % --inst_dismatching true
% 3.40/3.63 % --inst_eager_unprocessed_to_passive true
% 3.40/3.63 % --inst_prop_sim_given true
% 3.40/3.63 % --inst_prop_sim_new false
% 3.40/3.63 % --inst_orphan_elimination true
% 3.40/3.63 % --inst_learning_loop_flag true
% 3.40/3.63 % --inst_learning_start 3000
% 3.40/3.63 % --inst_learning_factor 2
% 3.40/3.63 % --inst_start_prop_sim_after_learn 3
% 3.40/3.63 % --inst_sel_renew solver
% 3.40/3.63 % --inst_lit_activity_flag true
% 3.40/3.63 % --inst_out_proof true
% 3.40/3.63
% 3.40/3.63 % ------ Resolution Options
% 3.40/3.63
% 3.40/3.63 % --resolution_flag true
% 3.40/3.63 % --res_lit_sel kbo_max
% 3.40/3.63 % --res_to_prop_solver none
% 3.40/3.63 % --res_prop_simpl_new false
% 3.40/3.63 % --res_prop_simpl_given false
% 3.40/3.63 % --res_passive_queue_type priority_queues
% 3.40/3.63 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 3.40/3.63 % --res_passive_queues_freq [15;5]
% 3.40/3.63 % --res_forward_subs full
% 3.40/3.63 % --res_backward_subs full
% 3.40/3.63 % --res_forward_subs_resolution true
% 3.40/3.63 % --res_backward_subs_resolution true
% 3.40/3.63 % --res_orphan_elimination false
% 3.40/3.63 % --res_time_limit 1000.
% 3.40/3.63 % --res_out_proof true
% 3.40/3.63 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_8b462d.s
% 3.40/3.63 % --modulo true
% 3.40/3.63
% 3.40/3.63 % ------ Combination Options
% 3.40/3.63
% 3.40/3.63 % --comb_res_mult 1000
% 3.40/3.63 % --comb_inst_mult 300
% 3.40/3.63 % ------
% 3.40/3.63
% 3.40/3.63
% 3.40/3.63
% 3.40/3.63 % ------ Proving...
% 3.40/3.63 %
% 3.40/3.63
% 3.40/3.63
% 3.40/3.63 % Resolution empty clause
% 3.40/3.63
% 3.40/3.63 % ------ Statistics
% 3.40/3.63
% 3.40/3.63 % ------ General
% 3.40/3.63
% 3.40/3.63 % num_of_input_clauses: 1301
% 3.40/3.63 % num_of_input_neg_conjectures: 1
% 3.40/3.63 % num_of_splits: 0
% 3.40/3.63 % num_of_split_atoms: 0
% 3.40/3.63 % num_of_sem_filtered_clauses: 0
% 3.40/3.63 % num_of_subtypes: 0
% 3.40/3.63 % monotx_restored_types: 0
% 3.40/3.63 % sat_num_of_epr_types: 0
% 3.40/3.63 % sat_num_of_non_cyclic_types: 0
% 3.40/3.63 % sat_guarded_non_collapsed_types: 0
% 3.40/3.63 % is_epr: 0
% 3.40/3.63 % is_horn: 0
% 3.40/3.63 % has_eq: 1
% 3.40/3.63 % num_pure_diseq_elim: 0
% 3.40/3.63 % simp_replaced_by: 0
% 3.40/3.63 % res_preprocessed: 2
% 3.40/3.63 % prep_upred: 0
% 3.40/3.63 % prep_unflattend: 0
% 3.40/3.63 % pred_elim_cands: 0
% 3.40/3.63 % pred_elim: 0
% 3.40/3.63 % pred_elim_cl: 0
% 3.40/3.63 % pred_elim_cycles: 0
% 3.40/3.63 % forced_gc_time: 0
% 3.40/3.63 % gc_basic_clause_elim: 0
% 3.40/3.63 % parsing_time: 0.069
% 3.40/3.63 % sem_filter_time: 0.
% 3.40/3.63 % pred_elim_time: 0.
% 3.40/3.63 % out_proof_time: 0.001
% 3.40/3.63 % monotx_time: 0.
% 3.40/3.63 % subtype_inf_time: 0.
% 3.40/3.63 % unif_index_cands_time: 0.
% 3.40/3.63 % unif_index_add_time: 0.
% 3.40/3.63 % total_time: 3.116
% 3.40/3.63 % num_of_symbols: 124
% 3.40/3.63 % num_of_terms: 4381
% 3.40/3.63
% 3.40/3.63 % ------ Propositional Solver
% 3.40/3.63
% 3.40/3.63 % prop_solver_calls: 1
% 3.40/3.63 % prop_fast_solver_calls: 3
% 3.40/3.63 % prop_num_of_clauses: 1224
% 3.40/3.63 % prop_preprocess_simplified: 3960
% 3.40/3.63 % prop_fo_subsumed: 0
% 3.40/3.63 % prop_solver_time: 0.
% 3.40/3.63 % prop_fast_solver_time: 0.
% 3.40/3.63 % prop_unsat_core_time: 0.
% 3.40/3.63
% 3.40/3.63 % ------ QBF
% 3.40/3.63
% 3.40/3.63 % qbf_q_res: 0
% 3.40/3.63 % qbf_num_tautologies: 0
% 3.40/3.63 % qbf_prep_cycles: 0
% 3.40/3.63
% 3.40/3.63 % ------ BMC1
% 3.40/3.63
% 3.40/3.63 % bmc1_current_bound: -1
% 3.40/3.63 % bmc1_last_solved_bound: -1
% 3.40/3.63 % bmc1_unsat_core_size: -1
% 3.40/3.63 % bmc1_unsat_core_parents_size: -1
% 3.40/3.63 % bmc1_merge_next_fun: 0
% 3.40/3.63 % bmc1_unsat_core_clauses_time: 0.
% 3.40/3.63
% 3.40/3.63 % ------ Instantiation
% 3.40/3.63
% 3.40/3.63 % inst_num_of_clauses: 1186
% 3.40/3.63 % inst_num_in_passive: 0
% 3.40/3.63 % inst_num_in_active: 0
% 3.40/3.63 % inst_num_in_unprocessed: 1301
% 3.40/3.63 % inst_num_of_loops: 0
% 3.40/3.63 % inst_num_of_learning_restarts: 0
% 3.40/3.63 % inst_num_moves_active_passive: 0
% 3.40/3.63 % inst_lit_activity: 0
% 3.40/3.63 % inst_lit_activity_moves: 0
% 3.40/3.63 % inst_num_tautologies: 0
% 3.40/3.63 % inst_num_prop_implied: 0
% 3.40/3.63 % inst_num_existing_simplified: 0
% 3.40/3.63 % inst_num_eq_res_simplified: 0
% 3.40/3.63 % inst_num_child_elim: 0
% 3.40/3.63 % inst_num_of_dismatching_blockings: 0
% 3.40/3.63 % inst_num_of_non_proper_insts: 0
% 3.40/3.63 % inst_num_of_duplicates: 0
% 3.40/3.63 % inst_inst_num_from_inst_to_res: 0
% 3.40/3.63 % inst_dismatching_checking_time: 0.
% 3.40/3.63
% 3.40/3.63 % ------ Resolution
% 3.40/3.63
% 3.40/3.63 % res_num_of_clauses: 1454
% 3.40/3.63 % res_num_in_passive: 108
% 3.40/3.63 % res_num_in_active: 530
% 3.40/3.63 % res_num_of_loops: 4
% 3.40/3.63 % res_forward_subset_subsumed: 680
% 3.40/3.63 % res_backward_subset_subsumed: 5
% 3.40/3.63 % res_forward_subsumed: 0
% 3.40/3.63 % res_backward_subsumed: 15
% 3.40/3.63 % res_forward_subsumption_resolution: 1
% 3.40/3.63 % res_backward_subsumption_resolution: 4
% 3.40/3.63 % res_clause_to_clause_subsumption: 19
% 3.40/3.63 % res_orphan_elimination: 0
% 3.40/3.63 % res_tautology_del: 0
% 3.40/3.63 % res_num_eq_res_simplified: 0
% 3.40/3.63 % res_num_sel_changes: 0
% 3.40/3.63 % res_moves_from_active_to_pass: 0
% 3.40/3.63
% 3.40/3.63 % Status Unsatisfiable
% 3.40/3.63 % SZS status Unsatisfiable
% 3.40/3.63 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------