TSTP Solution File: SCT061-1 by iProverMo---2.5-0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : SCT061-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n026.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 21:37:07 EDT 2022
% Result : Unsatisfiable 150.04s 150.85s
% Output : CNFRefutation 150.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 615
% Syntax : Number of formulae : 4488 ( 986 unt; 0 def)
% Number of atoms : 11544 (2338 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 12948 (5892 ~;7056 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 30 ( 28 usr; 1 prp; 0-6 aty)
% Number of functors : 96 ( 96 usr; 13 con; 0-7 aty)
% Number of variables : 16368 ( 801 sgn6480 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0,axiom,
! [X15,X5,X30,X21,X17,X6,X4] :
( c_in(c_Pair(X21,c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X21,X30,X5,X15,X4,X6,X17),X4,X17),X5,tc_prod(X4,X17))
| ~ c_in(c_Pair(X21,X30,X4,X6),c_Relation_Orel__comp(X5,X15,X4,X17,X6),tc_prod(X4,X6)) ),
file('<stdin>',cls_rel__compEpair_0) ).
fof(c_0_1,axiom,
! [X15,X5,X30,X21,X17,X6,X4] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X21,X30,X5,X15,X4,X6,X17),X30,X17,X6),X15,tc_prod(X17,X6))
| ~ c_in(c_Pair(X21,X30,X4,X6),c_Relation_Orel__comp(X5,X15,X4,X17,X6),tc_prod(X4,X6)) ),
file('<stdin>',cls_rel__compEpair_1) ).
fof(c_0_2,axiom,
! [X51,X20,X52,X21,X50,X10] :
( c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X50),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X50,v_sko__local__X1__1(X10,X50,X21,X52,X20,X51)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X10,v_sko__local__X1__1(X10,X50,X21,X52,X20,X51)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X50,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X10,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X20 = X52
| X21 = X51
| X52 = X51
| X21 = X20 ),
file('<stdin>',cls_1_1) ).
fof(c_0_3,axiom,
! [X51,X20,X52,X21,X50,X10] :
( c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X50),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X50,v_sko__local__X2__1(X10,X50,X21,X52,X20,X51)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X10,v_sko__local__X2__1(X10,X50,X21,X52,X20,X51)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X50,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X10,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X20 = X52
| X21 = X51
| X52 = X51
| X21 = X20 ),
file('<stdin>',cls_2_2) ).
fof(c_0_4,axiom,
! [X51,X20,X52,X21,X50,X10] :
( c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X50),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X50,v_sko__local__X2__1(X10,X50,X21,X52,X20,X51)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X10,v_sko__local__X2__1(X10,X50,X21,X52,X20,X51)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X50,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X10,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X20 = X52
| X21 = X51
| X52 = X51
| X21 = X20 ),
file('<stdin>',cls_2_3) ).
fof(c_0_5,axiom,
! [X51,X20,X52,X21,X50,X10] :
( c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X50),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X50,v_sko__local__X1__1(X10,X50,X21,X52,X20,X51)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X10,v_sko__local__X1__1(X10,X50,X21,X52,X20,X51)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X50,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X10,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X20 = X52
| X21 = X51
| X52 = X51
| X21 = X20 ),
file('<stdin>',cls_1_0) ).
fof(c_0_6,axiom,
! [X51,X20,X52,X21,X50,X10] :
( c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X50),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X50,v_sko__local__X2__1(X10,X50,X21,X52,X20,X51)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X10,v_sko__local__X2__1(X10,X50,X21,X52,X20,X51)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X50,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X10,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X20 = X52
| X21 = X51
| X52 = X51
| X21 = X20 ),
file('<stdin>',cls_2_0) ).
fof(c_0_7,axiom,
! [X51,X20,X52,X21,X50,X10] :
( c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X50),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X50,v_sko__local__X2__1(X10,X50,X21,X52,X20,X51)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X10,v_sko__local__X2__1(X10,X50,X21,X52,X20,X51)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X50,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X10,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X20 = X52
| X21 = X51
| X52 = X51
| X21 = X20 ),
file('<stdin>',cls_2_1) ).
fof(c_0_8,axiom,
! [X8,X5,X28,X29,X6,X4] :
( hAPP(X29,c_List_Osko__Recdef__Xcuts__eq__1__1(X29,X28,X5,X8,X4,X6)) != hAPP(X28,c_List_Osko__Recdef__Xcuts__eq__1__1(X29,X28,X5,X8,X4,X6))
| c_Recdef_Ocut(X29,X5,X8,X4,X6) = c_Recdef_Ocut(X28,X5,X8,X4,X6) ),
file('<stdin>',cls_cuts__eq_2) ).
fof(c_0_9,axiom,
! [X13,X12,X4] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X12,X13,tc_fun(tc_prod(X4,X4),tc_bool)),X4)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X12,X12,X4,X4,X4),c_Relation_Orel__comp(X13,X12,X4,X4,X4),tc_fun(tc_prod(X4,X4),tc_bool)),X13,tc_fun(tc_prod(X4,X4),tc_bool)),X4) ),
file('<stdin>',cls_wf__union__merge_1) ).
fof(c_0_10,axiom,
! [X8,X5,X28,X29,X6,X4] :
( c_Recdef_Ocut(X29,X5,X8,X4,X6) = c_Recdef_Ocut(X28,X5,X8,X4,X6)
| c_in(c_Pair(c_List_Osko__Recdef__Xcuts__eq__1__1(X29,X28,X5,X8,X4,X6),X8,X4,X4),X5,tc_prod(X4,X4)) ),
file('<stdin>',cls_cuts__eq_1) ).
fof(c_0_11,axiom,
! [X13,X12,X4] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X12,X12,X4,X4,X4),c_Relation_Orel__comp(X13,X12,X4,X4,X4),tc_fun(tc_prod(X4,X4),tc_bool)),X13,tc_fun(tc_prod(X4,X4),tc_bool)),X4)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X12,X13,tc_fun(tc_prod(X4,X4),tc_bool)),X4) ),
file('<stdin>',cls_wf__union__merge_0) ).
fof(c_0_12,axiom,
! [X29,X2,X3,X6,X4] :
( c_in(X29,c_FuncSet_OPi(X3,X2,X4,X6),tc_fun(X4,X6))
| ~ c_in(hAPP(X29,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X3,X2,X29,X4,X6)),hAPP(X2,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X3,X2,X29,X4,X6)),X6) ),
file('<stdin>',cls_Pi__I_H_1) ).
fof(c_0_13,axiom,
! [X29,X2,X3,X6,X4] :
( c_in(X29,c_FuncSet_OPi(X3,X2,X4,X6),tc_fun(X4,X6))
| ~ c_in(hAPP(X29,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X3,X2,X29,X4,X6)),hAPP(X2,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X3,X2,X29,X4,X6)),X6) ),
file('<stdin>',cls_Pi__I_1) ).
fof(c_0_14,axiom,
! [X41,X42,X43,X44,X45,X46,X29,X17,X6,X4] :
( hAPP(hAPP(X29,X44),X43) = hAPP(hAPP(X29,X42),X41)
| ~ c_in(c_Pair(X43,X41,X6,X6),X45,tc_prod(X6,X6))
| ~ c_in(c_Pair(X44,X42,X4,X4),X46,tc_prod(X4,X4))
| ~ c_Equiv__Relations_Ocongruent2(X46,X45,X29,X4,X6,X17) ),
file('<stdin>',cls_congruent2_Ocongruent2_0) ).
fof(c_0_15,axiom,
! [X45,X46,X29,X21,X3,X17,X6,X4] :
( c_Equiv__Relations_Ocongruent(X45,hAPP(X29,X21),X6,X17)
| ~ c_in(X21,X3,X4)
| ~ c_Equiv__Relations_Ocongruent2(X46,X45,X29,X4,X6,X17)
| ~ c_Equiv__Relations_Oequiv(X3,X46,X4) ),
file('<stdin>',cls_congruent2__implies__congruent_0) ).
fof(c_0_16,axiom,
! [X58,X28,X29,X48,X17,X6,X4] : c_Fun_Ocomp(X29,c_Fun_Ocomp(X28,X58,X48,X17,X4),X17,X6,X4) = c_Fun_Ocomp(c_Fun_Ocomp(X29,X28,X17,X6,X48),X58,X48,X6,X4),
file('<stdin>',cls_o__assoc_0) ).
fof(c_0_17,axiom,
! [X25,X13,X12,X48,X17,X6,X4] : c_Relation_Orel__comp(c_Relation_Orel__comp(X12,X13,X4,X48,X17),X25,X4,X17,X6) = c_Relation_Orel__comp(X12,c_Relation_Orel__comp(X13,X25,X48,X17,X6),X4,X48,X6),
file('<stdin>',cls_O__assoc_0) ).
fof(c_0_18,axiom,
! [X7,X8,X20,X21,X36] :
( c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X36,X7),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X36,X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X7,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X21,X20,X8,X7)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X8,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X21,X20,X8,X7)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X7,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_OIIA(X36) ),
file('<stdin>',cls_IIA__def_2) ).
fof(c_0_19,axiom,
! [X7,X8,X20,X21,X36] :
( c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X36,X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X36,X7),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X7,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X21,X20,X8,X7)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X8,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X21,X20,X8,X7)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X7,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_OIIA(X36) ),
file('<stdin>',cls_IIA__def_3) ).
fof(c_0_20,axiom,
! [X20,X21,X50,X10] :
( c_in(c_Pair(X20,X21,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X50),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X20,X21,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X50,v_sko__local__X3__1(X10,X50,X21,X20)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X10,v_sko__local__X3__1(X10,X50,X21,X20)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X50,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X10,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X21 = X20 ),
file('<stdin>',cls_3_2) ).
fof(c_0_21,axiom,
! [X20,X21,X50,X10] :
( c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X20,X21,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X50),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X20,X21,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X50,v_sko__local__X3__1(X10,X50,X21,X20)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X10,v_sko__local__X3__1(X10,X50,X21,X20)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X50,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X10,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X21 = X20 ),
file('<stdin>',cls_3_3) ).
fof(c_0_22,axiom,
! [X8,X5,X20,X21,X3,X4] :
( c_in(c_Pair(X21,X20,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(X8,c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X5,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4),c_Relation_OImage(X5,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4),tc_fun(X4,tc_bool)),X4)
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4) ),
file('<stdin>',cls_equiv__class__nondisjoint_0) ).
fof(c_0_23,axiom,
! [X25,X13,X12,X17,X6,X4] : c_Relation_Orel__comp(X12,c_Lattices_Oupper__semilattice__class_Osup(X13,X25,tc_fun(tc_prod(X17,X6),tc_bool)),X4,X17,X6) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X12,X13,X4,X17,X6),c_Relation_Orel__comp(X12,X25,X4,X17,X6),tc_fun(tc_prod(X4,X6),tc_bool)),
file('<stdin>',cls_rel__comp__distrib_0) ).
fof(c_0_24,axiom,
! [X25,X13,X12,X17,X6,X4] : c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X13,X25,tc_fun(tc_prod(X4,X17),tc_bool)),X12,X4,X17,X6) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X13,X12,X4,X17,X6),c_Relation_Orel__comp(X25,X12,X4,X17,X6),tc_fun(tc_prod(X4,X6),tc_bool)),
file('<stdin>',cls_rel__comp__distrib2_0) ).
fof(c_0_25,axiom,
! [X15,X5,X1,X2,X3,X17,X6,X4] :
( c_lessequals(c_Relation_Orel__comp(X5,X15,X4,X6,X17),c_Product__Type_OSigma(X3,c_COMBK(X1,tc_fun(X17,tc_bool),X4),X4,X17),tc_fun(tc_prod(X4,X17),tc_bool))
| ~ c_lessequals(X15,c_Product__Type_OSigma(X2,c_COMBK(X1,tc_fun(X17,tc_bool),X6),X6,X17),tc_fun(tc_prod(X6,X17),tc_bool))
| ~ c_lessequals(X5,c_Product__Type_OSigma(X3,c_COMBK(X2,tc_fun(X6,tc_bool),X4),X4,X6),tc_fun(tc_prod(X4,X6),tc_bool)) ),
file('<stdin>',cls_rel__comp__subset__Sigma_0) ).
fof(c_0_26,axiom,
! [X5,X20,X3,X6,X4] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X3,X20,X5,X6,X4),X20,X6,X4),X5,tc_prod(X6,X4))
| ~ c_in(X20,c_Relation_OImage(X5,X3,X6,X4),X4) ),
file('<stdin>',cls_ImageE_0) ).
fof(c_0_27,axiom,
! [X5,X20,X3,X6,X4] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X3,X20,X5,X6,X4),X20,X6,X4),X5,tc_prod(X6,X4))
| ~ c_in(X20,c_Relation_OImage(X5,X3,X6,X4),X4) ),
file('<stdin>',cls_Image__iff_1) ).
fof(c_0_28,axiom,
! [X20,X21,X2,X3,X6,X4] : c_Product__Type_OSigma(c_Set_Oinsert(X21,X3,X4),c_COMBK(c_Set_Oinsert(X20,X2,X6),tc_fun(X6,tc_bool),X4),X4,X6) = c_Set_Oinsert(c_Pair(X21,X20,X4,X6),c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X3,c_COMBK(c_Set_Oinsert(X20,X2,X6),tc_fun(X6,tc_bool),X4),X4,X6),c_Product__Type_OSigma(c_Set_Oinsert(X21,X3,X4),c_COMBK(X2,tc_fun(X6,tc_bool),X4),X4,X6),tc_fun(tc_prod(X4,X6),tc_bool)),tc_prod(X4,X6)),
file('<stdin>',cls_insert__times__insert_0) ).
fof(c_0_29,axiom,
! [X1,X2,X3,X4] :
( c_Relation_Orel__comp(X3,X1,X4,X4,X4) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool))
| c_Relation_Orel__comp(X3,X2,X4,X4,X4) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool))
| c_Relation_Orel__comp(X3,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(tc_prod(X4,X4),tc_bool)),X4,X4,X4) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool)) ),
file('<stdin>',cls_union__comp__emptyR_0) ).
fof(c_0_30,axiom,
! [X1,X2,X3,X4] :
( c_Relation_Orel__comp(X2,X1,X4,X4,X4) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool))
| c_Relation_Orel__comp(X3,X1,X4,X4,X4) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool))
| c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(tc_prod(X4,X4),tc_bool)),X1,X4,X4,X4) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool)) ),
file('<stdin>',cls_union__comp__emptyL_0) ).
fof(c_0_31,axiom,
! [X14,X15,X16,X5,X17,X6,X4] :
( c_lessequals(c_Relation_Orel__comp(X16,X14,X4,X6,X17),c_Relation_Orel__comp(X5,X15,X4,X6,X17),tc_fun(tc_prod(X4,X17),tc_bool))
| ~ c_lessequals(X14,X15,tc_fun(tc_prod(X6,X17),tc_bool))
| ~ c_lessequals(X16,X5,tc_fun(tc_prod(X4,X6),tc_bool)) ),
file('<stdin>',cls_rel__comp__mono_0) ).
fof(c_0_32,axiom,
! [X15,X5,X4] :
( c_lessequals(c_Transitive__Closure_Ortrancl(X5,X4),X15,tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Ortrancl(X5,X4),X15,tc_fun(tc_prod(X4,X4),tc_bool)),X5,X4,X4,X4),X15,tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_lessequals(c_Relation_OId(X4),X15,tc_fun(tc_prod(X4,X4),tc_bool)) ),
file('<stdin>',cls_rtrancl__Int__subset_0) ).
fof(c_0_33,axiom,
! [X15,X5,X4] :
( c_lessequals(c_Transitive__Closure_Otrancl(X5,X4),X15,tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Otrancl(X5,X4),X15,tc_fun(tc_prod(X4,X4),tc_bool)),X5,X4,X4,X4),X15,tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_lessequals(X5,X15,tc_fun(tc_prod(X4,X4),tc_bool)) ),
file('<stdin>',cls_trancl__Int__subset_0) ).
fof(c_0_34,axiom,
! [X7,X8,X20,X21,X36] :
( c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X36,X7),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X36,X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X7,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X21,X20,X8,X7)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X8,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X21,X20,X8,X7)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X7,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_OIIA(X36) ),
file('<stdin>',cls_IIA__def_0) ).
fof(c_0_35,axiom,
! [X7,X8,X20,X21,X36] :
( c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X36,X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X36,X7),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X7,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X21,X20,X8,X7)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X8,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X21,X20,X8,X7)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X7,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_OIIA(X36) ),
file('<stdin>',cls_IIA__def_1) ).
fof(c_0_36,axiom,
! [X20,X21,X50,X10] :
( c_in(c_Pair(X20,X21,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X50),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X20,X21,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X50,v_sko__local__X3__1(X10,X50,X21,X20)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X10,v_sko__local__X3__1(X10,X50,X21,X20)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X50,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X10,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X21 = X20 ),
file('<stdin>',cls_3_0) ).
fof(c_0_37,axiom,
! [X20,X21,X50,X10] :
( c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X20,X21,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X50),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X20,X21,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X50,v_sko__local__X3__1(X10,X50,X21,X20)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X10,v_sko__local__X3__1(X10,X50,X21,X20)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X50,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X10,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X21 = X20 ),
file('<stdin>',cls_3_1) ).
fof(c_0_38,axiom,
! [X53,X8,X54,X28,X55,X29,X56,X48,X17,X6,X4] :
( hAPP(X29,hAPP(X28,X8)) != hAPP(X55,hAPP(X54,X53))
| hAPP(c_Fun_Ocomp(X29,X28,X6,X4,X17),X8) = hAPP(c_Fun_Ocomp(X55,X54,X48,X4,X56),X53) ),
file('<stdin>',cls_comp__cong_0) ).
fof(c_0_39,axiom,
! [X15,X5,X30,X20,X21,X17,X6,X4] :
( c_in(c_Pair(X21,X30,X4,X17),c_Relation_Orel__comp(X5,X15,X4,X6,X17),tc_prod(X4,X17))
| ~ c_in(c_Pair(X20,X30,X6,X17),X15,tc_prod(X6,X17))
| ~ c_in(c_Pair(X21,X20,X4,X6),X5,tc_prod(X4,X6)) ),
file('<stdin>',cls_rel__compI_0) ).
fof(c_0_40,axiom,
! [X19,X8,X5,X28,X29,X6,X4] :
( c_Recdef_Ocut(X29,X5,X8,X4,X6) != c_Recdef_Ocut(X28,X5,X8,X4,X6)
| hAPP(X29,X19) = hAPP(X28,X19)
| ~ c_in(c_Pair(X19,X8,X4,X4),X5,tc_prod(X4,X4)) ),
file('<stdin>',cls_cuts__eq_0) ).
fof(c_0_41,axiom,
! [X13,X12,X4] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X12,X13,tc_fun(tc_prod(X4,X4),tc_bool)),X4)
| ~ c_lessequals(c_Relation_Orel__comp(X12,X13,X4,X4,X4),X12,tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_Wellfounded_Owf(X13,X4)
| ~ c_Wellfounded_Owf(X12,X4) ),
file('<stdin>',cls_wf__union__compatible_0) ).
fof(c_0_42,axiom,
! [X57,X32,X30,X20,X21,X48,X17,X6,X4] :
( c_Fun_Ocomp(X21,X20,X17,X6,X4) != c_Fun_Ocomp(X30,X32,X48,X6,X4)
| hAPP(X21,hAPP(X20,X57)) = hAPP(X30,hAPP(X32,X57)) ),
file('<stdin>',cls_o__eq__dest_0) ).
fof(c_0_43,axiom,
! [X12,X4] :
( c_Wellfounded_Owf(X12,X4)
| ~ c_Wellfounded_Owf(c_Relation_Orel__comp(X12,X12,X4,X4,X4),X4) ),
file('<stdin>',cls_wf__comp__self_1) ).
fof(c_0_44,axiom,
! [X15,X5,X17,X6,X4] : hAPP(c_Relation_Oconverse(X6,X4),c_Relation_Orel__comp(X5,X15,X6,X17,X4)) = c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X17,X4),X15),hAPP(c_Relation_Oconverse(X6,X17),X5),X4,X17,X6),
file('<stdin>',cls_converse__rel__comp_0) ).
fof(c_0_45,axiom,
! [X5,X20,X21,X3,X4] :
( c_in(c_Pair(X21,X20,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(X20,X3,X4)
| ~ c_lessequals(c_Relation_OImage(X5,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4),c_Relation_OImage(X5,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4),tc_fun(X4,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4) ),
file('<stdin>',cls_subset__equiv__class_0) ).
fof(c_0_46,axiom,
! [X5,X20,X21,X10,X4] :
( hBOOL(hAPP(X10,X20))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X10,X21,X5,X4),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X10,X21,X5,X4),X4,X4),X5,tc_prod(X4,X4))
| ~ hBOOL(hAPP(X10,X21))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_rtrancl__induct_1) ).
fof(c_0_47,axiom,
! [X5,X20,X21,X10,X4] :
( hBOOL(hAPP(X10,X21))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X10,X20,X5,X4),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X10,X20,X5,X4),X4,X4),X5,tc_prod(X4,X4))
| ~ hBOOL(hAPP(X10,X20))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_converse__rtrancl__induct_0) ).
fof(c_0_48,axiom,
! [X30,X2,X3,X6,X4] :
( c_in(c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1(X3,X2,X30,X4,X6),X3,X4)
| ~ c_in(X30,c_Product__Type_OSigma(X3,X2,X4,X6),tc_prod(X4,X6)) ),
file('<stdin>',cls_SigmaE_0) ).
fof(c_0_49,axiom,
! [X8,X29,X21,X12,X6,X4] :
( hAPP(c_Recdef_Ocut(X29,X12,X21,X4,X6),X8) = hAPP(X29,X8)
| ~ c_in(c_Pair(X8,X21,X4,X4),X12,tc_prod(X4,X4)) ),
file('<stdin>',cls_tfl__cut__apply_0) ).
fof(c_0_50,axiom,
! [X8,X5,X29,X21,X6,X4] :
( hAPP(c_Recdef_Ocut(X29,X5,X21,X4,X6),X8) = hAPP(X29,X8)
| ~ c_in(c_Pair(X8,X21,X4,X4),X5,tc_prod(X4,X4)) ),
file('<stdin>',cls_cut__apply_0) ).
fof(c_0_51,axiom,
! [X5,X20,X3,X6,X4] :
( c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X3,X20,X5,X6,X4),X3,X6)
| ~ c_in(X20,c_Relation_OImage(X5,X3,X6,X4),X4) ),
file('<stdin>',cls_ImageE_1) ).
fof(c_0_52,axiom,
! [X5,X20,X3,X6,X4] :
( c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X3,X20,X5,X6,X4),X3,X6)
| ~ c_in(X20,c_Relation_OImage(X5,X3,X6,X4),X4) ),
file('<stdin>',cls_Image__iff_0) ).
fof(c_0_53,axiom,
! [X18,X19,X8,X5,X4] :
( c_in(c_Pair(X18,X19,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| c_in(c_Pair(X19,X18,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X8,X18,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_Relation_Osingle__valued(X5,X4,X4) ),
file('<stdin>',cls_single__valued__confluent_0) ).
fof(c_0_54,axiom,
! [X5,X20,X21,X4] :
( c_in(c_Pair(X21,c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X21,X20,X5,X4),X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4))
| c_in(c_Pair(X21,X20,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_tranclE_0) ).
fof(c_0_55,axiom,
! [X18,X8,X5,X4] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X5,X8,X18,X4),X18,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4))
| c_in(c_Pair(X8,X18,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(c_Pair(X8,X18,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_converse__tranclE_1) ).
fof(c_0_56,axiom,
! [X18,X8,X5,X4] :
( c_in(c_Pair(X8,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X5,X8,X18,X4),X4,X4),X5,tc_prod(X4,X4))
| c_in(c_Pair(X8,X18,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(c_Pair(X8,X18,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_converse__tranclE_0) ).
fof(c_0_57,axiom,
! [X5,X20,X21,X4] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X21,X20,X5,X4),X20,X4,X4),X5,tc_prod(X4,X4))
| c_in(c_Pair(X21,X20,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_tranclE_1) ).
fof(c_0_58,axiom,
! [X29,X2,X3,X6,X4] :
( c_in(X29,c_FuncSet_OPi(X3,X2,X4,X6),tc_fun(X4,X6))
| c_in(c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X3,X2,X29,X4,X6),X3,X4) ),
file('<stdin>',cls_Pi__I_H_0) ).
fof(c_0_59,axiom,
! [X29,X2,X3,X6,X4] :
( c_in(X29,c_FuncSet_OPi(X3,X2,X4,X6),tc_fun(X4,X6))
| c_in(c_FuncSet_Osko__FuncSet__XPi__I__1__1(X3,X2,X29,X4,X6),X3,X4) ),
file('<stdin>',cls_Pi__I_0) ).
fof(c_0_60,axiom,
! [X12,X2,X3,X6,X4] : c_lessequals(c_Relation_OImage(X12,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X6,tc_bool)),X6,X4),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X12,X3,X6,X4),c_Relation_OImage(X12,X2,X6,X4),tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
file('<stdin>',cls_Image__Int__subset_0) ).
fof(c_0_61,axiom,
! [X5,X20,X21,X3,X4] :
( c_lessequals(c_Relation_OImage(X5,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4),c_Relation_OImage(X5,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4),tc_fun(X4,tc_bool))
| ~ c_in(c_Pair(X21,X20,X4,X4),X5,tc_prod(X4,X4))
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4) ),
file('<stdin>',cls_equiv__class__subset_0) ).
fof(c_0_62,axiom,
c_in(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
file('<stdin>',cls_cP_0) ).
fof(c_0_63,axiom,
! [X8,X1,X2,X3,X6,X4] :
( c_lessequals(X3,X2,tc_fun(X6,tc_bool))
| ~ c_lessequals(c_Product__Type_OSigma(X3,c_COMBK(X1,tc_fun(X4,tc_bool),X6),X6,X4),c_Product__Type_OSigma(X2,c_COMBK(X1,tc_fun(X4,tc_bool),X6),X6,X4),tc_fun(tc_prod(X6,X4),tc_bool))
| ~ c_in(X8,X1,X4) ),
file('<stdin>',cls_Times__subset__cancel2_0) ).
fof(c_0_64,axiom,
! [X5,X3,X4] :
( c_lessequals(X5,c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X4,X4),X5),X5,X4,X4,X4),tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_Relation_Orefl__on(X3,X5,X4) ),
file('<stdin>',cls_refl__on__comp__subset_0) ).
fof(c_0_65,axiom,
! [X19,X8,X5,X4] :
( ~ c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X19,X8,X4,X4),X5,tc_prod(X4,X4)),X4) ),
file('<stdin>',cls_wf__insert_1) ).
fof(c_0_66,axiom,
! [X19,X8,X5,X4] :
( ~ c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X19,X8,X4,X4),X5,tc_prod(X4,X4)),X4) ),
file('<stdin>',cls_acyclic__insert_1) ).
fof(c_0_67,axiom,
! [X15,X5,X17,X6,X4] :
( c_Relation_Osingle__valued(c_Relation_Orel__comp(X5,X15,X4,X6,X17),X4,X17)
| ~ c_Relation_Osingle__valued(X15,X6,X17)
| ~ c_Relation_Osingle__valued(X5,X4,X6) ),
file('<stdin>',cls_single__valued__rel__comp_0) ).
fof(c_0_68,axiom,
! [X5,X20,X21,X10,X4] :
( hBOOL(hAPP(X10,X21))
| ~ hBOOL(hAPP(X10,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X10,X20,X5,X4)))
| ~ hBOOL(hAPP(X10,X20))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_converse__rtrancl__induct_3) ).
fof(c_0_69,axiom,
! [X5,X20,X21,X10,X4] :
( hBOOL(hAPP(X10,X20))
| ~ hBOOL(hAPP(X10,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X10,X21,X5,X4)))
| ~ hBOOL(hAPP(X10,X21))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_rtrancl__induct_3) ).
fof(c_0_70,axiom,
! [X5,X4] : c_Transitive__Closure_Ortrancl(X5,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X4),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X5,X4),X5,X4,X4,X4),tc_fun(tc_prod(X4,X4),tc_bool)),
file('<stdin>',cls_rtrancl__unfold_0) ).
fof(c_0_71,axiom,
! [X5,X20,X21,X10,X4] :
( hBOOL(hAPP(X10,X20))
| c_in(c_Pair(X21,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X10,X21,X5,X4),X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ hBOOL(hAPP(X10,X21))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_rtrancl__induct_0) ).
fof(c_0_72,axiom,
! [X5,X20,X21,X10,X4] :
( hBOOL(hAPP(X10,X21))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X10,X20,X5,X4),X20,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ hBOOL(hAPP(X10,X20))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_converse__rtrancl__induct_1) ).
fof(c_0_73,axiom,
! [X5,X4] : c_Transitive__Closure_Otrancl(X5,X4) = c_Lattices_Oupper__semilattice__class_Osup(X5,c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X5,X4),X5,X4,X4,X4),tc_fun(tc_prod(X4,X4),tc_bool)),
file('<stdin>',cls_trancl__unfold_0) ).
fof(c_0_74,axiom,
! [X5,X20,X21,X4] :
( c_in(c_Pair(X21,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X21,X20,X5,X4),X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| X21 = X20
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_rtranclE_0) ).
fof(c_0_75,axiom,
! [X18,X8,X5,X4] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X5,X8,X18,X4),X18,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| X8 = X18
| ~ c_in(c_Pair(X8,X18,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_converse__rtranclE_1) ).
fof(c_0_76,axiom,
! [X19,X8,X12,X4] :
( c_in(c_Pair(X8,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X12,X8,X19,X4),X4,X4),c_Transitive__Closure_Ortrancl(X12,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Otrancl(X12,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_tranclD2_0) ).
fof(c_0_77,axiom,
! [X19,X8,X12,X4] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X12,X8,X19,X4),X19,X4,X4),c_Transitive__Closure_Ortrancl(X12,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Otrancl(X12,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_tranclD_1) ).
fof(c_0_78,axiom,
! [X18,X8,X5,X4] :
( c_in(c_Pair(X8,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X5,X8,X18,X4),X4,X4),X5,tc_prod(X4,X4))
| X8 = X18
| ~ c_in(c_Pair(X8,X18,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_converse__rtranclE_0) ).
fof(c_0_79,axiom,
! [X5,X20,X21,X4] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X21,X20,X5,X4),X20,X4,X4),X5,tc_prod(X4,X4))
| X21 = X20
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_rtranclE_1) ).
fof(c_0_80,axiom,
! [X19,X8,X12,X4] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X12,X8,X19,X4),X19,X4,X4),X12,tc_prod(X4,X4))
| ~ c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Otrancl(X12,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_tranclD2_1) ).
fof(c_0_81,axiom,
! [X19,X8,X12,X4] :
( c_in(c_Pair(X8,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X12,X8,X19,X4),X4,X4),X12,tc_prod(X4,X4))
| ~ c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Otrancl(X12,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_tranclD_0) ).
fof(c_0_82,axiom,
! [X5,X30,X20,X21,X4] :
( c_in(c_Pair(X21,X30,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X20,X30,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_trancl__trans_0) ).
fof(c_0_83,axiom,
! [X5,X30,X20,X21,X4] :
( c_in(c_Pair(X21,X30,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X20,X30,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_rtrancl__trans_0) ).
fof(c_0_84,axiom,
! [X18,X19,X8,X5,X4] :
( c_in(c_Pair(X8,X18,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X19,X18,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_rtrancl__trancl__trancl_0) ).
fof(c_0_85,axiom,
! [X5,X30,X20,X21,X4] :
( c_in(c_Pair(X21,X30,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X20,X30,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_trancl__rtrancl__trancl_0) ).
fof(c_0_86,axiom,
! [X8,X28,X29,X17,X6,X4] : hAPP(c_Fun_Ocomp(X29,X28,X6,X4,X17),X8) = hAPP(X29,hAPP(X28,X8)),
file('<stdin>',cls_o__apply_0) ).
fof(c_0_87,axiom,
! [X57,X20,X21,X17,X6,X4] : hAPP(X21,hAPP(X20,X57)) = hAPP(c_Fun_Ocomp(X21,X20,X17,X6,X4),X57),
file('<stdin>',cls_o__eq__dest__lhs_0) ).
fof(c_0_88,axiom,
! [X5,X4] : c_Relation_Orel__comp(X5,c_Transitive__Closure_Ortrancl(X5,X4),X4,X4,X4) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X5,X4),X5,X4,X4,X4),
file('<stdin>',cls_r__comp__rtrancl__eq_0) ).
fof(c_0_89,axiom,
! [X5,X20,X21,X3,X4] :
( c_in(X21,X3,X4)
| X21 = X20
| ~ c_lessequals(X5,c_Product__Type_OSigma(X3,c_COMBK(X3,tc_fun(X4,tc_bool),X4),X4,X4),tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_trancl__subset__Sigma__aux_0) ).
fof(c_0_90,axiom,
! [X5,X30,X20,X21,X4] :
( c_in(c_Pair(X21,X30,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X20,X30,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X20,X4,X4),X5,tc_prod(X4,X4)) ),
file('<stdin>',cls_converse__rtrancl__into__rtrancl_0) ).
fof(c_0_91,axiom,
! [X5,X30,X20,X21,X4] :
( c_in(c_Pair(X21,X30,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X20,X30,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_rtrancl__into__trancl1_0) ).
fof(c_0_92,axiom,
! [X5,X30,X20,X21,X4] :
( c_in(c_Pair(X21,X30,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X20,X30,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X20,X4,X4),X5,tc_prod(X4,X4)) ),
file('<stdin>',cls_rtrancl__into__trancl2_0) ).
fof(c_0_93,axiom,
! [X5,X30,X20,X21,X4] :
( c_in(c_Pair(X21,X30,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X20,X30,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_Transitive__Closure_Otrancl__into__trancl_0) ).
fof(c_0_94,axiom,
! [X5,X30,X20,X21,X4] :
( c_in(c_Pair(X21,X30,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X20,X30,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X20,X4,X4),X5,tc_prod(X4,X4)) ),
file('<stdin>',cls_trancl__into__trancl2_0) ).
fof(c_0_95,axiom,
! [X5,X30,X20,X21,X4] :
( c_in(c_Pair(X21,X30,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X20,X30,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_rtrancl_Ortrancl__into__rtrancl_0) ).
fof(c_0_96,axiom,
! [X12,X4] :
( c_Wellfounded_Owf(c_Relation_Orel__comp(X12,X12,X4,X4,X4),X4)
| ~ c_Wellfounded_Owf(X12,X4) ),
file('<stdin>',cls_wf__comp__self_0) ).
fof(c_0_97,axiom,
! [X5,X3,X4] :
( c_lessequals(c_Transitive__Closure_Otrancl(X5,X4),c_Product__Type_OSigma(X3,c_COMBK(X3,tc_fun(X4,tc_bool),X4),X4,X4),tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_lessequals(X5,c_Product__Type_OSigma(X3,c_COMBK(X3,tc_fun(X4,tc_bool),X4),X4,X4),tc_fun(tc_prod(X4,X4),tc_bool)) ),
file('<stdin>',cls_trancl__subset__Sigma_0) ).
fof(c_0_98,axiom,
! [X30,X20,X21,X12,X4] :
( c_in(c_Pair(X21,X30,X4,X4),c_Transitive__Closure_Otrancl(X12,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X20,X30,X4,X4),X12,tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X20,X4,X4),X12,tc_prod(X4,X4)) ),
file('<stdin>',cls_r__r__into__trancl_0) ).
fof(c_0_99,axiom,
! [X19,X8,X5,X29,X6,X4] :
( c_in(c_Pair(hAPP(X29,X8),hAPP(X29,X19),X6,X6),X5,tc_prod(X6,X6))
| ~ c_in(c_Pair(X8,X19,X4,X4),c_Relation_Oinv__image(X5,X29,X6,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_in__inv__image_0) ).
fof(c_0_100,axiom,
! [X1,X2,X3,X6,X4] : c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),c_COMBK(X1,tc_fun(X6,tc_bool),X4),X4,X6) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X3,c_COMBK(X1,tc_fun(X6,tc_bool),X4),X4,X6),c_Product__Type_OSigma(X2,c_COMBK(X1,tc_fun(X6,tc_bool),X4),X4,X6),tc_fun(tc_prod(X4,X6),tc_bool)),
file('<stdin>',cls_Times__Un__distrib1_0) ).
fof(c_0_101,axiom,
! [X1,X2,X3,X6,X4] : c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),c_COMBK(X1,tc_fun(X6,tc_bool),X4),X4,X6) = c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(X3,c_COMBK(X1,tc_fun(X6,tc_bool),X4),X4,X6),c_Product__Type_OSigma(X2,c_COMBK(X1,tc_fun(X6,tc_bool),X4),X4,X6),tc_fun(tc_prod(X4,X6),tc_bool)),
file('<stdin>',cls_Times__Int__distrib1_0) ).
fof(c_0_102,axiom,
! [X5,X38,X39] :
( c_in(c_Pair(X39,v_sko__Transitive__Closure__Xtrancl__Xcases__1(X39,X38,X5),t_a,t_a),c_Transitive__Closure_Otrancl(X5,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(X39,X38,t_a,t_a),X5,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X39,X38,t_a,t_a),c_Transitive__Closure_Otrancl(X5,t_a),tc_prod(t_a,t_a)) ),
file('<stdin>',cls_trancl_Ocases_0) ).
fof(c_0_103,axiom,
! [X19,X8,X5,X3,X4] :
( c_Relation_OImage(X5,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4) != c_Relation_OImage(X5,c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4)
| ~ c_in(X19,X3,X4)
| ~ c_in(X8,X3,X4)
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4)
| c_in(c_Pair(X8,X19,X4,X4),X5,tc_prod(X4,X4)) ),
file('<stdin>',cls_eq__equiv__class__iff_0) ).
fof(c_0_104,axiom,
! [X19,X8,X5,X3,X4] :
( c_Relation_OImage(X5,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4) != c_Relation_OImage(X5,c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4)
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4)
| c_in(c_Pair(X8,X19,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(X19,X3,X4)
| ~ c_in(X8,X3,X4) ),
file('<stdin>',cls_equiv__class__eq__iff_3) ).
fof(c_0_105,axiom,
! [X5,X38,X39] :
( c_in(c_Pair(v_sko__Transitive__Closure__Xtrancl__Xcases__1(X39,X38,X5),X38,t_a,t_a),X5,tc_prod(t_a,t_a))
| c_in(c_Pair(X39,X38,t_a,t_a),X5,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X39,X38,t_a,t_a),c_Transitive__Closure_Otrancl(X5,t_a),tc_prod(t_a,t_a)) ),
file('<stdin>',cls_trancl_Ocases_1) ).
fof(c_0_106,axiom,
! [X5,X20,X21,X3,X4] :
( c_Relation_OImage(X5,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4) != c_Relation_OImage(X5,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4)
| c_in(c_Pair(X21,X20,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(X20,X3,X4)
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4) ),
file('<stdin>',cls_eq__equiv__class_0) ).
fof(c_0_107,axiom,
! [X5,X4] :
( c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X4,X4),X5),X5,X4,X4,X4) != X5
| c_Equiv__Relations_Oequiv(c_Relation_ODomain(X5,X4,X4),X5,X4) ),
file('<stdin>',cls_comp__equivI_0) ).
fof(c_0_108,axiom,
! [X8,X20,X21,X36] :
( c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X36,X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X8,v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1(X21,X20,X8)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_Ounanimity(X36) ),
file('<stdin>',cls_unanimity__def_0) ).
fof(c_0_109,axiom,
! [X19,X8,X5,X29,X6,X4] :
( c_in(c_Pair(X8,X19,X4,X4),c_Relation_Oinv__image(X5,X29,X6,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(hAPP(X29,X8),hAPP(X29,X19),X6,X6),X5,tc_prod(X6,X6)) ),
file('<stdin>',cls_in__inv__image_1) ).
fof(c_0_110,axiom,
! [X5,X20,X21,X6,X4] :
( c_in(c_Pair(X21,X20,X6,X4),X5,tc_prod(X6,X4))
| ~ c_in(X20,c_Relation_OImage(X5,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X6),X6,X4),X4) ),
file('<stdin>',cls_Image__singleton__iff_0) ).
fof(c_0_111,axiom,
! [X19,X8,X5,X3,X4] :
( c_Relation_OImage(X5,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4) = c_Relation_OImage(X5,c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4)
| ~ c_in(c_Pair(X8,X19,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(X19,X3,X4)
| ~ c_in(X8,X3,X4)
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4) ),
file('<stdin>',cls_eq__equiv__class__iff_1) ).
fof(c_0_112,axiom,
! [X5,X20,X21,X10,X4] :
( hBOOL(hAPP(X10,X20))
| hBOOL(hAPP(X10,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X10,X21,X5,X4)))
| ~ hBOOL(hAPP(X10,X21))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_rtrancl__induct_2) ).
fof(c_0_113,axiom,
! [X5,X20,X21,X10,X4] :
( hBOOL(hAPP(X10,X21))
| hBOOL(hAPP(X10,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X10,X20,X5,X4)))
| ~ hBOOL(hAPP(X10,X20))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_converse__rtrancl__induct_2) ).
fof(c_0_114,axiom,
! [X12,X4] :
( c_Relation_Orel__comp(X12,X12,X4,X4,X4) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool))
| c_Wellfounded_Owf(X12,X4) ),
file('<stdin>',cls_wf__no__loop_0) ).
fof(c_0_115,axiom,
! [X5,X1,X2,X3,X6,X4] :
( c_lessequals(c_Relation_OImage(X5,X1,X4,X6),X2,tc_fun(X6,tc_bool))
| ~ c_lessequals(X5,c_Product__Type_OSigma(X3,c_COMBK(X2,tc_fun(X6,tc_bool),X4),X4,X6),tc_fun(tc_prod(X4,X6),tc_bool)) ),
file('<stdin>',cls_Image__subset_0) ).
fof(c_0_116,axiom,
! [X1,X2,X3,X4] : 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)),
file('<stdin>',cls_Un__Int__crazy_0) ).
fof(c_0_117,axiom,
! [X36] :
( c_Arrow__Order__Mirabelle_OIIA(X36)
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X36),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X36),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X36,v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X36)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X36),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X36),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X36,v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X36)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_IIA__def_9) ).
fof(c_0_118,axiom,
! [X8,X1,X2,X3,X6,X4] :
( c_lessequals(c_Product__Type_OSigma(X3,c_COMBK(X1,tc_fun(X4,tc_bool),X6),X6,X4),c_Product__Type_OSigma(X2,c_COMBK(X1,tc_fun(X4,tc_bool),X6),X6,X4),tc_fun(tc_prod(X6,X4),tc_bool))
| ~ c_lessequals(X3,X2,tc_fun(X6,tc_bool))
| ~ c_in(X8,X1,X4) ),
file('<stdin>',cls_Times__subset__cancel2_1) ).
fof(c_0_119,axiom,
! [X5,X20,X21,X3,X4] :
( c_Relation_OImage(X5,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4) = c_Relation_OImage(X5,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4)
| ~ c_in(c_Pair(X21,X20,X4,X4),X5,tc_prod(X4,X4))
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4) ),
file('<stdin>',cls_equiv__class__eq_0) ).
fof(c_0_120,axiom,
! [X19,X8,X5,X3,X4] :
( c_Relation_OImage(X5,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4) = c_Relation_OImage(X5,c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4)
| ~ c_in(c_Pair(X8,X19,X4,X4),X5,tc_prod(X4,X4))
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4) ),
file('<stdin>',cls_equiv__class__eq__iff_0) ).
fof(c_0_121,axiom,
! [X18,X19,X8,X5,X6,X4] :
( X19 = X18
| ~ c_in(c_Pair(X8,X18,X4,X6),X5,tc_prod(X4,X6))
| ~ c_in(c_Pair(X8,X19,X4,X6),X5,tc_prod(X4,X6))
| ~ c_Relation_Osingle__valued(X5,X4,X6) ),
file('<stdin>',cls_single__valuedD_0) ).
fof(c_0_122,axiom,
! [X19,X8,X5,X4] :
( c_in(c_Pair(X8,X19,X4,X4),hAPP(c_Relation_Oconverse(X4,X4),c_Transitive__Closure_Otrancl(X5,X4)),tc_prod(X4,X4))
| ~ c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Otrancl(hAPP(c_Relation_Oconverse(X4,X4),X5),X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_trancl__converseD_0) ).
fof(c_0_123,axiom,
! [X5,X20,X21,X6,X4] :
( c_in(X20,c_Relation_OImage(X5,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X6),X6,X4),X4)
| ~ c_in(c_Pair(X21,X20,X6,X4),X5,tc_prod(X6,X4)) ),
file('<stdin>',cls_Image__singleton__iff_1) ).
fof(c_0_124,axiom,
! [X19,X8,X5,X4] :
( c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Otrancl(hAPP(c_Relation_Oconverse(X4,X4),X5),X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X8,X19,X4,X4),hAPP(c_Relation_Oconverse(X4,X4),c_Transitive__Closure_Otrancl(X5,X4)),tc_prod(X4,X4)) ),
file('<stdin>',cls_trancl__converseI_0) ).
fof(c_0_125,axiom,
! [X5,X20,X21,X4] :
( c_Relation_OImage(X5,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4) != c_Relation_OImage(X5,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4)
| ~ c_in(X20,c_Relation_OField(X5,X4),X4)
| ~ c_in(X21,c_Relation_OField(X5,X4),X4)
| ~ c_Relation_Oantisym(X5,X4)
| ~ c_Relation_Orefl__on(c_Relation_OField(X5,X4),X5,X4)
| X21 = X20 ),
file('<stdin>',cls_Refl__antisym__eq__Image1__Image1__iff_0) ).
fof(c_0_126,axiom,
! [X19,X8,X5,X4] :
( c_Wellfounded_Owf(X5,X4)
| ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X19,X8,X4,X4),X5,tc_prod(X4,X4)),X4) ),
file('<stdin>',cls_wf__insert_0) ).
fof(c_0_127,axiom,
! [X19,X8,X5,X4] :
( c_Wellfounded_Oacyclic(X5,X4)
| ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X19,X8,X4,X4),X5,tc_prod(X4,X4)),X4) ),
file('<stdin>',cls_acyclic__insert_0) ).
fof(c_0_128,axiom,
! [X5,X20,X21,X4] :
( X21 = X20
| ~ c_in(c_Pair(X20,X21,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X20,X4,X4),X5,tc_prod(X4,X4))
| ~ c_Relation_Oantisym(X5,X4) ),
file('<stdin>',cls_antisymD_0) ).
fof(c_0_129,axiom,
! [X19,X8,X5,X4] :
( X8 = X19
| ~ c_in(c_Pair(X19,X8,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(c_Pair(X8,X19,X4,X4),X5,tc_prod(X4,X4))
| ~ c_Relation_Oantisym(X5,X4) ),
file('<stdin>',cls_antisym__def_0) ).
fof(c_0_130,axiom,
! [X8,X5,X21,X4] :
( ~ c_in(c_Pair(X8,X21,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X8,X4,X4),X5,tc_prod(X4,X4))
| ~ c_Wellfounded_Owf(X5,X4) ),
file('<stdin>',cls_wf__asym_0) ).
fof(c_0_131,axiom,
! [X5,X20,X6,X4] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X20,X5,X4,X6),X20,X6,X4),X5,tc_prod(X6,X4))
| ~ c_in(X20,c_Relation_ORange(X5,X6,X4),X4) ),
file('<stdin>',cls_RangeE_0) ).
fof(c_0_132,axiom,
! [X5,X21,X6,X4] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X21,X5,X4,X6),X21,X6,X4),X5,tc_prod(X6,X4))
| ~ c_in(X21,c_Relation_ORange(X5,X6,X4),X4) ),
file('<stdin>',cls_Range__iff_0) ).
fof(c_0_133,axiom,
! [X5,X21,X6,X4] :
( c_in(c_Pair(X21,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X21,X5,X4,X6),X4,X6),X5,tc_prod(X4,X6))
| ~ c_in(X21,c_Relation_ODomain(X5,X4,X6),X4) ),
file('<stdin>',cls_DomainE_0) ).
fof(c_0_134,axiom,
! [X5,X21,X6,X4] :
( c_in(c_Pair(X21,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X21,X5,X4,X6),X4,X6),X5,tc_prod(X4,X6))
| ~ c_in(X21,c_Relation_ODomain(X5,X4,X6),X4) ),
file('<stdin>',cls_Domain__iff_0) ).
fof(c_0_135,axiom,
! [X5,X20,X21,X4] : c_Relation_OField(c_Set_Oinsert(c_Pair(X21,X20,X4,X4),X5,tc_prod(X4,X4)),X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X21,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4),c_Relation_OField(X5,X4),tc_fun(X4,tc_bool)),
file('<stdin>',cls_Field__insert_0) ).
fof(c_0_136,axiom,
! [X19,X8,X5,X4] :
( c_in(c_Pair(X19,X8,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Ortrancl(hAPP(c_Relation_Oconverse(X4,X4),X5),X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_rtrancl__converseD_0) ).
fof(c_0_137,axiom,
! [X19,X8,X5,X4] :
( c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X19,X8,X4,X4),X5,tc_prod(X4,X4)),X4)
| c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_Wellfounded_Owf(X5,X4) ),
file('<stdin>',cls_wf__insert_2) ).
fof(c_0_138,axiom,
! [X19,X8,X5,X4] :
( c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X19,X8,X4,X4),X5,tc_prod(X4,X4)),X4)
| c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_Wellfounded_Oacyclic(X5,X4) ),
file('<stdin>',cls_acyclic__insert_2) ).
fof(c_0_139,axiom,
! [X20,X21,X2,X3,X6,X4] :
( c_in(X20,hAPP(X2,X21),X6)
| ~ c_in(c_Pair(X21,X20,X4,X6),c_Product__Type_OSigma(X3,X2,X4,X6),tc_prod(X4,X6)) ),
file('<stdin>',cls_SigmaD2_0) ).
fof(c_0_140,axiom,
! [X20,X21,X2,X3,X6,X4] :
( c_in(X21,X3,X4)
| ~ c_in(c_Pair(X21,X20,X4,X6),c_Product__Type_OSigma(X3,X2,X4,X6),tc_prod(X4,X6)) ),
file('<stdin>',cls_SigmaD1_0) ).
fof(c_0_141,axiom,
! [X5,X38,X39] :
( c_in(c_Pair(X39,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X39,X38,X5),t_a,t_a),c_Transitive__Closure_Ortrancl(X5,t_a),tc_prod(t_a,t_a))
| X38 = X39
| ~ c_in(c_Pair(X39,X38,t_a,t_a),c_Transitive__Closure_Ortrancl(X5,t_a),tc_prod(t_a,t_a)) ),
file('<stdin>',cls_rtrancl_Ocases_0) ).
fof(c_0_142,axiom,
! [X19,X8,X5,X4] :
( c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Ortrancl(hAPP(c_Relation_Oconverse(X4,X4),X5),X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X19,X8,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_rtrancl__converseI_0) ).
fof(c_0_143,axiom,
! [X5,X38,X39] :
( c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X39,X38,X5),X38,t_a,t_a),X5,tc_prod(t_a,t_a))
| X38 = X39
| ~ c_in(c_Pair(X39,X38,t_a,t_a),c_Transitive__Closure_Ortrancl(X5,t_a),tc_prod(t_a,t_a)) ),
file('<stdin>',cls_rtrancl_Ocases_1) ).
fof(c_0_144,axiom,
! [X19,X8,X5,X3,X4] :
( c_Equiv__Relations_Oquotient(c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X5,X4) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X5,X4)
| ~ c_in(c_Pair(X8,X19,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(X19,X3,X4)
| ~ c_in(X8,X3,X4)
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4) ),
file('<stdin>',cls_eq__equiv__class__iff2_1) ).
fof(c_0_145,axiom,
! [X12,X2,X3,X6,X4] :
( c_Relation_OImage(X12,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X6,tc_bool)),X6,X4) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X12,X3,X6,X4),c_Relation_OImage(X12,X2,X6,X4),tc_fun(X4,tc_bool))
| ~ c_Relation_Osingle__valued(hAPP(c_Relation_Oconverse(X6,X4),X12),X4,X6) ),
file('<stdin>',cls_Image__Int__eq_0) ).
fof(c_0_146,axiom,
! [X19,X8,X5,X3,X4] :
( c_Equiv__Relations_Oquotient(c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X5,X4) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X5,X4)
| ~ c_in(X19,X3,X4)
| ~ c_in(X8,X3,X4)
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4)
| c_in(c_Pair(X8,X19,X4,X4),X5,tc_prod(X4,X4)) ),
file('<stdin>',cls_eq__equiv__class__iff2_0) ).
fof(c_0_147,axiom,
! [X37,X36] :
( c_Arrow__Order__Mirabelle_OIIA(X36)
| c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X36),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X36),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X36),X37),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X36),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X36),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X36),X37),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_IIA__def_6) ).
fof(c_0_148,axiom,
! [X37,X36] :
( c_Arrow__Order__Mirabelle_OIIA(X36)
| c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X36),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X36),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X36),X37),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X36),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X36),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X36),X37),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_IIA__def_7) ).
fof(c_0_149,axiom,
! [X8,X5,X4] :
( ~ c_in(c_Pair(X8,X8,X4,X4),X5,tc_prod(X4,X4))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X5,X4),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X5,X4),X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_irrefl__trancl__rD_0) ).
fof(c_0_150,axiom,
! [X5,X20,X21,X6,X4] :
( c_in(c_Pair(X20,X21,X6,X4),X5,tc_prod(X6,X4))
| ~ c_in(c_Pair(X21,X20,X4,X6),hAPP(c_Relation_Oconverse(X6,X4),X5),tc_prod(X4,X6)) ),
file('<stdin>',cls_converseD_0) ).
fof(c_0_151,axiom,
! [X13,X12,X3,X6,X4] : c_Relation_OImage(c_Lattices_Oupper__semilattice__class_Osup(X12,X13,tc_fun(tc_prod(X6,X4),tc_bool)),X3,X6,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X12,X3,X6,X4),c_Relation_OImage(X13,X3,X6,X4),tc_fun(X4,tc_bool)),
file('<stdin>',cls_Un__Image_0) ).
fof(c_0_152,axiom,
! [X5,X20,X21,X6,X4] :
( c_in(c_Pair(X20,X21,X6,X4),hAPP(c_Relation_Oconverse(X4,X6),X5),tc_prod(X6,X4))
| ~ c_in(c_Pair(X21,X20,X4,X6),X5,tc_prod(X4,X6)) ),
file('<stdin>',cls_converseI_0) ).
fof(c_0_153,axiom,
! [X5,X20,X21,X6,X4] :
( c_in(c_Pair(X21,X20,X4,X6),hAPP(c_Relation_Oconverse(X6,X4),X5),tc_prod(X4,X6))
| ~ c_in(c_Pair(X20,X21,X6,X4),X5,tc_prod(X6,X4)) ),
file('<stdin>',cls_converse__iff_1) ).
fof(c_0_154,axiom,
! [X8,X29,X2,X3,X6,X4] :
( c_in(hAPP(X29,X8),X2,X6)
| ~ c_in(X8,X3,X4)
| ~ c_in(X29,c_FuncSet_OPi(X3,c_COMBK(X2,tc_fun(X6,tc_bool),X4),X4,X6),tc_fun(X4,X6)) ),
file('<stdin>',cls_funcset__mem_0) ).
fof(c_0_155,axiom,
! [X20,X21,X12,X4] :
( c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Otrancl(X12,X4),tc_prod(X4,X4))
| X21 = X20
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Ortrancl(X12,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_rtranclD_0) ).
fof(c_0_156,axiom,
! [X19,X8,X12,X4] :
( c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Otrancl(X12,X4),tc_prod(X4,X4))
| X8 = X19
| ~ c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Ortrancl(X12,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_rtrancl__eq__or__trancl_0) ).
fof(c_0_157,axiom,
! [X19,X8,X12,X4] :
( c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Ortrancl(X12,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Otrancl(X12,X4),tc_prod(X4,X4))
| X8 = X19 ),
file('<stdin>',cls_rtrancl__eq__or__trancl_2) ).
fof(c_0_158,axiom,
! [X5,X20,X21,X4] :
( c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_trancl__into__rtrancl_0) ).
fof(c_0_159,axiom,
! [X8,X5,X20,X3,X6,X4] :
( c_in(X20,c_Relation_OImage(X5,X3,X6,X4),X4)
| ~ c_in(c_Pair(X8,X20,X6,X4),X5,tc_prod(X6,X4))
| ~ c_in(X8,X3,X6) ),
file('<stdin>',cls_Image__iff_2) ).
fof(c_0_160,axiom,
! [X5,X20,X21,X3,X6,X4] :
( c_in(X20,c_Relation_OImage(X5,X3,X4,X6),X6)
| ~ c_in(c_Pair(X21,X20,X4,X6),X5,tc_prod(X4,X6))
| ~ c_in(X21,X3,X4) ),
file('<stdin>',cls_rev__ImageI_0) ).
fof(c_0_161,axiom,
! [X22,X23,X1,X6,X4] : c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(X23,X22,tc_fun(X4,tc_bool)),X1,X4,X6) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X23,X1,X4,X6),c_Product__Type_OSigma(X22,X1,X4,X6),tc_fun(tc_prod(X4,X6),tc_bool)),
file('<stdin>',cls_Sigma__Un__distrib1_0) ).
fof(c_0_162,axiom,
! [X22,X23,X1,X6,X4] : c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(X23,X22,tc_fun(X4,tc_bool)),X1,X4,X6) = c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(X23,X1,X4,X6),c_Product__Type_OSigma(X22,X1,X4,X6),tc_fun(tc_prod(X4,X6),tc_bool)),
file('<stdin>',cls_Sigma__Int__distrib1_0) ).
fof(c_0_163,axiom,
! [X5,X20,X21,X4] :
( c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X20,X4,X4),X5,tc_prod(X4,X4)) ),
file('<stdin>',cls_trancl_Or__into__trancl_0) ).
fof(c_0_164,axiom,
! [X5,X20,X21,X4] :
( c_in(c_Pair(X20,X21,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X20,X4,X4),X5,tc_prod(X4,X4))
| ~ c_Relation_Osym(X5,X4) ),
file('<stdin>',cls_symD_0) ).
fof(c_0_165,axiom,
! [X19,X8,X5,X4] :
( c_in(c_Pair(X19,X8,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(c_Pair(X8,X19,X4,X4),X5,tc_prod(X4,X4))
| ~ c_Relation_Osym(X5,X4) ),
file('<stdin>',cls_sym__def_0) ).
fof(c_0_166,axiom,
! [X37] :
( c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X37),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X37),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_iff_0) ).
fof(c_0_167,axiom,
! [X37] :
( c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X37),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X37),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_iff_1) ).
fof(c_0_168,axiom,
! [X18,X19,X8,X49] :
( c_in(c_Pair(X8,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X49,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X8 = X18
| ~ c_in(c_Pair(X8,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X49,X18),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_in__mkbot_2) ).
fof(c_0_169,axiom,
! [X18,X19,X8,X49] :
( c_in(c_Pair(X8,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X49,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X19 = X18
| ~ c_in(c_Pair(X8,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X49,X18),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_in__mktop_2) ).
fof(c_0_170,axiom,
! [X18,X19,X8,X49] :
( c_in(c_Pair(X8,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X49,X18),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X8,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X49,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X8 = X18
| X19 = X18 ),
file('<stdin>',cls_in__mkbot_3) ).
fof(c_0_171,axiom,
! [X18,X19,X8,X49] :
( c_in(c_Pair(X8,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X49,X18),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X8,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X49,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X8 = X19
| X19 = X18 ),
file('<stdin>',cls_in__mkbot_5) ).
fof(c_0_172,axiom,
! [X18,X19,X8,X49] :
( c_in(c_Pair(X8,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X49,X18),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X8,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X49,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X19 = X18
| X8 = X18 ),
file('<stdin>',cls_in__mktop_3) ).
fof(c_0_173,axiom,
! [X18,X19,X8,X49] :
( c_in(c_Pair(X8,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X49,X18),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X8,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X49,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X8 = X19
| X8 = X18 ),
file('<stdin>',cls_in__mktop_5) ).
fof(c_0_174,axiom,
! [X12,X2,X3,X6,X4] : c_Relation_OImage(X12,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X6,tc_bool)),X6,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X12,X3,X6,X4),c_Relation_OImage(X12,X2,X6,X4),tc_fun(X4,tc_bool)),
file('<stdin>',cls_Image__Un_0) ).
fof(c_0_175,axiom,
! [X12,X17,X6,X4] : c_Relation_Orel__comp(X12,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X17,X6),tc_bool)),X4,X17,X6) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X6),tc_bool)),
file('<stdin>',cls_rel__comp__empty2_0) ).
fof(c_0_176,axiom,
! [X12,X17,X6,X4] : c_Relation_Orel__comp(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X17),tc_bool)),X12,X4,X17,X6) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X6),tc_bool)),
file('<stdin>',cls_rel__comp__empty1_0) ).
fof(c_0_177,axiom,
! [X19,X8,X12,X9,X4] :
( ~ c_in(X19,X9,X4)
| ~ c_in(c_Pair(X19,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X9,X12,X4),X4,X4),X12,tc_prod(X4,X4))
| ~ c_in(X8,X9,X4)
| ~ c_Wellfounded_Owf(X12,X4) ),
file('<stdin>',cls_wfE__min_1) ).
fof(c_0_178,axiom,
! [X19,X7,X5,X9,X4] :
( ~ c_in(X19,X9,X4)
| ~ c_in(c_Pair(X19,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X9,X5,X4),X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(X7,X9,X4)
| ~ c_Wellfounded_Owf(X5,X4) ),
file('<stdin>',cls_wf__eq__minimal_1) ).
fof(c_0_179,axiom,
! [X8,X5,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Relation_Oconverse(X4,X4),X5),c_Transitive__Closure_Ortrancl(X5,X4),tc_fun(tc_prod(X4,X4),tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_in(c_Pair(X8,X8,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_irrefl__tranclI_0) ).
fof(c_0_180,axiom,
! [X19,X5,X21,X10,X4] :
( hBOOL(hAPP(X10,X21))
| hBOOL(hAPP(X10,X19))
| ~ c_in(c_Pair(X19,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X10,X5,X4),X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(X21,c_Wellfounded_Oacc(X5,X4),X4) ),
file('<stdin>',cls_acc__induct__rule_1) ).
fof(c_0_181,axiom,
! [X19,X5,X21,X10,X4] :
( hBOOL(hAPP(X10,X21))
| hBOOL(hAPP(X10,X19))
| ~ c_in(c_Pair(X19,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X10,X5,X4),X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(X21,c_Wellfounded_Oacc(X5,X4),X4) ),
file('<stdin>',cls_acc__induct_1) ).
fof(c_0_182,axiom,
! [X7,X8,X5,X3,X4] :
( c_in(c_Pair(X7,X8,X4,X4),X5,tc_prod(X4,X4))
| c_in(c_Pair(X8,X7,X4,X4),X5,tc_prod(X4,X4))
| X8 = X7
| ~ c_in(X7,X3,X4)
| ~ c_in(X8,X3,X4)
| ~ c_Relation_Ototal__on(X3,X5,X4) ),
file('<stdin>',cls_total__on__def_0) ).
fof(c_0_183,axiom,
! [X16,X5,X35,X3,X6,X4] :
( c_lessequals(c_Relation_OImage(X16,X35,X4,X6),c_Relation_OImage(X5,X3,X4,X6),tc_fun(X6,tc_bool))
| ~ c_lessequals(X35,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X16,X5,tc_fun(tc_prod(X4,X6),tc_bool)) ),
file('<stdin>',cls_Image__mono_0) ).
fof(c_0_184,axiom,
! [X5,X3,X4] :
( c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X4,X4),X5),X5,X4,X4,X4) = X5
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4) ),
file('<stdin>',cls_equiv__comp__eq_0) ).
fof(c_0_185,axiom,
! [X5,X20,X21,X6,X4] : c_Relation_ORange(c_Set_Oinsert(c_Pair(X21,X20,X6,X4),X5,tc_prod(X6,X4)),X6,X4) = c_Set_Oinsert(X20,c_Relation_ORange(X5,X6,X4),X4),
file('<stdin>',cls_Range__insert_0) ).
fof(c_0_186,axiom,
! [X5,X20,X21,X6,X4] : c_Relation_ODomain(c_Set_Oinsert(c_Pair(X21,X20,X4,X6),X5,tc_prod(X4,X6)),X4,X6) = c_Set_Oinsert(X21,c_Relation_ODomain(X5,X4,X6),X4),
file('<stdin>',cls_Domain__insert_0) ).
fof(c_0_187,axiom,
! [X8,X1,X2,X3,X6,X4] :
( c_Product__Type_OSigma(X3,c_COMBK(X1,tc_fun(X4,tc_bool),X6),X6,X4) != c_Product__Type_OSigma(X2,c_COMBK(X1,tc_fun(X4,tc_bool),X6),X6,X4)
| ~ c_in(X8,X1,X4)
| X3 = X2 ),
file('<stdin>',cls_Times__eq__cancel2_0) ).
fof(c_0_188,axiom,
! [X19,X5,X21,X10,X4] :
( hBOOL(hAPP(X10,X21))
| hBOOL(hAPP(X10,X19))
| ~ c_in(c_Pair(X19,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X10,X5,X4),X4,X4),X5,tc_prod(X4,X4))
| ~ c_Wellfounded_Owf(X5,X4) ),
file('<stdin>',cls_wf__induct_0) ).
fof(c_0_189,axiom,
! [X19,X40,X12,X10,X4] :
( hBOOL(hAPP(X10,X40))
| hBOOL(hAPP(X10,X19))
| ~ c_in(c_Pair(X19,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X10,X12,X4),X4,X4),X12,tc_prod(X4,X4))
| ~ c_Wellfounded_Owf(X12,X4) ),
file('<stdin>',cls_tfl__wf__induct_0) ).
fof(c_0_190,axiom,
! [X19,X7,X5,X10,X4] :
( hBOOL(hAPP(X10,X7))
| hBOOL(hAPP(X10,X19))
| ~ c_in(c_Pair(X19,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X10,X5,X4),X4,X4),X5,tc_prod(X4,X4))
| ~ c_Wellfounded_Owf(X5,X4) ),
file('<stdin>',cls_wf__def_0) ).
fof(c_0_191,axiom,
! [X19,X5,X21,X10,X4] :
( hBOOL(hAPP(X10,X21))
| hBOOL(hAPP(X10,X19))
| ~ c_in(c_Pair(X19,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X10,X5,X4),X4,X4),X5,tc_prod(X4,X4))
| ~ c_Wellfounded_Owf(X5,X4) ),
file('<stdin>',cls_wf__induct__rule_0) ).
fof(c_0_192,axiom,
! [X18,X19,X5,X29,X6,X4] :
( hAPP(X29,X19) = hAPP(X29,X18)
| ~ c_in(c_Pair(X19,X18,X4,X4),X5,tc_prod(X4,X4))
| ~ c_Equiv__Relations_Ocongruent(X5,X29,X4,X6) ),
file('<stdin>',cls_congruent_Ocongruent_0) ).
fof(c_0_193,axiom,
! [X20,X21,X2,X3,X6,X4] :
( c_in(c_Pair(X21,X20,X4,X6),c_Product__Type_OSigma(X3,X2,X4,X6),tc_prod(X4,X6))
| ~ c_in(X20,hAPP(X2,X21),X6)
| ~ c_in(X21,X3,X4) ),
file('<stdin>',cls_SigmaI_0) ).
fof(c_0_194,axiom,
! [X20,X21,X2,X3,X6,X4] :
( c_in(c_Pair(X21,X20,X4,X6),c_Product__Type_OSigma(X3,X2,X4,X6),tc_prod(X4,X6))
| ~ c_in(X20,hAPP(X2,X21),X6)
| ~ c_in(X21,X3,X4) ),
file('<stdin>',cls_mem__Sigma__iff_2) ).
fof(c_0_195,axiom,
! [X2,X3,X6,X4] : c_lessequals(c_Relation_ORange(c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(tc_prod(X6,X4),tc_bool)),X6,X4),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(X3,X6,X4),c_Relation_ORange(X2,X6,X4),tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
file('<stdin>',cls_Range__Int__subset_0) ).
fof(c_0_196,axiom,
! [X2,X3,X6,X4] : c_lessequals(c_Relation_ODomain(c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(tc_prod(X4,X6),tc_bool)),X4,X6),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X3,X4,X6),c_Relation_ODomain(X2,X4,X6),tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
file('<stdin>',cls_Domain__Int__subset_0) ).
fof(c_0_197,axiom,
! [X12,X4] : c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X12,X4),c_Transitive__Closure_Ortrancl(X12,X4),X4,X4,X4) = c_Transitive__Closure_Ortrancl(X12,X4),
file('<stdin>',cls_rtrancl__idemp__self__comp_0) ).
fof(c_0_198,axiom,
! [X36] :
( c_Arrow__Order__Mirabelle_OIIA(X36)
| c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X36),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X36),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X36,v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X36)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X36),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X36),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X36,v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X36)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_IIA__def_8) ).
fof(c_0_199,axiom,
! [X5,X4] : c_Transitive__Closure_Otrancl(X5,X4) = c_Relation_Orel__comp(X5,c_Transitive__Closure_Ortrancl(X5,X4),X4,X4,X4),
file('<stdin>',cls_trancl__unfold__left_0) ).
fof(c_0_200,axiom,
! [X5,X4] : c_Transitive__Closure_Otrancl(X5,X4) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X5,X4),X5,X4,X4,X4),
file('<stdin>',cls_trancl__unfold__right_0) ).
fof(c_0_201,axiom,
! [X12,X6,X4] : c_Relation_Orel__comp(X12,c_Relation_OId(X6),X4,X6,X6) = X12,
file('<stdin>',cls_R__O__Id_0) ).
fof(c_0_202,axiom,
! [X12,X6,X4] : c_Relation_Orel__comp(c_Relation_OId(X4),X12,X4,X4,X6) = X12,
file('<stdin>',cls_Id__O__R_0) ).
fof(c_0_203,axiom,
! [X47,X8,X5,X10] :
( hBOOL(hAPP(X10,X8))
| c_in(X47,c_Wellfounded_Oacc(X5,t_a),t_a)
| ~ c_in(c_Pair(X47,v_sko__Wellfounded__Xacc__Xinducts__1(X10,X5),t_a,t_a),X5,tc_prod(t_a,t_a))
| ~ c_in(X8,c_Wellfounded_Oacc(X5,t_a),t_a) ),
file('<stdin>',cls_acc_Oinducts_0) ).
fof(c_0_204,axiom,
! [X47,X8,X5,X10] :
( hBOOL(hAPP(X10,X8))
| c_in(X47,c_Wellfounded_Oacc(X5,t_a),t_a)
| ~ c_in(c_Pair(X47,v_sko__Wellfounded__Xacc__Xinduct__1(X10,X5),t_a,t_a),X5,tc_prod(t_a,t_a))
| ~ c_in(X8,c_Wellfounded_Oacc(X5,t_a),t_a) ),
file('<stdin>',cls_acc_Oinduct_0) ).
fof(c_0_205,axiom,
! [X5,X20,X21,X4] :
( c_in(X20,c_Wellfounded_Oacc(X5,X4),X4)
| ~ c_in(X21,c_Wellfounded_Oacc(X5,X4),X4)
| ~ c_in(c_Pair(X20,X21,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_acc__downwards__aux_0) ).
fof(c_0_206,axiom,
! [X5,X20,X21,X4] :
( c_in(X20,c_Wellfounded_Oacc(X5,X4),X4)
| ~ c_in(c_Pair(X20,X21,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(X21,c_Wellfounded_Oacc(X5,X4),X4) ),
file('<stdin>',cls_acc__downwards_0) ).
fof(c_0_207,axiom,
! [X19,X8,X5,X10] :
( hBOOL(hAPP(X10,X8))
| hBOOL(hAPP(X10,X19))
| ~ c_in(c_Pair(X19,v_sko__Wellfounded__Xacc__Xinduct__1(X10,X5),t_a,t_a),X5,tc_prod(t_a,t_a))
| ~ c_in(X8,c_Wellfounded_Oacc(X5,t_a),t_a) ),
file('<stdin>',cls_acc_Oinduct_1) ).
fof(c_0_208,axiom,
! [X19,X8,X5,X10] :
( hBOOL(hAPP(X10,X8))
| hBOOL(hAPP(X10,X19))
| ~ c_in(c_Pair(X19,v_sko__Wellfounded__Xacc__Xinducts__1(X10,X5),t_a,t_a),X5,tc_prod(t_a,t_a))
| ~ c_in(X8,c_Wellfounded_Oacc(X5,t_a),t_a) ),
file('<stdin>',cls_acc_Oinducts_1) ).
fof(c_0_209,axiom,
! [X5,X21,X3,X4] :
( c_in(X21,c_Relation_OImage(X5,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4),X4)
| ~ c_in(X21,X3,X4)
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4) ),
file('<stdin>',cls_equiv__class__self_0) ).
fof(c_0_210,axiom,
! [X19,X5,X21,X4] :
( c_in(X19,c_Wellfounded_Oacc(X5,X4),X4)
| ~ c_in(c_Pair(X19,X21,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(X21,c_Wellfounded_Oacc(X5,X4),X4) ),
file('<stdin>',cls_acc_Ocases_0) ).
fof(c_0_211,axiom,
! [X5,X20,X21,X4] :
( c_in(X21,c_Wellfounded_Oacc(X5,X4),X4)
| ~ c_in(c_Pair(X21,X20,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(X20,c_Wellfounded_Oacc(X5,X4),X4) ),
file('<stdin>',cls_acc__downward_0) ).
fof(c_0_212,axiom,
! [X5,X4] : c_lessequals(c_Transitive__Closure_Otrancl(X5,X4),c_Product__Type_OSigma(c_Relation_OField(X5,X4),c_COMBK(c_Relation_OField(X5,X4),tc_fun(X4,tc_bool),X4),X4,X4),tc_fun(tc_prod(X4,X4),tc_bool)),
file('<stdin>',cls_trancl__subset__Field2_0) ).
fof(c_0_213,axiom,
! [X19,X8,X12,X4] :
( X8 = X19
| ~ c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Ortrancl(X12,X4),tc_prod(X4,X4))
| c_in(X8,c_Relation_ODomain(X12,X4,X4),X4) ),
file('<stdin>',cls_Not__Domain__rtrancl_0) ).
fof(c_0_214,axiom,
! [X8,X29,X2,X3,X6,X4] :
( ~ c_in(X8,X3,X4)
| c_in(hAPP(X29,X8),hAPP(X2,X8),X6)
| ~ c_in(X29,c_FuncSet_OPi(X3,X2,X4,X6),tc_fun(X4,X6)) ),
file('<stdin>',cls_PiE_0) ).
fof(c_0_215,axiom,
! [X8,X29,X2,X3,X6,X4] :
( c_in(hAPP(X29,X8),hAPP(X2,X8),X6)
| ~ c_in(X8,X3,X4)
| ~ c_in(X29,c_FuncSet_OPi(X3,X2,X4,X6),tc_fun(X4,X6)) ),
file('<stdin>',cls_Pi__mem_0) ).
fof(c_0_216,axiom,
! [X5,X4] :
( c_Nitpick_Orefl_H(X5,X4)
| ~ c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X5,X4),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X5,X4),X4,X4),X5,tc_prod(X4,X4)) ),
file('<stdin>',cls_Nitpick_Orefl_H__def_1) ).
fof(c_0_217,axiom,
! [X5,X20,X21,X6,X4] :
( c_in(X21,c_Relation_ODomain(X5,X4,X6),X4)
| ~ c_in(c_Pair(X21,X20,X4,X6),X5,tc_prod(X4,X6)) ),
file('<stdin>',cls_DomainI_0) ).
fof(c_0_218,axiom,
! [X8,X5,X21,X6,X4] :
( c_in(X21,c_Relation_ODomain(X5,X4,X6),X4)
| ~ c_in(c_Pair(X21,X8,X4,X6),X5,tc_prod(X4,X6)) ),
file('<stdin>',cls_Domain__iff_1) ).
fof(c_0_219,axiom,
! [X5,X20,X21,X6,X4] :
( c_in(X20,c_Relation_ORange(X5,X4,X6),X6)
| ~ c_in(c_Pair(X21,X20,X4,X6),X5,tc_prod(X4,X6)) ),
file('<stdin>',cls_RangeI_0) ).
fof(c_0_220,axiom,
! [X8,X5,X21,X6,X4] :
( c_in(X21,c_Relation_ORange(X5,X6,X4),X4)
| ~ c_in(c_Pair(X8,X21,X6,X4),X5,tc_prod(X6,X4)) ),
file('<stdin>',cls_Range__iff_1) ).
fof(c_0_221,axiom,
! [X19,X8,X5,X3,X4] :
( c_in(X8,X3,X4)
| ~ c_in(c_Pair(X8,X19,X4,X4),X5,tc_prod(X4,X4))
| ~ c_Relation_Orefl__on(X3,X5,X4) ),
file('<stdin>',cls_refl__onD1_0) ).
fof(c_0_222,axiom,
! [X19,X8,X5,X3,X4] :
( c_in(X19,X3,X4)
| ~ c_in(c_Pair(X8,X19,X4,X4),X5,tc_prod(X4,X4))
| ~ c_Relation_Orefl__on(X3,X5,X4) ),
file('<stdin>',cls_refl__onD2_0) ).
fof(c_0_223,axiom,
! [X19,X8,X5,X3,X4] :
( c_in(X8,X3,X4)
| ~ c_in(c_Pair(X8,X19,X4,X4),X5,tc_prod(X4,X4))
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4) ),
file('<stdin>',cls_equiv__class__eq__iff_1) ).
fof(c_0_224,axiom,
! [X19,X8,X5,X3,X4] :
( c_in(X19,X3,X4)
| ~ c_in(c_Pair(X8,X19,X4,X4),X5,tc_prod(X4,X4))
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4) ),
file('<stdin>',cls_equiv__class__eq__iff_2) ).
fof(c_0_225,axiom,
! [X13,X12,X4] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X12,X4),c_Transitive__Closure_Ortrancl(X13,X4),tc_fun(tc_prod(X4,X4),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X12,X13,tc_fun(tc_prod(X4,X4),tc_bool)),X4),tc_fun(tc_prod(X4,X4),tc_bool)),
file('<stdin>',cls_rtrancl__Un__subset_0) ).
fof(c_0_226,axiom,
! [X5,X3,X4] :
( c_lessequals(X5,c_Product__Type_OSigma(X3,c_COMBK(X3,tc_fun(X4,tc_bool),X4),X4,X4),tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4) ),
file('<stdin>',cls_equiv__type_0) ).
fof(c_0_227,axiom,
! [X5,X3,X4] :
( c_lessequals(X5,c_Product__Type_OSigma(X3,c_COMBK(X3,tc_fun(X4,tc_bool),X4),X4,X4),tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_Relation_Orefl__on(X3,X5,X4) ),
file('<stdin>',cls_refl__on__def_0) ).
fof(c_0_228,axiom,
! [X19,X8,X3,X4] :
( c_in(X8,X3,X4)
| ~ c_in(c_Pair(X8,X19,X4,X4),c_Relation_OId__on(X3,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_Id__on__iff_1) ).
fof(c_0_229,axiom,
! [X36] :
( c_Arrow__Order__Mirabelle_Ounanimity(X36)
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3(X36),v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4(X36),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X36,v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2(X36)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_unanimity__def_3) ).
fof(c_0_230,axiom,
! [X8,X5,X4] :
( ~ c_in(c_Pair(X8,X8,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4))
| ~ c_Wellfounded_Oacyclic(X5,X4) ),
file('<stdin>',cls_acyclic__def_0) ).
fof(c_0_231,axiom,
! [X3,X4] : c_lessequals(c_Relation_OId__on(X3,X4),c_Product__Type_OSigma(X3,c_COMBK(X3,tc_fun(X4,tc_bool),X4),X4,X4),tc_fun(tc_prod(X4,X4),tc_bool)),
file('<stdin>',cls_Id__on__subset__Times_0) ).
fof(c_0_232,axiom,
! [X12,X3,X4] :
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ c_lessequals(X3,c_Relation_OImage(X12,X3,X4,X4),tc_fun(X4,tc_bool))
| ~ c_Wellfounded_Owf(X12,X4) ),
file('<stdin>',cls_wfE__pf_0) ).
fof(c_0_233,axiom,
! [X19,X8,X3,X4] :
( X8 = X19
| ~ c_in(c_Pair(X8,X19,X4,X4),c_Relation_OId__on(X3,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_Id__on__iff_0) ).
fof(c_0_234,axiom,
! [X5,X21,X4] :
( ~ c_in(c_Pair(X21,X21,X4,X4),X5,tc_prod(X4,X4))
| ~ c_Wellfounded_Owf(X5,X4) ),
file('<stdin>',cls_wf__irrefl_0) ).
fof(c_0_235,axiom,
! [X7,X8,X49] : ~ c_in(c_Pair(X7,X8,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X49,X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('<stdin>',cls_in__mkbot_0) ).
fof(c_0_236,axiom,
! [X8,X49] : ~ c_in(c_Pair(X8,X8,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X49,X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('<stdin>',cls_in__mkbot_1) ).
fof(c_0_237,axiom,
! [X19,X8,X49] : ~ c_in(c_Pair(X8,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X49,X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('<stdin>',cls_in__mktop_0) ).
fof(c_0_238,axiom,
! [X8,X49] : ~ c_in(c_Pair(X8,X8,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X49,X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('<stdin>',cls_in__mktop_1) ).
fof(c_0_239,axiom,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Olattice(X4)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4),c_Lattices_Olower__semilattice__class_Oinf(X8,X18,X4),X4),c_Lattices_Olower__semilattice__class_Oinf(X8,c_Lattices_Oupper__semilattice__class_Osup(X19,X18,X4),X4),X4) ),
file('<stdin>',cls_distrib__inf__le_0) ).
fof(c_0_240,axiom,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Olattice(X4)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Lattices_Olower__semilattice__class_Oinf(X19,X18,X4),X4),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4),c_Lattices_Oupper__semilattice__class_Osup(X8,X18,X4),X4),X4) ),
file('<stdin>',cls_distrib__sup__le_0) ).
fof(c_0_241,axiom,
! [X20,X21,X4] :
( X21 = X20
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Relation_OId(X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_pair__in__Id__conv_0) ).
fof(c_0_242,axiom,
! [X8,X12,X4] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X12,X8,X4),X8,X4,X4),X12,tc_prod(X4,X4))
| c_in(X8,c_Wellfounded_Oacc(X12,X4),X4) ),
file('<stdin>',cls_not__acc__down_0) ).
fof(c_0_243,axiom,
! [X8,X5,X4] :
( c_in(X8,c_Wellfounded_Oacc(X5,X4),X4)
| c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X5,X8,X4),X8,X4,X4),X5,tc_prod(X4,X4)) ),
file('<stdin>',cls_acc_OaccI_0) ).
fof(c_0_244,axiom,
! [X29,X12,X6,X4] : hAPP(c_Relation_Oconverse(X4,X4),c_Relation_Oinv__image(X12,X29,X6,X4)) = c_Relation_Oinv__image(hAPP(c_Relation_Oconverse(X6,X6),X12),X29,X6,X4),
file('<stdin>',cls_converse__inv__image_0) ).
fof(c_0_245,axiom,
! [X32,X30,X20,X21,X4] :
( c_Set_Oinsert(X21,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X30,c_Set_Oinsert(X32,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)
| X20 = X30
| X20 = X32 ),
file('<stdin>',cls_doubleton__eq__iff_3) ).
fof(c_0_246,axiom,
! [X32,X30,X20,X21,X4] :
( c_Set_Oinsert(X21,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X30,c_Set_Oinsert(X32,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)
| X21 = X32
| X20 = X32 ),
file('<stdin>',cls_doubleton__eq__iff_2) ).
fof(c_0_247,axiom,
! [X32,X30,X20,X21,X4] :
( c_Set_Oinsert(X21,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X30,c_Set_Oinsert(X32,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)
| X20 = X30
| X21 = X30 ),
file('<stdin>',cls_doubleton__eq__iff_1) ).
fof(c_0_248,axiom,
! [X32,X30,X20,X21,X4] :
( c_Set_Oinsert(X21,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X30,c_Set_Oinsert(X32,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)
| X21 = X32
| X21 = X30 ),
file('<stdin>',cls_doubleton__eq__iff_0) ).
fof(c_0_249,axiom,
! [X15,X5,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X5,X4,X4),c_Relation_ORange(X15,X4,X4),tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ c_Wellfounded_Owf(X15,X4)
| ~ c_Wellfounded_Owf(X5,X4)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X5,X15,tc_fun(tc_prod(X4,X4),tc_bool)),X4) ),
file('<stdin>',cls_wf__Un_0) ).
fof(c_0_250,axiom,
! [X1,X2,X3,X4] :
( c_Lattices_Oupper__semilattice__class_Osup(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_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_Un__Int__assoc__eq_0) ).
fof(c_0_251,axiom,
! [X8,X13,X12,X4] :
( c_in(X8,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X12,X13,tc_fun(tc_prod(X4,X4),tc_bool)),X4),tc_prod(X4,X4))
| ~ c_in(X8,c_Transitive__Closure_Ortrancl(X13,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_in__rtrancl__UnI_1) ).
fof(c_0_252,axiom,
! [X8,X13,X12,X4] :
( c_in(X8,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X12,X13,tc_fun(tc_prod(X4,X4),tc_bool)),X4),tc_prod(X4,X4))
| ~ c_in(X8,c_Transitive__Closure_Ortrancl(X12,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_in__rtrancl__UnI_0) ).
fof(c_0_253,axiom,
! [X51,X20,X52,X21,X6,X4] :
( c_Pair(X21,X20,X4,X6) != c_Pair(X52,X51,X4,X6)
| X21 = X52 ),
file('<stdin>',cls_Pair__eq_0) ).
fof(c_0_254,axiom,
! [X51,X20,X52,X21,X6,X4] :
( c_Pair(X21,X20,X4,X6) != c_Pair(X52,X51,X4,X6)
| X20 = X51 ),
file('<stdin>',cls_Pair__eq_1) ).
fof(c_0_255,axiom,
! [X8,X12,X4] :
( c_in(X8,c_Relation_ODomain(X12,X4,X4),X4)
| c_in(c_Pair(X8,X8,X4,X4),c_Transitive__Closure_Ortrancl(X12,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_Not__Domain__rtrancl_1) ).
fof(c_0_256,axiom,
! [X5,X21,X3,X4] :
( c_in(c_Pair(X21,X21,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(X21,X3,X4)
| ~ c_Relation_Orefl__on(X3,X5,X4) ),
file('<stdin>',cls_refl__onD_0) ).
fof(c_0_257,axiom,
! [X8,X5,X3,X4] :
( c_in(c_Pair(X8,X8,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(X8,X3,X4)
| ~ c_Relation_Orefl__on(X3,X5,X4) ),
file('<stdin>',cls_refl__on__def_1) ).
fof(c_0_258,axiom,
! [X8,X3,X4] :
( c_in(c_Pair(X8,X8,X4,X4),c_Relation_OId__on(X3,X4),tc_prod(X4,X4))
| ~ c_in(X8,X3,X4) ),
file('<stdin>',cls_Id__on__eqI_0) ).
fof(c_0_259,axiom,
! [X13,X12,X4] : c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X12,X4),c_Transitive__Closure_Ortrancl(X13,X4),tc_fun(tc_prod(X4,X4),tc_bool)),X4) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X12,X13,tc_fun(tc_prod(X4,X4),tc_bool)),X4),
file('<stdin>',cls_rtrancl__Un__rtrancl_0) ).
fof(c_0_260,axiom,
! [X15,X5,X2,X3,X4] :
( c_Relation_Orefl__on(c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X5,X15,tc_fun(tc_prod(X4,X4),tc_bool)),X4)
| ~ c_Relation_Orefl__on(X2,X15,X4)
| ~ c_Relation_Orefl__on(X3,X5,X4) ),
file('<stdin>',cls_refl__on__Int_0) ).
fof(c_0_261,axiom,
! [X15,X5,X2,X3,X4] :
( c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X5,X15,tc_fun(tc_prod(X4,X4),tc_bool)),X4)
| ~ c_Relation_Orefl__on(X2,X15,X4)
| ~ c_Relation_Orefl__on(X3,X5,X4) ),
file('<stdin>',cls_refl__on__Un_0) ).
fof(c_0_262,axiom,
! [X30,X3,X4] :
( X30 = c_Pair(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X3,X30,X4),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X3,X30,X4),X4,X4)
| ~ c_in(X30,c_Relation_OId__on(X3,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_Id__onE_1) ).
fof(c_0_263,axiom,
! [X37,X36] :
( c_Arrow__Order__Mirabelle_Ounanimity(X36)
| c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3(X36),v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4(X36),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2(X36),X37),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_unanimity__def_2) ).
fof(c_0_264,axiom,
! [X33,X1,X2,X3,X4] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X33,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| ~ c_lessequals(X2,X33,tc_fun(X4,tc_bool))
| ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_Int__mono_0) ).
fof(c_0_265,axiom,
! [X33,X1,X2,X3,X4] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X1,X33,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| ~ c_lessequals(X2,X33,tc_fun(X4,tc_bool))
| ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_Un__mono_0) ).
fof(c_0_266,axiom,
! [X1,X2,X3,X4] : 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)),
file('<stdin>',cls_Un__Int__distrib2_0) ).
fof(c_0_267,axiom,
! [X1,X2,X3,X4] : 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)),
file('<stdin>',cls_Un__Int__distrib_0) ).
fof(c_0_268,axiom,
! [X1,X2,X3,X4] : 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)),
file('<stdin>',cls_Int__Un__distrib2_0) ).
fof(c_0_269,axiom,
! [X1,X2,X3,X4] : 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)),
file('<stdin>',cls_Int__Un__distrib_0) ).
fof(c_0_270,axiom,
! [X2,X3,X6,X4] : c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(tc_prod(X6,X4),tc_bool)),X6,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X3,X6,X4),c_Relation_ORange(X2,X6,X4),tc_fun(X4,tc_bool)),
file('<stdin>',cls_Range__Un__eq_0) ).
fof(c_0_271,axiom,
! [X2,X3,X6,X4] : c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(tc_prod(X4,X6),tc_bool)),X4,X6) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X3,X4,X6),c_Relation_ODomain(X2,X4,X6),tc_fun(X4,tc_bool)),
file('<stdin>',cls_Domain__Un__eq_0) ).
fof(c_0_272,axiom,
! [X8,X12,X4] : c_in(c_Pair(X8,X8,X4,X4),c_Transitive__Closure_Ortrancl(X12,X4),tc_prod(X4,X4)),
file('<stdin>',cls_rtrancl__eq__or__trancl_1) ).
fof(c_0_273,axiom,
! [X5,X21,X4] : c_in(c_Pair(X21,X21,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)),
file('<stdin>',cls_rtrancl_Ortrancl__refl_0) ).
fof(c_0_274,axiom,
! [X8,X5,X4] :
( c_in(c_Pair(X8,X8,X4,X4),X5,tc_prod(X4,X4))
| ~ c_Nitpick_Orefl_H(X5,X4) ),
file('<stdin>',cls_Nitpick_Orefl_H__def_0) ).
fof(c_0_275,axiom,
! [X7,X8,X49] :
( X7 = X8
| X7 = X8
| c_in(c_Pair(X7,X8,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X49,X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_in__mktop_4) ).
fof(c_0_276,axiom,
! [X19,X8,X49] :
( X8 = X19
| X19 = X8
| c_in(c_Pair(X8,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X49,X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_in__mkbot_4) ).
fof(c_0_277,axiom,
! [X20,X21] :
( c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X21,X20),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X21 = X20 ),
file('<stdin>',cls_complete__Lin_1) ).
fof(c_0_278,axiom,
! [X8,X3,X4] :
( X3 = c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4)
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ c_lessequals(X3,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_subset__singletonD_0) ).
fof(c_0_279,axiom,
! [X8,X2,X3,X4] :
( hBOOL(hAPP(X2,X8))
| hBOOL(hAPP(X3,X8))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X8)) ),
file('<stdin>',cls_sup1E_0) ).
fof(c_0_280,axiom,
! [X3,X6,X4] : c_Product__Type_OSigma(X3,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),tc_fun(X6,tc_bool),X4),X4,X6) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X6),tc_bool)),
file('<stdin>',cls_Sigma__empty2_0) ).
fof(c_0_281,axiom,
! [X1,X2,X3,X4] :
( c_Lattices_Oupper__semilattice__class_Osup(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_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_Un__Int__assoc__eq_1) ).
fof(c_0_282,axiom,
! [X15,X5,X6,X4] : hAPP(c_Relation_Oconverse(X6,X4),c_Lattices_Olower__semilattice__class_Oinf(X5,X15,tc_fun(tc_prod(X6,X4),tc_bool))) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Relation_Oconverse(X6,X4),X5),hAPP(c_Relation_Oconverse(X6,X4),X15),tc_fun(tc_prod(X4,X6),tc_bool)),
file('<stdin>',cls_converse__Int_0) ).
fof(c_0_283,axiom,
! [X15,X5,X6,X4] : hAPP(c_Relation_Oconverse(X6,X4),c_Lattices_Oupper__semilattice__class_Osup(X5,X15,tc_fun(tc_prod(X6,X4),tc_bool))) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Relation_Oconverse(X6,X4),X5),hAPP(c_Relation_Oconverse(X6,X4),X15),tc_fun(tc_prod(X4,X6),tc_bool)),
file('<stdin>',cls_converse__Un_0) ).
fof(c_0_284,axiom,
! [X21,X4] : c_in(c_Pair(X21,X21,X4,X4),c_Relation_OId(X4),tc_prod(X4,X4)),
file('<stdin>',cls_IdI_0) ).
fof(c_0_285,axiom,
! [X8,X4] : c_in(c_Pair(X8,X8,X4,X4),c_Relation_OId(X4),tc_prod(X4,X4)),
file('<stdin>',cls_pair__in__Id__conv_1) ).
fof(c_0_286,axiom,
! [X8,X2,X3,X4] :
( hBOOL(hAPP(X3,X8))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),X8)) ),
file('<stdin>',cls_inf1E_0) ).
fof(c_0_287,axiom,
! [X8,X2,X3,X4] :
( hBOOL(hAPP(X2,X8))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),X8)) ),
file('<stdin>',cls_inf1E_1) ).
fof(c_0_288,axiom,
! [X5,X21,X10,X4] :
( hBOOL(hAPP(X10,X21))
| ~ hBOOL(hAPP(X10,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X10,X5,X4)))
| ~ c_in(X21,c_Wellfounded_Oacc(X5,X4),X4) ),
file('<stdin>',cls_acc__induct_2) ).
fof(c_0_289,axiom,
! [X5,X21,X10,X4] :
( hBOOL(hAPP(X10,X21))
| ~ hBOOL(hAPP(X10,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X10,X5,X4)))
| ~ c_in(X21,c_Wellfounded_Oacc(X5,X4),X4) ),
file('<stdin>',cls_acc__induct__rule_2) ).
fof(c_0_290,axiom,
! [X7,X8,X4] : c_Set_Oinsert(X7,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) = c_Set_Oinsert(X8,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4),
file('<stdin>',cls_doubleton__eq__iff_4) ).
fof(c_0_291,axiom,
! [X5,X29,X6,X4] :
( c_Relation_Osym(c_Relation_Oinv__image(X5,X29,X4,X6),X6)
| ~ c_Relation_Osym(X5,X4) ),
file('<stdin>',cls_sym__inv__image_0) ).
fof(c_0_292,axiom,
! [X5,X29,X6,X4] :
( c_Wellfounded_Owf(c_Relation_Oinv__image(X5,X29,X4,X6),X6)
| ~ c_Wellfounded_Owf(X5,X4) ),
file('<stdin>',cls_wf__inv__image_0) ).
fof(c_0_293,axiom,
! [X21,X2,X3,X4] : c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X21,X3,X4),c_Set_Oinsert(X21,X2,X4),tc_fun(X4,tc_bool)) = c_Set_Oinsert(X21,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),X4),
file('<stdin>',cls_insert__inter__insert_0) ).
fof(c_0_294,axiom,
! [X15,X5,X6,X4] :
( c_lessequals(c_Relation_ODomain(X5,X4,X6),c_Relation_ODomain(X15,X4,X6),tc_fun(X4,tc_bool))
| ~ c_lessequals(X5,X15,tc_fun(tc_prod(X4,X6),tc_bool)) ),
file('<stdin>',cls_Domain__mono_0) ).
fof(c_0_295,axiom,
! [X15,X5,X34,X4] :
( c_in(X34,c_Transitive__Closure_Otrancl(X15,X4),tc_prod(X4,X4))
| ~ c_lessequals(X5,X15,tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_in(X34,c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_trancl__mono_0) ).
fof(c_0_296,axiom,
! [X21,X2,X3,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(X3,c_Set_Oinsert(X21,X2,X4),tc_fun(X4,tc_bool)) = c_Set_Oinsert(X21,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),X4)
| ~ c_in(X21,X3,X4) ),
file('<stdin>',cls_Int__insert__right_0) ).
fof(c_0_297,axiom,
! [X21,X1,X2,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X21,X2,X4),X1,tc_fun(X4,tc_bool)) = c_Set_Oinsert(X21,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X4,tc_bool)),X4)
| ~ c_in(X21,X1,X4) ),
file('<stdin>',cls_Int__insert__left_0) ).
fof(c_0_298,axiom,
! [X13,X12,X4] :
( c_Transitive__Closure_Ortrancl(X13,X4) = c_Transitive__Closure_Ortrancl(X12,X4)
| ~ c_lessequals(X13,c_Transitive__Closure_Ortrancl(X12,X4),tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_lessequals(X12,X13,tc_fun(tc_prod(X4,X4),tc_bool)) ),
file('<stdin>',cls_rtrancl__subset_0) ).
fof(c_0_299,axiom,
! [X1,X2,X3,X4] :
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_Int__subset__iff_2) ).
fof(c_0_300,axiom,
! [X1,X2,X3,X4] :
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_Int__greatest_0) ).
fof(c_0_301,axiom,
! [X1,X2,X3,X4] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X1,tc_fun(X4,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X4,tc_bool))
| ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_Un__least_0) ).
fof(c_0_302,axiom,
! [X1,X2,X3,X4] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X1,tc_fun(X4,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X4,tc_bool))
| ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_Un__subset__iff_2) ).
fof(c_0_303,axiom,
! [X1,X2,X3,X4] : 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)),
file('<stdin>',cls_Int__left__commute_0) ).
fof(c_0_304,axiom,
! [X1,X2,X3,X4] : 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)),
file('<stdin>',cls_Int__assoc_0) ).
fof(c_0_305,axiom,
! [X1,X2,X3,X4] : 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)),
file('<stdin>',cls_Un__left__commute_0) ).
fof(c_0_306,axiom,
! [X1,X2,X3,X4] : 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)),
file('<stdin>',cls_Un__assoc_0) ).
fof(c_0_307,axiom,
! [X5,X4] :
( c_Relation_Oantisym(X5,X4)
| ~ c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X5,c_Relation_OId(X4),tc_fun(tc_prod(X4,X4),tc_bool)),X4) ),
file('<stdin>',cls_antisym__reflcl_0) ).
fof(c_0_308,axiom,
! [X1,X2,X3,X4] :
( c_lessequals(X2,X1,tc_fun(X4,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X1,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_Un__subset__iff_1) ).
fof(c_0_309,axiom,
! [X1,X2,X3,X4] :
( c_lessequals(X3,X1,tc_fun(X4,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X1,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_Un__subset__iff_0) ).
fof(c_0_310,axiom,
! [X1,X2,X3,X4] :
( c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_Int__subset__iff_0) ).
fof(c_0_311,axiom,
! [X1,X2,X3,X4] :
( c_lessequals(X1,X2,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_Int__subset__iff_1) ).
fof(c_0_312,axiom,
! [X34,X4] :
( X34 = c_Pair(c_ATP__Linkup_Osko__Relation__XIdE__1__1(X34,X4),c_ATP__Linkup_Osko__Relation__XIdE__1__1(X34,X4),X4,X4)
| ~ c_in(X34,c_Relation_OId(X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_IdE_0) ).
fof(c_0_313,axiom,
! [X5,X21,X10,X4] :
( hBOOL(hAPP(X10,X21))
| ~ hBOOL(hAPP(X10,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X10,X5,X4)))
| ~ c_Wellfounded_Owf(X5,X4) ),
file('<stdin>',cls_wf__induct__rule_1) ).
fof(c_0_314,axiom,
! [X24,X5,X10,X4] :
( hBOOL(hAPP(X10,X24))
| ~ hBOOL(hAPP(X10,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X10,X5,X4)))
| ~ c_Wellfounded_Owf(X5,X4) ),
file('<stdin>',cls_wf__def_1) ).
fof(c_0_315,axiom,
! [X5,X21,X10,X4] :
( hBOOL(hAPP(X10,X21))
| ~ hBOOL(hAPP(X10,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X10,X5,X4)))
| ~ c_Wellfounded_Owf(X5,X4) ),
file('<stdin>',cls_wf__induct_1) ).
fof(c_0_316,axiom,
! [X11,X12,X10,X4] :
( hBOOL(hAPP(X10,X11))
| ~ hBOOL(hAPP(X10,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X10,X12,X4)))
| ~ c_Wellfounded_Owf(X12,X4) ),
file('<stdin>',cls_tfl__wf__induct_1) ).
fof(c_0_317,axiom,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Odistrib__lattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X8,c_Lattices_Olower__semilattice__class_Oinf(X19,X18,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4),c_Lattices_Oupper__semilattice__class_Osup(X8,X18,X4),X4) ),
file('<stdin>',cls_sup__inf__distrib1_0) ).
fof(c_0_318,axiom,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Odistrib__lattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X19,X18,X4),X8,X4) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X19,X8,X4),c_Lattices_Oupper__semilattice__class_Osup(X18,X8,X4),X4) ),
file('<stdin>',cls_sup__inf__distrib2_0) ).
fof(c_0_319,axiom,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Odistrib__lattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X8,c_Lattices_Oupper__semilattice__class_Osup(X19,X18,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4),c_Lattices_Olower__semilattice__class_Oinf(X8,X18,X4),X4) ),
file('<stdin>',cls_inf__sup__distrib1_0) ).
fof(c_0_320,axiom,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Odistrib__lattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X19,X18,X4),X8,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X19,X8,X4),c_Lattices_Olower__semilattice__class_Oinf(X18,X8,X4),X4) ),
file('<stdin>',cls_inf__sup__distrib2_0) ).
fof(c_0_321,axiom,
! [X30,X2,X3,X4] :
( c_in(X30,X2,X4)
| c_in(X30,X3,X4)
| ~ c_in(X30,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X4) ),
file('<stdin>',cls_UnE_0) ).
fof(c_0_322,axiom,
! [X8,X2,X3,X4] :
( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),X8))
| ~ hBOOL(hAPP(X2,X8))
| ~ hBOOL(hAPP(X3,X8)) ),
file('<stdin>',cls_inf1I_0) ).
fof(c_0_323,axiom,
! [X5,X4] : c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X5,hAPP(c_Relation_Oconverse(X4,X4),X5),tc_fun(tc_prod(X4,X4),tc_bool)),X4),
file('<stdin>',cls_sym__Int__converse_0) ).
fof(c_0_324,axiom,
! [X5,X4] : c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X5,hAPP(c_Relation_Oconverse(X4,X4),X5),tc_fun(tc_prod(X4,X4),tc_bool)),X4),
file('<stdin>',cls_sym__Un__converse_0) ).
fof(c_0_325,axiom,
! [X15,X5,X4] :
( c_lessequals(c_Transitive__Closure_Ortrancl(X5,X4),c_Transitive__Closure_Ortrancl(X15,X4),tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_lessequals(X5,c_Transitive__Closure_Ortrancl(X15,X4),tc_fun(tc_prod(X4,X4),tc_bool)) ),
file('<stdin>',cls_rtrancl__subset__rtrancl_0) ).
fof(c_0_326,axiom,
! [X8,X2,X3,X4] :
( c_lessequals(X3,X2,tc_fun(X4,tc_bool))
| ~ c_lessequals(X3,c_Set_Oinsert(X8,X2,X4),tc_fun(X4,tc_bool))
| c_in(X8,X3,X4) ),
file('<stdin>',cls_subset__insert_0) ).
fof(c_0_327,axiom,
! [X8,X2,X3,X4] :
( c_lessequals(X3,X2,tc_fun(X4,tc_bool))
| c_in(X8,X3,X4)
| ~ c_lessequals(X3,c_Set_Oinsert(X8,X2,X4),tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_subset__insert__iff_1) ).
fof(c_0_328,axiom,
! [X20,X21,X4] :
( X20 = X21
| ~ c_in(X20,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
file('<stdin>',cls_singletonE_0) ).
fof(c_0_329,axiom,
! [X19,X8,X3,X4] :
( hBOOL(hAPP(X3,X8))
| X19 = X8
| ~ hBOOL(hAPP(c_Set_Oinsert(X19,X3,X4),X8)) ),
file('<stdin>',cls_insert__code_0) ).
fof(c_0_330,axiom,
! [X21,X33,X1,X4] :
( c_lessequals(c_Set_Oinsert(X21,X1,X4),c_Set_Oinsert(X21,X33,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,X33,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_insert__mono_0) ).
fof(c_0_331,axiom,
! [X15,X5,X4] : c_Relation_OField(c_Lattices_Oupper__semilattice__class_Osup(X5,X15,tc_fun(tc_prod(X4,X4),tc_bool)),X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OField(X5,X4),c_Relation_OField(X15,X4),tc_fun(X4,tc_bool)),
file('<stdin>',cls_Field__Un_0) ).
fof(c_0_332,axiom,
! [X8,X2,X3,X4] :
( c_lessequals(c_Set_Oinsert(X8,X3,X4),X2,tc_fun(X4,tc_bool))
| ~ c_lessequals(X3,X2,tc_fun(X4,tc_bool))
| ~ c_in(X8,X2,X4) ),
file('<stdin>',cls_insert__subset_2) ).
fof(c_0_333,axiom,
! [X21,X2,X3,X4] : c_Lattices_Oupper__semilattice__class_Osup(X3,c_Set_Oinsert(X21,X2,X4),tc_fun(X4,tc_bool)) = c_Set_Oinsert(X21,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X4),
file('<stdin>',cls_Un__insert__right_0) ).
fof(c_0_334,axiom,
! [X21,X1,X2,X4] : c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X21,X2,X4),X1,tc_fun(X4,tc_bool)) = c_Set_Oinsert(X21,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X4,tc_bool)),X4),
file('<stdin>',cls_Un__insert__left_0) ).
fof(c_0_335,axiom,
! [X15,X5,X4] :
( c_lessequals(c_Transitive__Closure_Ortrancl(X5,X4),c_Transitive__Closure_Ortrancl(X15,X4),tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_lessequals(X5,X15,tc_fun(tc_prod(X4,X4),tc_bool)) ),
file('<stdin>',cls_rtrancl__mono_0) ).
fof(c_0_336,axiom,
! [X8,X2,X3,X4] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X8))
| ~ hBOOL(hAPP(X3,X8)) ),
file('<stdin>',cls_sup1CI_1) ).
fof(c_0_337,axiom,
! [X8,X2,X3,X4] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X8))
| ~ hBOOL(hAPP(X2,X8)) ),
file('<stdin>',cls_sup1CI_0) ).
fof(c_0_338,axiom,
! [X30,X2,X3,X4] :
( c_in(X30,X3,X4)
| ~ c_in(X30,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),X4) ),
file('<stdin>',cls_IntE_0) ).
fof(c_0_339,axiom,
! [X30,X2,X3,X4] :
( c_in(X30,X2,X4)
| ~ c_in(X30,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),X4) ),
file('<stdin>',cls_IntE_1) ).
fof(c_0_340,axiom,
! [X30,X2,X3,X4] :
( c_in(X30,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),X4)
| ~ c_in(X30,X2,X4)
| ~ c_in(X30,X3,X4) ),
file('<stdin>',cls_IntI_0) ).
fof(c_0_341,axiom,
! [X30,X2,X3,X4] :
( c_in(X30,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),X4)
| ~ c_in(X30,X2,X4)
| ~ c_in(X30,X3,X4) ),
file('<stdin>',cls_Int__iff_2) ).
fof(c_0_342,axiom,
! [X2,X6,X4] : c_Product__Type_OSigma(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X2,X4,X6) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X6),tc_bool)),
file('<stdin>',cls_Sigma__empty1_0) ).
fof(c_0_343,axiom,
! [X8,X12,X4] :
( ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X12,X8,X4),c_Wellfounded_Oacc(X12,X4),X4)
| c_in(X8,c_Wellfounded_Oacc(X12,X4),X4) ),
file('<stdin>',cls_not__acc__down_1) ).
fof(c_0_344,axiom,
! [X8,X5,X4] :
( c_in(X8,c_Wellfounded_Oacc(X5,X4),X4)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X5,X8,X4),c_Wellfounded_Oacc(X5,X4),X4) ),
file('<stdin>',cls_acc_OaccI_1) ).
fof(c_0_345,axiom,
! [X8,X2,X3,X4] :
( c_lessequals(X3,X2,tc_fun(X4,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X8,X3,X4),X2,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_insert__subset_1) ).
fof(c_0_346,axiom,
! [X8,X37,X36] :
( hAPP(X36,X8) = hAPP(X8,X37)
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_Odictator(X36,X37) ),
file('<stdin>',cls_dictator__def_0) ).
fof(c_0_347,axiom,
! [X8,X2,X3,X4] :
( c_lessequals(X3,c_Set_Oinsert(X8,X2,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X3,X2,tc_fun(X4,tc_bool))
| c_in(X8,X3,X4) ),
file('<stdin>',cls_subset__insert_1) ).
fof(c_0_348,axiom,
! [X8,X2,X3,X4] :
( c_lessequals(X3,c_Set_Oinsert(X8,X2,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X3,X2,tc_fun(X4,tc_bool))
| c_in(X8,X3,X4) ),
file('<stdin>',cls_subset__insert__iff_2) ).
fof(c_0_349,axiom,
! [X2,X3,X4] : c_Relation_OImage(c_Relation_OId__on(X3,X4),X2,X4,X4) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),
file('<stdin>',cls_Image__Id__on_0) ).
fof(c_0_350,axiom,
! [X5,X21,X10,X4] :
( hBOOL(hAPP(X10,X21))
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X10,X5,X4),c_Wellfounded_Oacc(X5,X4),X4)
| ~ c_in(X21,c_Wellfounded_Oacc(X5,X4),X4) ),
file('<stdin>',cls_acc__induct__rule_0) ).
fof(c_0_351,axiom,
! [X5,X21,X10,X4] :
( hBOOL(hAPP(X10,X21))
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X10,X5,X4),c_Wellfounded_Oacc(X5,X4),X4)
| ~ c_in(X21,c_Wellfounded_Oacc(X5,X4),X4) ),
file('<stdin>',cls_acc__induct_0) ).
fof(c_0_352,axiom,
! [X15,X5,X6,X4] :
( c_Relation_Osingle__valued(X5,X4,X6)
| ~ c_Relation_Osingle__valued(X15,X4,X6)
| ~ c_lessequals(X5,X15,tc_fun(tc_prod(X4,X6),tc_bool)) ),
file('<stdin>',cls_single__valued__subset_0) ).
fof(c_0_353,axiom,
! [X8,X2,X3,X4] :
( c_in(X8,X2,X4)
| ~ c_lessequals(c_Set_Oinsert(X8,X3,X4),X2,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_insert__subset_0) ).
fof(c_0_354,axiom,
! [X21,X3,X4] : c_Set_Oinsert(X21,X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X3,tc_fun(X4,tc_bool)),
file('<stdin>',cls_insert__is__Un_0) ).
fof(c_0_355,axiom,
! [X8,X20,X21,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(X8,c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X4),X4)
| ~ c_lessequals(X8,X20,X4)
| ~ c_lessequals(X8,X21,X4) ),
file('<stdin>',cls_le__infI_0) ).
fof(c_0_356,axiom,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(X8,c_Lattices_Olower__semilattice__class_Oinf(X19,X18,X4),X4)
| ~ c_lessequals(X8,X18,X4)
| ~ c_lessequals(X8,X19,X4) ),
file('<stdin>',cls_le__inf__iff_2) ).
fof(c_0_357,axiom,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(X8,c_Lattices_Olower__semilattice__class_Oinf(X19,X18,X4),X4)
| ~ c_lessequals(X8,X18,X4)
| ~ c_lessequals(X8,X19,X4) ),
file('<stdin>',cls_inf__greatest_0) ).
fof(c_0_358,axiom,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4),X18,X4)
| ~ c_lessequals(X19,X18,X4)
| ~ c_lessequals(X8,X18,X4) ),
file('<stdin>',cls_le__sup__iff_2) ).
fof(c_0_359,axiom,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X19,X18,X4),X8,X4)
| ~ c_lessequals(X18,X8,X4)
| ~ c_lessequals(X19,X8,X4) ),
file('<stdin>',cls_sup__least_0) ).
fof(c_0_360,axiom,
! [X8,X20,X21,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X4),X8,X4)
| ~ c_lessequals(X20,X8,X4)
| ~ c_lessequals(X21,X8,X4) ),
file('<stdin>',cls_le__supI_0) ).
fof(c_0_361,axiom,
! [X8,X2,X3,X4] :
( ~ c_in(X8,X2,X4)
| ~ c_in(X8,X3,X4)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_disjoint__iff__not__equal_0) ).
fof(c_0_362,axiom,
! [X20,X21,X4] :
( c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4) != c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4)
| X21 = X20 ),
file('<stdin>',cls_singleton__inject_0) ).
fof(c_0_363,axiom,
! [X15,X5,X4] :
( c_lessequals(c_Relation_OField(X5,X4),c_Relation_OField(X15,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X5,X15,tc_fun(tc_prod(X4,X4),tc_bool)) ),
file('<stdin>',cls_mono__Field_0) ).
fof(c_0_364,axiom,
! [X26,X27,X4] :
( c_lessequals(c_Wellfounded_Oacc(X26,X4),c_Wellfounded_Oacc(X27,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X27,X26,tc_fun(tc_prod(X4,X4),tc_bool)) ),
file('<stdin>',cls_acc__subset_0) ).
fof(c_0_365,axiom,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4),X18,X4) = c_Lattices_Oupper__semilattice__class_Osup(X8,c_Lattices_Oupper__semilattice__class_Osup(X19,X18,X4),X4) ),
file('<stdin>',cls_inf__sup__aci_I6_J_0) ).
fof(c_0_366,axiom,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X8,c_Lattices_Oupper__semilattice__class_Osup(X19,X18,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X19,c_Lattices_Oupper__semilattice__class_Osup(X8,X18,X4),X4) ),
file('<stdin>',cls_inf__sup__aci_I7_J_0) ).
fof(c_0_367,axiom,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X8,c_Lattices_Oupper__semilattice__class_Osup(X19,X18,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X19,c_Lattices_Oupper__semilattice__class_Osup(X8,X18,X4),X4) ),
file('<stdin>',cls_sup__left__commute_0) ).
fof(c_0_368,axiom,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4),X18,X4) = c_Lattices_Oupper__semilattice__class_Osup(X8,c_Lattices_Oupper__semilattice__class_Osup(X19,X18,X4),X4) ),
file('<stdin>',cls_sup__assoc_0) ).
fof(c_0_369,axiom,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4),X18,X4) = c_Lattices_Olower__semilattice__class_Oinf(X8,c_Lattices_Olower__semilattice__class_Oinf(X19,X18,X4),X4) ),
file('<stdin>',cls_inf__assoc_0) ).
fof(c_0_370,axiom,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X8,c_Lattices_Olower__semilattice__class_Oinf(X19,X18,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X19,c_Lattices_Olower__semilattice__class_Oinf(X8,X18,X4),X4) ),
file('<stdin>',cls_inf__left__commute_0) ).
fof(c_0_371,axiom,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X8,c_Lattices_Olower__semilattice__class_Oinf(X19,X18,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X19,c_Lattices_Olower__semilattice__class_Oinf(X8,X18,X4),X4) ),
file('<stdin>',cls_inf__sup__aci_I3_J_0) ).
fof(c_0_372,axiom,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4),X18,X4) = c_Lattices_Olower__semilattice__class_Oinf(X8,c_Lattices_Olower__semilattice__class_Oinf(X19,X18,X4),X4) ),
file('<stdin>',cls_inf__sup__aci_I2_J_0) ).
fof(c_0_373,axiom,
! [X30,X3,X4] :
( c_in(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X3,X30,X4),X3,X4)
| ~ c_in(X30,c_Relation_OId__on(X3,X4),tc_prod(X4,X4)) ),
file('<stdin>',cls_Id__onE_0) ).
fof(c_0_374,axiom,
! [X12,X6,X4] : c_Relation_OImage(X12,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X6,X4) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
file('<stdin>',cls_Image__empty_0) ).
fof(c_0_375,axiom,
! [X19,X8,X3,X4] : c_Set_Oinsert(X8,c_Set_Oinsert(X19,X3,X4),X4) = c_Set_Oinsert(X19,c_Set_Oinsert(X8,X3,X4),X4),
file('<stdin>',cls_insert__commute_0) ).
fof(c_0_376,axiom,
! [X1,X2,X3,X4] :
( c_lessequals(X3,X1,tc_fun(X4,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X4,tc_bool))
| ~ c_lessequals(X3,X2,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_subset__trans_0) ).
fof(c_0_377,axiom,
! [X21,X1,X2,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X21,X2,X4),X1,tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X4,tc_bool))
| c_in(X21,X1,X4) ),
file('<stdin>',cls_Int__insert__left_1) ).
fof(c_0_378,axiom,
! [X21,X2,X3,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(X3,c_Set_Oinsert(X21,X2,X4),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool))
| c_in(X21,X3,X4) ),
file('<stdin>',cls_Int__insert__right_1) ).
fof(c_0_379,axiom,
! [X15,X5,X4] :
( c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X5,X15,tc_fun(tc_prod(X4,X4),tc_bool)),X4)
| ~ c_Relation_Osym(X15,X4)
| ~ c_Relation_Osym(X5,X4) ),
file('<stdin>',cls_sym__Int_0) ).
fof(c_0_380,axiom,
! [X15,X5,X4] :
( c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X5,X15,tc_fun(tc_prod(X4,X4),tc_bool)),X4)
| ~ c_Relation_Osym(X15,X4)
| ~ c_Relation_Osym(X5,X4) ),
file('<stdin>',cls_sym__Un_0) ).
fof(c_0_381,axiom,
! [X8,X20,X21,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_lessequals(X21,X8,X4)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X4),X8,X4) ),
file('<stdin>',cls_le__supE_0) ).
fof(c_0_382,axiom,
! [X8,X20,X21,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_lessequals(X20,X8,X4)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X4),X8,X4) ),
file('<stdin>',cls_le__supE_1) ).
fof(c_0_383,axiom,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_lessequals(X8,X18,X4)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4),X18,X4) ),
file('<stdin>',cls_le__sup__iff_0) ).
fof(c_0_384,axiom,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_lessequals(X19,X18,X4)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4),X18,X4) ),
file('<stdin>',cls_le__sup__iff_1) ).
fof(c_0_385,axiom,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(X8,X18,X4)
| ~ c_lessequals(X8,c_Lattices_Olower__semilattice__class_Oinf(X19,X18,X4),X4) ),
file('<stdin>',cls_le__inf__iff_1) ).
fof(c_0_386,axiom,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(X8,X19,X4)
| ~ c_lessequals(X8,c_Lattices_Olower__semilattice__class_Oinf(X19,X18,X4),X4) ),
file('<stdin>',cls_le__inf__iff_0) ).
fof(c_0_387,axiom,
! [X8,X20,X21,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(X8,X20,X4)
| ~ c_lessequals(X8,c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X4),X4) ),
file('<stdin>',cls_le__infE_1) ).
fof(c_0_388,axiom,
! [X8,X20,X21,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(X8,X21,X4)
| ~ c_lessequals(X8,c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X4),X4) ),
file('<stdin>',cls_le__infE_0) ).
fof(c_0_389,axiom,
! [X20,X21,X3,X4] :
( c_in(X21,X3,X4)
| X21 = X20
| ~ c_in(X21,c_Set_Oinsert(X20,X3,X4),X4) ),
file('<stdin>',cls_insertE_0) ).
fof(c_0_390,axiom,
! [X2,X3,X4] : c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),
file('<stdin>',cls_Int__left__absorb_0) ).
fof(c_0_391,axiom,
! [X2,X3,X4] : c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),
file('<stdin>',cls_Un__left__absorb_0) ).
fof(c_0_392,axiom,
! [X20,X2,X3,X4] :
( c_lessequals(X3,c_Set_Oinsert(X20,X2,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X3,X2,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_subset__insertI2_0) ).
fof(c_0_393,axiom,
! [X5,X4] :
( c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X5,c_Relation_OId(X4),tc_fun(tc_prod(X4,X4),tc_bool)),X4)
| ~ c_Relation_Oantisym(X5,X4) ),
file('<stdin>',cls_antisym__reflcl_1) ).
fof(c_0_394,axiom,
! [X5,X4] : c_Relation_OField(X5,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X5,X4,X4),c_Relation_ORange(X5,X4,X4),tc_fun(X4,tc_bool)),
file('<stdin>',cls_Field__def_0) ).
fof(c_0_395,axiom,
! [X5,X4] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X5,c_Relation_OId(X4),tc_fun(tc_prod(X4,X4),tc_bool)),X4) = c_Transitive__Closure_Ortrancl(X5,X4),
file('<stdin>',cls_trancl__reflcl_0) ).
fof(c_0_396,axiom,
! [X12,X4] : c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X12,c_Relation_OId(X4),tc_fun(tc_prod(X4,X4),tc_bool)),X4) = c_Transitive__Closure_Ortrancl(X12,X4),
file('<stdin>',cls_rtrancl__reflcl_0) ).
fof(c_0_397,axiom,
! [X30,X2,X3,X4] :
( c_in(X30,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X4)
| ~ c_in(X30,X2,X4) ),
file('<stdin>',cls_UnCI_0) ).
fof(c_0_398,axiom,
! [X30,X2,X3,X4] :
( c_in(X30,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X4)
| ~ c_in(X30,X3,X4) ),
file('<stdin>',cls_UnCI_1) ).
fof(c_0_399,axiom,
! [X16,X5,X4] :
( c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X16,X5,tc_fun(tc_prod(X4,X4),tc_bool)),X4)
| ~ c_Wellfounded_Owf(X5,X4) ),
file('<stdin>',cls_wf__Int2_0) ).
fof(c_0_400,axiom,
! [X16,X5,X4] :
( c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X5,X16,tc_fun(tc_prod(X4,X4),tc_bool)),X4)
| ~ c_Wellfounded_Owf(X5,X4) ),
file('<stdin>',cls_wf__Int1_0) ).
fof(c_0_401,axiom,
! [X19,X8,X3,X4] :
( hBOOL(hAPP(c_Set_Oinsert(X19,X3,X4),X8))
| ~ hBOOL(hAPP(X3,X8)) ),
file('<stdin>',cls_insert__code_2) ).
fof(c_0_402,axiom,
! [X5,X4] :
( c_Wellfounded_Owf(hAPP(c_Relation_Oconverse(X4,X4),c_Transitive__Closure_Otrancl(X5,X4)),X4)
| ~ c_Wellfounded_Owf(hAPP(c_Relation_Oconverse(X4,X4),X5),X4) ),
file('<stdin>',cls_wf__converse__trancl_0) ).
fof(c_0_403,axiom,
! [X2,X4] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool)),X2,tc_fun(tc_prod(X4,X4),tc_bool)),
file('<stdin>',cls_less__by__empty_0) ).
fof(c_0_404,axiom,
! [X8,X2,X3,X4] :
( c_Set_Oinsert(X8,X3,X4) != c_Set_Oinsert(X8,X2,X4)
| c_in(X8,X2,X4)
| c_in(X8,X3,X4)
| X3 = X2 ),
file('<stdin>',cls_insert__ident_0) ).
fof(c_0_405,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)),
file('<stdin>',cls_Field__def__raw_0) ).
fof(c_0_406,axiom,
! [X8,X5,X10] :
( hBOOL(hAPP(X10,X8))
| ~ hBOOL(hAPP(X10,v_sko__Wellfounded__Xacc__Xinducts__1(X10,X5)))
| ~ c_in(X8,c_Wellfounded_Oacc(X5,t_a),t_a) ),
file('<stdin>',cls_acc_Oinducts_2) ).
fof(c_0_407,axiom,
! [X8,X5,X10] :
( hBOOL(hAPP(X10,X8))
| ~ hBOOL(hAPP(X10,v_sko__Wellfounded__Xacc__Xinduct__1(X10,X5)))
| ~ c_in(X8,c_Wellfounded_Oacc(X5,t_a),t_a) ),
file('<stdin>',cls_acc_Oinduct_2) ).
fof(c_0_408,axiom,
! [X7,X5,X9,X4] :
( c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X9,X5,X4),X9,X4)
| ~ c_in(X7,X9,X4)
| ~ c_Wellfounded_Owf(X5,X4) ),
file('<stdin>',cls_wf__eq__minimal_0) ).
fof(c_0_409,axiom,
! [X8,X12,X9,X4] :
( c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X9,X12,X4),X9,X4)
| ~ c_in(X8,X9,X4)
| ~ c_Wellfounded_Owf(X12,X4) ),
file('<stdin>',cls_wfE__min_0) ).
fof(c_0_410,axiom,
! [X8,X4] : c_in(X8,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4),
file('<stdin>',cls_singleton__iff_1) ).
fof(c_0_411,axiom,
! [X5,X3,X4] :
( c_Relation_Ototal__on(X3,X5,X4)
| ~ c_Relation_Ototal__on(X3,hAPP(c_Relation_Oconverse(X4,X4),X5),X4) ),
file('<stdin>',cls_total__on__converse_0) ).
fof(c_0_412,axiom,
! [X5,X3,X4] :
( c_Relation_Orefl__on(X3,X5,X4)
| ~ c_Relation_Orefl__on(X3,hAPP(c_Relation_Oconverse(X4,X4),X5),X4) ),
file('<stdin>',cls_refl__on__converse_0) ).
fof(c_0_413,axiom,
! [X8,X2,X3,X4] :
( c_in(X8,X2,X4)
| ~ c_in(X8,X3,X4)
| ~ c_lessequals(X3,X2,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_set__mp_0) ).
fof(c_0_414,axiom,
! [X30,X2,X3,X4] :
( c_in(X30,X2,X4)
| ~ c_in(X30,X3,X4)
| ~ c_lessequals(X3,X2,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_subsetD_0) ).
fof(c_0_415,axiom,
! [X8,X2,X3,X4] :
( c_in(X8,X2,X4)
| ~ c_lessequals(X3,X2,tc_fun(X4,tc_bool))
| ~ c_in(X8,X3,X4) ),
file('<stdin>',cls_set__rev__mp_0) ).
fof(c_0_416,axiom,
! [X31,X2,X3,X4] :
( c_in(X31,X2,X4)
| ~ c_in(X31,X3,X4)
| ~ c_lessequals(X3,X2,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_subset__iff_0) ).
fof(c_0_417,axiom,
! [X4] : c_Relation_Orefl__on(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool)),X4),
file('<stdin>',cls_refl__on__empty_0) ).
fof(c_0_418,axiom,
! [X8,X20,X21,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_lessequals(X8,c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X4),X4)
| ~ c_lessequals(X8,X21,X4) ),
file('<stdin>',cls_le__supI1_0) ).
fof(c_0_419,axiom,
! [X8,X20,X21,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_lessequals(X8,c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X4),X4)
| ~ c_lessequals(X8,X20,X4) ),
file('<stdin>',cls_le__supI2_0) ).
fof(c_0_420,axiom,
! [X8,X20,X21,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X4),X8,X4)
| ~ c_lessequals(X20,X8,X4) ),
file('<stdin>',cls_le__infI2_0) ).
fof(c_0_421,axiom,
! [X8,X20,X21,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X4),X8,X4)
| ~ c_lessequals(X21,X8,X4) ),
file('<stdin>',cls_le__infI1_0) ).
fof(c_0_422,axiom,
! [X3,X4] : c_Relation_OImage(c_Relation_OId(X4),X3,X4,X4) = X3,
file('<stdin>',cls_Image__Id_0) ).
fof(c_0_423,axiom,
! [X4] : c_Transitive__Closure_Otrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool)),X4) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool)),
file('<stdin>',cls_trancl__empty_0) ).
fof(c_0_424,axiom,
! [X20,X21,X2,X4] :
( c_in(X21,c_Set_Oinsert(X20,X2,X4),X4)
| ~ c_in(X21,X2,X4) ),
file('<stdin>',cls_insertCI_0) ).
fof(c_0_425,axiom,
! [X20,X21,X3,X4] :
( c_in(X21,c_Set_Oinsert(X20,X3,X4),X4)
| ~ c_in(X21,X3,X4) ),
file('<stdin>',cls_insert__iff_2) ).
fof(c_0_426,axiom,
! [X2,X3,X4] :
( X3 = X2
| ~ c_lessequals(X2,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X3,X2,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_set__eq__subset_2) ).
fof(c_0_427,axiom,
! [X2,X3,X4] :
( X3 = X2
| ~ c_lessequals(X2,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X3,X2,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_equalityI_0) ).
fof(c_0_428,axiom,
! [X8,X3,X4] : hBOOL(hAPP(c_Set_Oinsert(X8,X3,X4),X8)),
file('<stdin>',cls_insert__code_1) ).
fof(c_0_429,axiom,
! [X37,X36] :
( c_Arrow__Order__Mirabelle_Odictator(X36,X37)
| c_in(v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(X36,X37),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
file('<stdin>',cls_dictator__def_1) ).
fof(c_0_430,axiom,
! [X15,X5,X4] :
( c_Wellfounded_Oacyclic(X5,X4)
| ~ c_lessequals(X5,X15,tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_Wellfounded_Oacyclic(X15,X4) ),
file('<stdin>',cls_acyclic__subset_0) ).
fof(c_0_431,axiom,
! [X15,X5,X4] :
( c_Relation_Oantisym(X5,X4)
| ~ c_Relation_Oantisym(X15,X4)
| ~ c_lessequals(X5,X15,tc_fun(tc_prod(X4,X4),tc_bool)) ),
file('<stdin>',cls_antisym__subset_0) ).
fof(c_0_432,axiom,
! [X5,X34,X4] :
( c_Wellfounded_Owf(X34,X4)
| ~ c_lessequals(X34,X5,tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_Wellfounded_Owf(X5,X4) ),
file('<stdin>',cls_wf__subset_0) ).
fof(c_0_433,axiom,
! [X8,X28,X29,X6,X4] :
( ~ class_HOL_Oord(X6)
| c_lessequals(hAPP(X29,X8),hAPP(X28,X8),X6)
| ~ c_lessequals(X29,X28,tc_fun(X4,X6)) ),
file('<stdin>',cls_le__funD_0) ).
fof(c_0_434,axiom,
! [X6,X4] : c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X6,X4),tc_bool)),X6,X4) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
file('<stdin>',cls_Range__empty_0) ).
fof(c_0_435,axiom,
! [X6,X4] : c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X6),tc_bool)),X4,X6) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
file('<stdin>',cls_Domain__empty_0) ).
fof(c_0_436,axiom,
! [X18,X19,X8,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_lessequals(X8,X18,X4)
| ~ c_lessequals(X19,X18,X4)
| ~ c_lessequals(X8,X19,X4) ),
file('<stdin>',cls_order__trans_0) ).
fof(c_0_437,axiom,
! [X18,X19,X8,X4] :
( ~ class_Orderings_Oorder(X4)
| c_lessequals(X18,X8,X4)
| ~ c_lessequals(X18,X19,X4)
| ~ c_lessequals(X19,X8,X4) ),
file('<stdin>',cls_xt1_I6_J_0) ).
fof(c_0_438,axiom,
! [X5,X34,X4] :
( c_in(X34,c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(X34,X5,tc_prod(X4,X4)) ),
file('<stdin>',cls_r__into__trancl_H_0) ).
fof(c_0_439,axiom,
! [X5,X34,X4] :
( c_in(X34,c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(X34,X5,tc_prod(X4,X4)) ),
file('<stdin>',cls_r__into__rtrancl_0) ).
fof(c_0_440,axiom,
! [X3,X4] :
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ c_lessequals(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_subset__empty_0) ).
fof(c_0_441,axiom,
! [X2,X3,X4] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),X2,tc_fun(X4,tc_bool)),
file('<stdin>',cls_Int__lower2_0) ).
fof(c_0_442,axiom,
! [X2,X3,X4] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)),
file('<stdin>',cls_Int__lower1_0) ).
fof(c_0_443,axiom,
! [X2,X3,X4] : c_lessequals(X3,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
file('<stdin>',cls_Un__upper1_0) ).
fof(c_0_444,axiom,
! [X2,X3,X4] : c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
file('<stdin>',cls_Un__upper2_0) ).
fof(c_0_445,axiom,
! [X19,X8,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X8,c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4) ),
file('<stdin>',cls_inf__left__idem_0) ).
fof(c_0_446,axiom,
! [X19,X8,X4] :
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X8,c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4) ),
file('<stdin>',cls_inf__sup__aci_I4_J_0) ).
fof(c_0_447,axiom,
! [X19,X8,X4] :
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X8,c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4) ),
file('<stdin>',cls_inf__sup__aci_I8_J_0) ).
fof(c_0_448,axiom,
! [X19,X8,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X8,c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4) ),
file('<stdin>',cls_sup__left__idem_0) ).
fof(c_0_449,axiom,
! [X5,X3,X4] :
( c_Relation_Ototal__on(X3,hAPP(c_Relation_Oconverse(X4,X4),X5),X4)
| ~ c_Relation_Ototal__on(X3,X5,X4) ),
file('<stdin>',cls_total__on__converse_1) ).
fof(c_0_450,axiom,
! [X5,X3,X4] :
( c_Relation_Orefl__on(X3,hAPP(c_Relation_Oconverse(X4,X4),X5),X4)
| ~ c_Relation_Orefl__on(X3,X5,X4) ),
file('<stdin>',cls_refl__on__converse_1) ).
fof(c_0_451,axiom,
! [X8,X3,X4] : c_Set_Oinsert(X8,c_Set_Oinsert(X8,X3,X4),X4) = c_Set_Oinsert(X8,X3,X4),
file('<stdin>',cls_insert__absorb2_0) ).
fof(c_0_452,axiom,
! [X8,X10,X4] :
( ~ hBOOL(hAPP(X10,X8))
| ~ c_in(X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4) ),
file('<stdin>',cls_bex__empty_0) ).
fof(c_0_453,axiom,
! [X36] :
( c_Arrow__Order__Mirabelle_Ounanimity(X36)
| c_in(v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2(X36),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
file('<stdin>',cls_unanimity__def_1) ).
fof(c_0_454,axiom,
! [X36] :
( c_Arrow__Order__Mirabelle_OIIA(X36)
| c_in(v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X36),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
file('<stdin>',cls_IIA__def_4) ).
fof(c_0_455,axiom,
! [X36] :
( c_Arrow__Order__Mirabelle_OIIA(X36)
| c_in(v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X36),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
file('<stdin>',cls_IIA__def_5) ).
fof(c_0_456,axiom,
! [X8,X4] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X8)),
file('<stdin>',cls_bot1E_0) ).
fof(c_0_457,axiom,
! [X5,X6,X4] :
( c_Relation_ORange(X5,X6,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| X5 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X6,X4),tc_bool)) ),
file('<stdin>',cls_Range__empty__iff_0) ).
fof(c_0_458,axiom,
! [X5,X6,X4] :
( c_Relation_ODomain(X5,X4,X6) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| X5 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X6),tc_bool)) ),
file('<stdin>',cls_Domain__empty__iff_0) ).
fof(c_0_459,axiom,
! [X4] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
file('<stdin>',cls_Un__empty_2) ).
fof(c_0_460,axiom,
! [X2,X3,X4] :
( c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)) != X2
| c_lessequals(X3,X2,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_subset__Un__eq_1) ).
fof(c_0_461,axiom,
! [X2,X3,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)) = X2
| ~ c_lessequals(X2,X3,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_Int__absorb1_0) ).
fof(c_0_462,axiom,
! [X2,X3,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)) = X3
| ~ c_lessequals(X3,X2,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_Int__absorb2_0) ).
fof(c_0_463,axiom,
! [X2,X3,X4] :
( c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)) = X3
| ~ c_lessequals(X2,X3,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_Un__absorb2_0) ).
fof(c_0_464,axiom,
! [X2,X3,X4] :
( c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)) = X2
| ~ c_lessequals(X3,X2,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_Un__absorb1_0) ).
fof(c_0_465,axiom,
! [X8,X9,X10,X4] :
( hBOOL(hAPP(X9,X8))
| ~ c_lessequals(X10,X9,tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(X10,X8)) ),
file('<stdin>',cls_rev__predicate1D_0) ).
fof(c_0_466,axiom,
! [X8,X9,X10,X4] :
( hBOOL(hAPP(X9,X8))
| ~ hBOOL(hAPP(X10,X8))
| ~ c_lessequals(X10,X9,tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_predicate1D_0) ).
fof(c_0_467,axiom,
c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
file('<stdin>',cls_A_I5_J_0) ).
fof(c_0_468,axiom,
c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
file('<stdin>',cls_A_I4_J_0) ).
fof(c_0_469,axiom,
! [X8,X10,X4] :
( hBOOL(hAPP(X10,X8))
| ~ c_in(X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4) ),
file('<stdin>',cls_ball__empty_0) ).
fof(c_0_470,axiom,
! [X4] : c_Relation_OField(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool)),X4) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
file('<stdin>',cls_Field__empty_0) ).
fof(c_0_471,axiom,
! [X2,X3,X4] :
( c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_Un__empty_0) ).
fof(c_0_472,axiom,
! [X2,X3,X4] :
( c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
file('<stdin>',cls_Un__empty_1) ).
fof(c_0_473,axiom,
! [X5,X6,X4] : c_Relation_ORange(X5,X6,X4) = c_Relation_ODomain(hAPP(c_Relation_Oconverse(X6,X4),X5),X4,X6),
file('<stdin>',cls_Range__def_0) ).
fof(c_0_474,axiom,
! [X5,X6,X4] : c_Relation_ODomain(hAPP(c_Relation_Oconverse(X6,X4),X5),X4,X6) = c_Relation_ORange(X5,X6,X4),
file('<stdin>',cls_Domain__converse_0) ).
fof(c_0_475,axiom,
! [X5,X6,X4] : c_Relation_ORange(hAPP(c_Relation_Oconverse(X4,X6),X5),X6,X4) = c_Relation_ODomain(X5,X4,X6),
file('<stdin>',cls_Range__converse_0) ).
fof(c_0_476,axiom,
! [X21,X2,X4] : c_lessequals(X2,c_Set_Oinsert(X21,X2,X4),tc_fun(X4,tc_bool)),
file('<stdin>',cls_subset__insertI_0) ).
fof(c_0_477,axiom,
! [X7,X8,X4] :
( c_Set_Oinsert(X8,X7,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| c_in(X8,X7,X4) ),
file('<stdin>',cls_comm__monoid__add_Ononempty__iff_2) ).
fof(c_0_478,axiom,
! [X5,X4] :
( c_Wellfounded_Owf(X5,X4)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X5,X4),c_Wellfounded_Oacc(X5,X4),X4) ),
file('<stdin>',cls_acc__wfI_0) ).
fof(c_0_479,axiom,
! [X5,X4] :
( c_Wellfounded_Owf(X5,X4)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X5,X4),c_Wellfounded_Oacc(X5,X4),X4) ),
file('<stdin>',cls_wf__acc__iff_1) ).
fof(c_0_480,axiom,
! [X19,X8,X4] :
( ~ class_Orderings_Oorder(X4)
| X8 = X19
| ~ c_lessequals(X8,X19,X4)
| ~ c_lessequals(X19,X8,X4) ),
file('<stdin>',cls_order__antisym__conv_0) ).
fof(c_0_481,axiom,
! [X19,X8,X4] :
( ~ class_Orderings_Oorder(X4)
| X8 = X19
| ~ c_lessequals(X19,X8,X4)
| ~ c_lessequals(X8,X19,X4) ),
file('<stdin>',cls_order__antisym_0) ).
fof(c_0_482,axiom,
! [X19,X8,X4] :
( ~ class_Orderings_Oorder(X4)
| X8 = X19
| ~ c_lessequals(X19,X8,X4)
| ~ c_lessequals(X8,X19,X4) ),
file('<stdin>',cls_order__eq__iff_2) ).
fof(c_0_483,axiom,
! [X4] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
file('<stdin>',cls_subset__empty_1) ).
fof(c_0_484,axiom,
! [X5,X4] : c_Transitive__Closure_Ortrancl(X5,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X5,X4),c_Relation_OId(X4),tc_fun(tc_prod(X4,X4),tc_bool)),
file('<stdin>',cls_Nitpick_Ortrancl__def_0) ).
fof(c_0_485,axiom,
! [X5,X4] : c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X5,X4),c_Relation_OId(X4),tc_fun(tc_prod(X4,X4),tc_bool)) = c_Transitive__Closure_Ortrancl(X5,X4),
file('<stdin>',cls_reflcl__trancl_0) ).
fof(c_0_486,axiom,
! [X12,X4] : c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X12,X4),c_Relation_OId(X4),tc_fun(tc_prod(X4,X4),tc_bool)) = c_Transitive__Closure_Ortrancl(X12,X4),
file('<stdin>',cls_rtrancl__reflcl__absorb_0) ).
fof(c_0_487,axiom,
! [X4] : c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool)),X4) = c_Relation_OId(X4),
file('<stdin>',cls_rtrancl__empty_0) ).
fof(c_0_488,axiom,
! [X4] : c_Relation_Oantisym(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool)),X4),
file('<stdin>',cls_antisym__empty_0) ).
fof(c_0_489,axiom,
! [X4] : c_Wellfounded_Owf(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool)),X4),
file('<stdin>',cls_wf__empty_0) ).
fof(c_0_490,axiom,
! [X19,X8,X4] :
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X8,c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4),X4) = X8 ),
file('<stdin>',cls_inf__sup__absorb_0) ).
fof(c_0_491,axiom,
! [X19,X8,X4] :
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X8,c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4),X4) = X8 ),
file('<stdin>',cls_sup__inf__absorb_0) ).
fof(c_0_492,axiom,
! [X19,X8,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4),X8,X4) ),
file('<stdin>',cls_inf__le1_0) ).
fof(c_0_493,axiom,
! [X19,X8,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4),X19,X4) ),
file('<stdin>',cls_inf__le2_0) ).
fof(c_0_494,axiom,
! [X19,X8,X4] :
( ~ class_Lattices_Olattice(X4)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4),X19,X4) ),
file('<stdin>',cls_inf__sup__ord_I2_J_0) ).
fof(c_0_495,axiom,
! [X19,X8,X4] :
( ~ class_Lattices_Olattice(X4)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4),X8,X4) ),
file('<stdin>',cls_inf__sup__ord_I1_J_0) ).
fof(c_0_496,axiom,
! [X19,X8,X4] :
( ~ class_Lattices_Olattice(X4)
| c_lessequals(X8,c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4),X4) ),
file('<stdin>',cls_inf__sup__ord_I3_J_0) ).
fof(c_0_497,axiom,
! [X19,X8,X4] :
( ~ class_Lattices_Olattice(X4)
| c_lessequals(X19,c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4),X4) ),
file('<stdin>',cls_inf__sup__ord_I4_J_0) ).
fof(c_0_498,axiom,
! [X19,X8,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_lessequals(X19,c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4),X4) ),
file('<stdin>',cls_sup__ge2_0) ).
fof(c_0_499,axiom,
! [X19,X8,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_lessequals(X8,c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4),X4) ),
file('<stdin>',cls_sup__ge1_0) ).
fof(c_0_500,axiom,
! [X21,X4] : ~ c_in(X21,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),
file('<stdin>',cls_emptyE_0) ).
fof(c_0_501,axiom,
! [X30,X4] : ~ c_in(X30,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),
file('<stdin>',cls_empty__iff_0) ).
fof(c_0_502,axiom,
! [X8,X4] : ~ c_in(X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),
file('<stdin>',cls_ex__in__conv_0) ).
fof(c_0_503,axiom,
c_Relation_ORange(v_r,t_a,t_b) = c_Relation_ODomain(hAPP(c_Relation_Oconverse(t_a,t_b),v_r),t_b,t_a),
file('<stdin>',cls_Range__def__raw_0) ).
fof(c_0_504,axiom,
! [X8,X2,X4] : c_in(X8,c_Set_Oinsert(X8,X2,X4),X4),
file('<stdin>',cls_insertCI_1) ).
fof(c_0_505,axiom,
! [X21,X2,X4] : c_in(X21,c_Set_Oinsert(X21,X2,X4),X4),
file('<stdin>',cls_insertI1_0) ).
fof(c_0_506,axiom,
! [X8,X3,X4] : c_in(X8,c_Set_Oinsert(X8,X3,X4),X4),
file('<stdin>',cls_insert__iff_1) ).
fof(c_0_507,axiom,
! [X5,X4] :
( c_Relation_Oantisym(X5,X4)
| ~ c_Relation_Oantisym(hAPP(c_Relation_Oconverse(X4,X4),X5),X4) ),
file('<stdin>',cls_antisym__converse_0) ).
fof(c_0_508,axiom,
! [X5,X4] :
( c_Relation_Osym(X5,X4)
| ~ c_Relation_Osym(hAPP(c_Relation_Oconverse(X4,X4),X5),X4) ),
file('<stdin>',cls_sym__converse_0) ).
fof(c_0_509,axiom,
! [X5,X4] :
( c_Wellfounded_Oacyclic(X5,X4)
| ~ c_Wellfounded_Oacyclic(hAPP(c_Relation_Oconverse(X4,X4),X5),X4) ),
file('<stdin>',cls_acyclic__converse_0) ).
fof(c_0_510,axiom,
! [X5,X4] : c_Transitive__Closure_Ortrancl(hAPP(c_Relation_Oconverse(X4,X4),X5),X4) = hAPP(c_Relation_Oconverse(X4,X4),c_Transitive__Closure_Ortrancl(X5,X4)),
file('<stdin>',cls_rtrancl__converse_0) ).
fof(c_0_511,axiom,
! [X5,X4] : c_Transitive__Closure_Otrancl(hAPP(c_Relation_Oconverse(X4,X4),X5),X4) = hAPP(c_Relation_Oconverse(X4,X4),c_Transitive__Closure_Otrancl(X5,X4)),
file('<stdin>',cls_trancl__converse_0) ).
fof(c_0_512,axiom,
! [X3,X4] : c_Lattices_Olower__semilattice__class_Oinf(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
file('<stdin>',cls_Int__empty__right_0) ).
fof(c_0_513,axiom,
! [X2,X4] : c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X2,tc_fun(X4,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
file('<stdin>',cls_Int__empty__left_0) ).
fof(c_0_514,axiom,
! [X2,X3,X4] : c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),
file('<stdin>',cls_Un__commute_0) ).
fof(c_0_515,axiom,
! [X2,X3,X4] : c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),
file('<stdin>',cls_Int__commute_0) ).
fof(c_0_516,axiom,
! [X19,X8,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4) != X8
| c_lessequals(X8,X19,X4) ),
file('<stdin>',cls_le__iff__inf_1) ).
fof(c_0_517,axiom,
! [X19,X8,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4) != X19
| c_lessequals(X8,X19,X4) ),
file('<stdin>',cls_le__iff__sup_1) ).
fof(c_0_518,axiom,
! [X19,X8,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4) = X19
| ~ c_lessequals(X19,X8,X4) ),
file('<stdin>',cls_inf__absorb2_0) ).
fof(c_0_519,axiom,
! [X19,X8,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4) = X8
| ~ c_lessequals(X8,X19,X4) ),
file('<stdin>',cls_le__iff__inf_0) ).
fof(c_0_520,axiom,
! [X19,X8,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4) = X19
| ~ c_lessequals(X8,X19,X4) ),
file('<stdin>',cls_le__iff__sup_0) ).
fof(c_0_521,axiom,
! [X19,X8,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4) = X8
| ~ c_lessequals(X19,X8,X4) ),
file('<stdin>',cls_sup__absorb1_0) ).
fof(c_0_522,axiom,
! [X4] : c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool)),
file('<stdin>',cls_Id__on__empty_0) ).
fof(c_0_523,axiom,
! [X21,X3,X4] :
( c_Set_Oinsert(X21,X3,X4) = X3
| ~ c_in(X21,X3,X4) ),
file('<stdin>',cls_insert__absorb_0) ).
fof(c_0_524,axiom,
! [X5,X3,X4] :
( c_Relation_Orefl__on(X3,X5,X4)
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4) ),
file('<stdin>',cls_equiv_Orefl__on_0) ).
fof(c_0_525,axiom,
! [X37,X36] :
( hAPP(X36,v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(X36,X37)) != hAPP(v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(X36,X37),X37)
| c_Arrow__Order__Mirabelle_Odictator(X36,X37) ),
file('<stdin>',cls_dictator__def_2) ).
fof(c_0_526,axiom,
! [X5,X4] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X5,X4),X4,X4) = c_Relation_ORange(X5,X4,X4),
file('<stdin>',cls_trancl__range_0) ).
fof(c_0_527,axiom,
! [X5,X4] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X5,X4),X4,X4) = c_Relation_ODomain(X5,X4,X4),
file('<stdin>',cls_trancl__domain_0) ).
fof(c_0_528,axiom,
! [X3,X4] : c_Lattices_Oupper__semilattice__class_Osup(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = X3,
file('<stdin>',cls_Un__empty__right_0) ).
fof(c_0_529,axiom,
! [X2,X4] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X2,tc_fun(X4,tc_bool)) = X2,
file('<stdin>',cls_Un__empty__left_0) ).
fof(c_0_530,axiom,
! [X3,X4] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)),
file('<stdin>',cls_empty__subsetI_0) ).
fof(c_0_531,axiom,
! [X21,X3,X4] : c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) != c_Set_Oinsert(X21,X3,X4),
file('<stdin>',cls_empty__not__insert_0) ).
fof(c_0_532,axiom,
! [X21,X3,X4] : c_Set_Oinsert(X21,X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
file('<stdin>',cls_insert__not__empty_0) ).
fof(c_0_533,axiom,
! [X9,X10,X6,X4] : hAPP(c_COMBK(X10,X4,X6),X9) = X10,
file('<stdin>',cls_COMBK__def_0) ).
fof(c_0_534,axiom,
! [X5,X6,X4] : hAPP(c_Relation_Oconverse(X6,X4),hAPP(c_Relation_Oconverse(X4,X6),X5)) = X5,
file('<stdin>',cls_converse__converse_0) ).
fof(c_0_535,axiom,
! [X19,X8,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_lessequals(X19,X8,X4)
| c_lessequals(X8,X19,X4) ),
file('<stdin>',cls_linorder__linear_0) ).
fof(c_0_536,axiom,
! [X8,X13,X4] :
( hBOOL(hAPP(X13,X8))
| ~ c_in(X8,X13,X4) ),
file('<stdin>',cls_mem__def_0) ).
fof(c_0_537,axiom,
! [X19,X8,X4] :
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4) = c_Lattices_Oupper__semilattice__class_Osup(X19,X8,X4) ),
file('<stdin>',cls_inf__sup__aci_I5_J_0) ).
fof(c_0_538,axiom,
! [X19,X8,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4) = c_Lattices_Oupper__semilattice__class_Osup(X19,X8,X4) ),
file('<stdin>',cls_sup__commute_0) ).
fof(c_0_539,axiom,
! [X19,X8,X4] :
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4) = c_Lattices_Olower__semilattice__class_Oinf(X19,X8,X4) ),
file('<stdin>',cls_inf__sup__aci_I1_J_0) ).
fof(c_0_540,axiom,
! [X19,X8,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4) = c_Lattices_Olower__semilattice__class_Oinf(X19,X8,X4) ),
file('<stdin>',cls_inf__commute_0) ).
fof(c_0_541,axiom,
! [X5,X4] :
( c_Relation_Oantisym(hAPP(c_Relation_Oconverse(X4,X4),X5),X4)
| ~ c_Relation_Oantisym(X5,X4) ),
file('<stdin>',cls_antisym__converse_1) ).
fof(c_0_542,axiom,
! [X5,X4] :
( c_Relation_Osym(hAPP(c_Relation_Oconverse(X4,X4),X5),X4)
| ~ c_Relation_Osym(X5,X4) ),
file('<stdin>',cls_sym__converse_1) ).
fof(c_0_543,axiom,
! [X5,X4] :
( c_Wellfounded_Oacyclic(hAPP(c_Relation_Oconverse(X4,X4),X5),X4)
| ~ c_Wellfounded_Oacyclic(X5,X4) ),
file('<stdin>',cls_acyclic__converse_1) ).
fof(c_0_544,axiom,
! [X5,X4] : c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X5,X4),
file('<stdin>',cls_total__on__empty_0) ).
fof(c_0_545,axiom,
! [X5,X4] : c_Relation_OField(hAPP(c_Relation_Oconverse(X4,X4),X5),X4) = c_Relation_OField(X5,X4),
file('<stdin>',cls_Field__converse_0) ).
fof(c_0_546,axiom,
! [X2,X3,X4] :
( ~ class_Lattices_Obounded__lattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X4) != c_Orderings_Obot__class_Obot(X4)
| X2 = c_Orderings_Obot__class_Obot(X4) ),
file('<stdin>',cls_sup__eq__bot__eq2_0) ).
fof(c_0_547,axiom,
! [X2,X3,X4] :
( ~ class_Lattices_Obounded__lattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X4) != c_Orderings_Obot__class_Obot(X4)
| X3 = c_Orderings_Obot__class_Obot(X4) ),
file('<stdin>',cls_sup__eq__bot__eq1_0) ).
fof(c_0_548,axiom,
! [X8,X5,X4] :
( c_in(X8,c_Wellfounded_Oacc(X5,X4),X4)
| ~ c_Wellfounded_Owf(X5,X4) ),
file('<stdin>',cls_acc__wfD_0) ).
fof(c_0_549,axiom,
! [X8,X13,X4] :
( c_in(X8,X13,X4)
| ~ hBOOL(hAPP(X13,X8)) ),
file('<stdin>',cls_mem__def_1) ).
fof(c_0_550,axiom,
! [X5,X3,X4] :
( c_Relation_Osym(X5,X4)
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4) ),
file('<stdin>',cls_equiv_Osym_0) ).
fof(c_0_551,axiom,
! [X61,X62,X4] :
( X62 = X61
| ~ c_fequal(X62,X61,X4) ),
file('<stdin>',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(c_0_552,axiom,
! [X3,X4] : c_Relation_ORange(c_Relation_OId__on(X3,X4),X4,X4) = X3,
file('<stdin>',cls_Range__Id__on_0) ).
fof(c_0_553,axiom,
! [X3,X4] : c_Relation_ODomain(c_Relation_OId__on(X3,X4),X4,X4) = X3,
file('<stdin>',cls_Domain__Id__on_0) ).
fof(c_0_554,axiom,
! [X3,X4] : c_Relation_Orefl__on(X3,c_Relation_OId__on(X3,X4),X4),
file('<stdin>',cls_refl__on__Id__on_0) ).
fof(c_0_555,axiom,
! [X3,X4] : c_Relation_Osingle__valued(c_Relation_OId__on(X3,X4),X4,X4),
file('<stdin>',cls_single__valued__Id__on_0) ).
fof(c_0_556,axiom,
! [X3,X4] : hAPP(c_Relation_Oconverse(X4,X4),c_Relation_OId__on(X3,X4)) = c_Relation_OId__on(X3,X4),
file('<stdin>',cls_converse__Id__on_0) ).
fof(c_0_557,axiom,
! [X5,X4] :
( hAPP(c_Relation_Oconverse(X4,X4),X5) != X5
| c_Relation_Osym(X5,X4) ),
file('<stdin>',cls_sym__conv__converse__eq_1) ).
fof(c_0_558,axiom,
! [X3,X4] : c_Lattices_Olower__semilattice__class_Oinf(X3,X3,tc_fun(X4,tc_bool)) = X3,
file('<stdin>',cls_Int__absorb_0) ).
fof(c_0_559,axiom,
! [X3,X4] : c_Lattices_Oupper__semilattice__class_Osup(X3,X3,tc_fun(X4,tc_bool)) = X3,
file('<stdin>',cls_Un__absorb_0) ).
fof(c_0_560,axiom,
! [X3,X4] : c_lessequals(X3,X3,tc_fun(X4,tc_bool)),
file('<stdin>',cls_subset__refl_0) ).
fof(c_0_561,axiom,
! [X8,X4] : c_lessequals(X8,X8,tc_fun(X4,tc_bool)),
file('<stdin>',cls_equalityE_0) ).
fof(c_0_562,axiom,
! [X8,X4] :
( ~ class_Lattices_Obounded__lattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X4),X8,X4) = c_Orderings_Obot__class_Obot(X4) ),
file('<stdin>',cls_inf__bot__left_0) ).
fof(c_0_563,axiom,
! [X8,X4] :
( ~ class_Lattices_Obounded__lattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X8,c_Orderings_Obot__class_Obot(X4),X4) = c_Orderings_Obot__class_Obot(X4) ),
file('<stdin>',cls_inf__bot__right_0) ).
fof(c_0_564,axiom,
! [X8,X4] :
( ~ class_Lattices_Obounded__lattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X4),X8,X4) = X8 ),
file('<stdin>',cls_sup__bot__left_0) ).
fof(c_0_565,axiom,
! [X8,X4] :
( ~ class_Lattices_Obounded__lattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X8,c_Orderings_Obot__class_Obot(X4),X4) = X8 ),
file('<stdin>',cls_sup__bot__right_0) ).
fof(c_0_566,axiom,
! [X8,X4] :
( ~ class_Orderings_Obot(X4)
| c_lessequals(c_Orderings_Obot__class_Obot(X4),X8,X4) ),
file('<stdin>',cls_bot__least_0) ).
fof(c_0_567,axiom,
! [X5,X4] :
( hAPP(c_Relation_Oconverse(X4,X4),X5) = X5
| ~ c_Relation_Osym(X5,X4) ),
file('<stdin>',cls_sym__conv__converse__eq_0) ).
fof(c_0_568,axiom,
! [X5,X4] :
( c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X5,X4),X4)
| ~ c_Wellfounded_Owf(X5,X4) ),
file('<stdin>',cls_wf__trancl_0) ).
fof(c_0_569,axiom,
! [X5,X4] :
( c_Relation_Osym(c_Transitive__Closure_Ortrancl(X5,X4),X4)
| ~ c_Relation_Osym(X5,X4) ),
file('<stdin>',cls_sym__rtrancl_0) ).
fof(c_0_570,axiom,
! [X5,X4] :
( c_Relation_Osym(c_Transitive__Closure_Otrancl(X5,X4),X4)
| ~ c_Relation_Osym(X5,X4) ),
file('<stdin>',cls_sym__trancl_0) ).
fof(c_0_571,axiom,
! [X5,X4] :
( c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X5,X4),X4)
| ~ c_Wellfounded_Oacyclic(X5,X4) ),
file('<stdin>',cls_acyclic__impl__antisym__rtrancl_0) ).
fof(c_0_572,axiom,
! [X8,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X8,X8,X4) = X8 ),
file('<stdin>',cls_inf__idem_0) ).
fof(c_0_573,axiom,
! [X8,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X8,X8,X4) = X8 ),
file('<stdin>',cls_sup__idem_0) ).
fof(c_0_574,axiom,
! [X8,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_lessequals(X8,X8,X4) ),
file('<stdin>',cls_order__eq__refl_0) ).
fof(c_0_575,axiom,
! [X8,X4] :
( ~ class_Orderings_Oorder(X4)
| c_lessequals(X8,X8,X4) ),
file('<stdin>',cls_order__eq__iff_0) ).
fof(c_0_576,axiom,
! [X4] : c_Relation_Osingle__valued(c_Relation_OId(X4),X4,X4),
file('<stdin>',cls_single__valued__Id_0) ).
fof(c_0_577,axiom,
! [X8,X4] : c_fequal(X8,X8,X4),
file('<stdin>',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(c_0_578,axiom,
! [X5,X4] : c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X5,X4),X4) = c_Transitive__Closure_Ortrancl(X5,X4),
file('<stdin>',cls_rtrancl__idemp_0) ).
fof(c_0_579,axiom,
! [X12,X4] : c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X12,X4),X4) = c_Transitive__Closure_Ortrancl(X12,X4),
file('<stdin>',cls_trancl__rtrancl__absorb_0) ).
fof(c_0_580,axiom,
! [X12,X4] : c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X12,X4),X4) = c_Transitive__Closure_Ortrancl(X12,X4),
file('<stdin>',cls_rtrancl__trancl__absorb_0) ).
fof(c_0_581,axiom,
! [X4] : hAPP(c_Relation_Oconverse(X4,X4),c_Relation_OId(X4)) = c_Relation_OId(X4),
file('<stdin>',cls_converse__Id_0) ).
fof(c_0_582,axiom,
! [X3,X4] : c_Relation_Osym(c_Relation_OId__on(X3,X4),X4),
file('<stdin>',cls_sym__Id__on_0) ).
fof(c_0_583,axiom,
! [X3,X4] : c_Relation_Oantisym(c_Relation_OId__on(X3,X4),X4),
file('<stdin>',cls_antisym__Id__on_0) ).
fof(c_0_584,axiom,
! [X59,X60] :
( class_HOL_Oord(tc_fun(X59,X60))
| ~ class_HOL_Oord(X60) ),
file('<stdin>',clsarity_fun__HOL_Oord) ).
fof(c_0_585,axiom,
! [X59,X60] :
( class_Orderings_Obot(tc_fun(X59,X60))
| ~ class_Orderings_Obot(X60) ),
file('<stdin>',clsarity_fun__Orderings_Obot) ).
fof(c_0_586,axiom,
! [X59,X60] :
( class_Orderings_Oorder(tc_fun(X59,X60))
| ~ class_Orderings_Oorder(X60) ),
file('<stdin>',clsarity_fun__Orderings_Oorder) ).
fof(c_0_587,axiom,
! [X59,X60] :
( class_Lattices_Olattice(tc_fun(X59,X60))
| ~ class_Lattices_Olattice(X60) ),
file('<stdin>',clsarity_fun__Lattices_Olattice) ).
fof(c_0_588,axiom,
! [X59,X60] :
( class_Orderings_Opreorder(tc_fun(X59,X60))
| ~ class_Orderings_Opreorder(X60) ),
file('<stdin>',clsarity_fun__Orderings_Opreorder) ).
fof(c_0_589,axiom,
! [X59,X60] :
( class_Lattices_Obounded__lattice(tc_fun(X59,X60))
| ~ class_Lattices_Obounded__lattice(X60) ),
file('<stdin>',clsarity_fun__Lattices_Obounded__lattice) ).
fof(c_0_590,axiom,
! [X59,X60] :
( class_Lattices_Odistrib__lattice(tc_fun(X59,X60))
| ~ class_Lattices_Odistrib__lattice(X60) ),
file('<stdin>',clsarity_fun__Lattices_Odistrib__lattice) ).
fof(c_0_591,axiom,
! [X59,X60] :
( class_Lattices_Olower__semilattice(tc_fun(X59,X60))
| ~ class_Lattices_Olattice(X60) ),
file('<stdin>',clsarity_fun__Lattices_Olower__semilattice) ).
fof(c_0_592,axiom,
! [X59,X60] :
( class_Lattices_Oupper__semilattice(tc_fun(X59,X60))
| ~ class_Lattices_Olattice(X60) ),
file('<stdin>',clsarity_fun__Lattices_Oupper__semilattice) ).
fof(c_0_593,axiom,
! [X5,X4] :
( c_Wellfounded_Oacyclic(X5,X4)
| ~ c_Wellfounded_Owf(X5,X4) ),
file('<stdin>',cls_wf__acyclic_0) ).
fof(c_0_594,axiom,
! [X4] : c_Relation_Oantisym(c_Relation_OId(X4),X4),
file('<stdin>',cls_antisym__Id_0) ).
fof(c_0_595,axiom,
! [X4] : c_Relation_Osym(c_Relation_OId(X4),X4),
file('<stdin>',cls_sym__Id_0) ).
fof(c_0_596,axiom,
class_HOL_Oord(tc_bool),
file('<stdin>',clsarity_bool__HOL_Oord) ).
fof(c_0_597,axiom,
class_Orderings_Obot(tc_bool),
file('<stdin>',clsarity_bool__Orderings_Obot) ).
fof(c_0_598,axiom,
class_Orderings_Oorder(tc_bool),
file('<stdin>',clsarity_bool__Orderings_Oorder) ).
fof(c_0_599,axiom,
class_Lattices_Olattice(tc_bool),
file('<stdin>',clsarity_bool__Lattices_Olattice) ).
fof(c_0_600,axiom,
class_Orderings_Opreorder(tc_bool),
file('<stdin>',clsarity_bool__Orderings_Opreorder) ).
fof(c_0_601,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('<stdin>',clsarity_bool__Lattices_Obounded__lattice) ).
fof(c_0_602,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
file('<stdin>',clsarity_bool__Lattices_Odistrib__lattice) ).
fof(c_0_603,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('<stdin>',clsarity_bool__Lattices_Olower__semilattice) ).
fof(c_0_604,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('<stdin>',clsarity_bool__Lattices_Oupper__semilattice) ).
fof(c_0_605,axiom,
c_Arrow__Order__Mirabelle_OIIA(v_F),
file('<stdin>',cls_assms_I3_J_0) ).
fof(c_0_606,axiom,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
file('<stdin>',cls_u_0) ).
fof(c_0_607,axiom,
v_a____ != v_c____,
file('<stdin>',cls_A_I3_J_0) ).
fof(c_0_608,axiom,
v_b____ != v_c____,
file('<stdin>',cls_A_I2_J_0) ).
fof(c_0_609,axiom,
v_a____ != v_b____,
file('<stdin>',cls_A_I1_J_0) ).
fof(c_0_610,plain,
! [X15,X5,X30,X21,X17,X6,X4] :
( c_in(c_Pair(X21,c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X21,X30,X5,X15,X4,X6,X17),X4,X17),X5,tc_prod(X4,X17))
| ~ c_in(c_Pair(X21,X30,X4,X6),c_Relation_Orel__comp(X5,X15,X4,X17,X6),tc_prod(X4,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_611,plain,
! [X15,X5,X30,X21,X17,X6,X4] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X21,X30,X5,X15,X4,X6,X17),X30,X17,X6),X15,tc_prod(X17,X6))
| ~ c_in(c_Pair(X21,X30,X4,X6),c_Relation_Orel__comp(X5,X15,X4,X17,X6),tc_prod(X4,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_612,plain,
! [X51,X20,X52,X21,X50,X10] :
( c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X50),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X50,v_sko__local__X1__1(X10,X50,X21,X52,X20,X51)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X10,v_sko__local__X1__1(X10,X50,X21,X52,X20,X51)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X50,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X10,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X20 = X52
| X21 = X51
| X52 = X51
| X21 = X20 ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_613,plain,
! [X51,X20,X52,X21,X50,X10] :
( c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X50),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X50,v_sko__local__X2__1(X10,X50,X21,X52,X20,X51)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X10,v_sko__local__X2__1(X10,X50,X21,X52,X20,X51)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X50,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X10,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X20 = X52
| X21 = X51
| X52 = X51
| X21 = X20 ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_614,plain,
! [X51,X20,X52,X21,X50,X10] :
( c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X50),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X50,v_sko__local__X2__1(X10,X50,X21,X52,X20,X51)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X10,v_sko__local__X2__1(X10,X50,X21,X52,X20,X51)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X50,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X10,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X20 = X52
| X21 = X51
| X52 = X51
| X21 = X20 ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_615,plain,
! [X51,X20,X52,X21,X50,X10] :
( c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X50),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X50,v_sko__local__X1__1(X10,X50,X21,X52,X20,X51)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X10,v_sko__local__X1__1(X10,X50,X21,X52,X20,X51)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X50,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X10,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X20 = X52
| X21 = X51
| X52 = X51
| X21 = X20 ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_616,plain,
! [X51,X20,X52,X21,X50,X10] :
( c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X50),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X50,v_sko__local__X2__1(X10,X50,X21,X52,X20,X51)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X10,v_sko__local__X2__1(X10,X50,X21,X52,X20,X51)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X50,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X10,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X20 = X52
| X21 = X51
| X52 = X51
| X21 = X20 ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_617,plain,
! [X51,X20,X52,X21,X50,X10] :
( c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X50),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X50,v_sko__local__X2__1(X10,X50,X21,X52,X20,X51)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X10,v_sko__local__X2__1(X10,X50,X21,X52,X20,X51)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X50,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X10,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X20 = X52
| X21 = X51
| X52 = X51
| X21 = X20 ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_618,axiom,
! [X8,X5,X28,X29,X6,X4] :
( hAPP(X29,c_List_Osko__Recdef__Xcuts__eq__1__1(X29,X28,X5,X8,X4,X6)) != hAPP(X28,c_List_Osko__Recdef__Xcuts__eq__1__1(X29,X28,X5,X8,X4,X6))
| c_Recdef_Ocut(X29,X5,X8,X4,X6) = c_Recdef_Ocut(X28,X5,X8,X4,X6) ),
c_0_8 ).
fof(c_0_619,plain,
! [X13,X12,X4] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X12,X13,tc_fun(tc_prod(X4,X4),tc_bool)),X4)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X12,X12,X4,X4,X4),c_Relation_Orel__comp(X13,X12,X4,X4,X4),tc_fun(tc_prod(X4,X4),tc_bool)),X13,tc_fun(tc_prod(X4,X4),tc_bool)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_620,axiom,
! [X8,X5,X28,X29,X6,X4] :
( c_Recdef_Ocut(X29,X5,X8,X4,X6) = c_Recdef_Ocut(X28,X5,X8,X4,X6)
| c_in(c_Pair(c_List_Osko__Recdef__Xcuts__eq__1__1(X29,X28,X5,X8,X4,X6),X8,X4,X4),X5,tc_prod(X4,X4)) ),
c_0_10 ).
fof(c_0_621,plain,
! [X13,X12,X4] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X12,X12,X4,X4,X4),c_Relation_Orel__comp(X13,X12,X4,X4,X4),tc_fun(tc_prod(X4,X4),tc_bool)),X13,tc_fun(tc_prod(X4,X4),tc_bool)),X4)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X12,X13,tc_fun(tc_prod(X4,X4),tc_bool)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_622,plain,
! [X29,X2,X3,X6,X4] :
( c_in(X29,c_FuncSet_OPi(X3,X2,X4,X6),tc_fun(X4,X6))
| ~ c_in(hAPP(X29,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X3,X2,X29,X4,X6)),hAPP(X2,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X3,X2,X29,X4,X6)),X6) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_623,plain,
! [X29,X2,X3,X6,X4] :
( c_in(X29,c_FuncSet_OPi(X3,X2,X4,X6),tc_fun(X4,X6))
| ~ c_in(hAPP(X29,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X3,X2,X29,X4,X6)),hAPP(X2,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X3,X2,X29,X4,X6)),X6) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_624,plain,
! [X41,X42,X43,X44,X45,X46,X29,X17,X6,X4] :
( hAPP(hAPP(X29,X44),X43) = hAPP(hAPP(X29,X42),X41)
| ~ c_in(c_Pair(X43,X41,X6,X6),X45,tc_prod(X6,X6))
| ~ c_in(c_Pair(X44,X42,X4,X4),X46,tc_prod(X4,X4))
| ~ c_Equiv__Relations_Ocongruent2(X46,X45,X29,X4,X6,X17) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_625,plain,
! [X45,X46,X29,X21,X3,X17,X6,X4] :
( c_Equiv__Relations_Ocongruent(X45,hAPP(X29,X21),X6,X17)
| ~ c_in(X21,X3,X4)
| ~ c_Equiv__Relations_Ocongruent2(X46,X45,X29,X4,X6,X17)
| ~ c_Equiv__Relations_Oequiv(X3,X46,X4) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_626,axiom,
! [X58,X28,X29,X48,X17,X6,X4] : c_Fun_Ocomp(X29,c_Fun_Ocomp(X28,X58,X48,X17,X4),X17,X6,X4) = c_Fun_Ocomp(c_Fun_Ocomp(X29,X28,X17,X6,X48),X58,X48,X6,X4),
c_0_16 ).
fof(c_0_627,axiom,
! [X25,X13,X12,X48,X17,X6,X4] : c_Relation_Orel__comp(c_Relation_Orel__comp(X12,X13,X4,X48,X17),X25,X4,X17,X6) = c_Relation_Orel__comp(X12,c_Relation_Orel__comp(X13,X25,X48,X17,X6),X4,X48,X6),
c_0_17 ).
fof(c_0_628,plain,
! [X7,X8,X20,X21,X36] :
( c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X36,X7),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X36,X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X7,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X21,X20,X8,X7)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X8,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X21,X20,X8,X7)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X7,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_OIIA(X36) ),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_629,plain,
! [X7,X8,X20,X21,X36] :
( c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X36,X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X36,X7),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X7,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X21,X20,X8,X7)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X8,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X21,X20,X8,X7)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X7,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_OIIA(X36) ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_630,plain,
! [X20,X21,X50,X10] :
( c_in(c_Pair(X20,X21,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X50),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X20,X21,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X50,v_sko__local__X3__1(X10,X50,X21,X20)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X10,v_sko__local__X3__1(X10,X50,X21,X20)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X50,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X10,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X21 = X20 ),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_631,plain,
! [X20,X21,X50,X10] :
( c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X20,X21,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X50),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X20,X21,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X50,v_sko__local__X3__1(X10,X50,X21,X20)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X10,v_sko__local__X3__1(X10,X50,X21,X20)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X50,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X10,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X21 = X20 ),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_632,plain,
! [X8,X5,X20,X21,X3,X4] :
( c_in(c_Pair(X21,X20,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(X8,c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X5,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4),c_Relation_OImage(X5,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4),tc_fun(X4,tc_bool)),X4)
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_633,axiom,
! [X25,X13,X12,X17,X6,X4] : c_Relation_Orel__comp(X12,c_Lattices_Oupper__semilattice__class_Osup(X13,X25,tc_fun(tc_prod(X17,X6),tc_bool)),X4,X17,X6) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X12,X13,X4,X17,X6),c_Relation_Orel__comp(X12,X25,X4,X17,X6),tc_fun(tc_prod(X4,X6),tc_bool)),
c_0_23 ).
fof(c_0_634,axiom,
! [X25,X13,X12,X17,X6,X4] : c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X13,X25,tc_fun(tc_prod(X4,X17),tc_bool)),X12,X4,X17,X6) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X13,X12,X4,X17,X6),c_Relation_Orel__comp(X25,X12,X4,X17,X6),tc_fun(tc_prod(X4,X6),tc_bool)),
c_0_24 ).
fof(c_0_635,plain,
! [X15,X5,X1,X2,X3,X17,X6,X4] :
( c_lessequals(c_Relation_Orel__comp(X5,X15,X4,X6,X17),c_Product__Type_OSigma(X3,c_COMBK(X1,tc_fun(X17,tc_bool),X4),X4,X17),tc_fun(tc_prod(X4,X17),tc_bool))
| ~ c_lessequals(X15,c_Product__Type_OSigma(X2,c_COMBK(X1,tc_fun(X17,tc_bool),X6),X6,X17),tc_fun(tc_prod(X6,X17),tc_bool))
| ~ c_lessequals(X5,c_Product__Type_OSigma(X3,c_COMBK(X2,tc_fun(X6,tc_bool),X4),X4,X6),tc_fun(tc_prod(X4,X6),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_636,plain,
! [X5,X20,X3,X6,X4] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X3,X20,X5,X6,X4),X20,X6,X4),X5,tc_prod(X6,X4))
| ~ c_in(X20,c_Relation_OImage(X5,X3,X6,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_637,plain,
! [X5,X20,X3,X6,X4] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X3,X20,X5,X6,X4),X20,X6,X4),X5,tc_prod(X6,X4))
| ~ c_in(X20,c_Relation_OImage(X5,X3,X6,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_638,axiom,
! [X20,X21,X2,X3,X6,X4] : c_Product__Type_OSigma(c_Set_Oinsert(X21,X3,X4),c_COMBK(c_Set_Oinsert(X20,X2,X6),tc_fun(X6,tc_bool),X4),X4,X6) = c_Set_Oinsert(c_Pair(X21,X20,X4,X6),c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X3,c_COMBK(c_Set_Oinsert(X20,X2,X6),tc_fun(X6,tc_bool),X4),X4,X6),c_Product__Type_OSigma(c_Set_Oinsert(X21,X3,X4),c_COMBK(X2,tc_fun(X6,tc_bool),X4),X4,X6),tc_fun(tc_prod(X4,X6),tc_bool)),tc_prod(X4,X6)),
c_0_28 ).
fof(c_0_639,axiom,
! [X1,X2,X3,X4] :
( c_Relation_Orel__comp(X3,X1,X4,X4,X4) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool))
| c_Relation_Orel__comp(X3,X2,X4,X4,X4) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool))
| c_Relation_Orel__comp(X3,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(tc_prod(X4,X4),tc_bool)),X4,X4,X4) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool)) ),
c_0_29 ).
fof(c_0_640,axiom,
! [X1,X2,X3,X4] :
( c_Relation_Orel__comp(X2,X1,X4,X4,X4) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool))
| c_Relation_Orel__comp(X3,X1,X4,X4,X4) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool))
| c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(tc_prod(X4,X4),tc_bool)),X1,X4,X4,X4) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool)) ),
c_0_30 ).
fof(c_0_641,plain,
! [X14,X15,X16,X5,X17,X6,X4] :
( c_lessequals(c_Relation_Orel__comp(X16,X14,X4,X6,X17),c_Relation_Orel__comp(X5,X15,X4,X6,X17),tc_fun(tc_prod(X4,X17),tc_bool))
| ~ c_lessequals(X14,X15,tc_fun(tc_prod(X6,X17),tc_bool))
| ~ c_lessequals(X16,X5,tc_fun(tc_prod(X4,X6),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_642,plain,
! [X15,X5,X4] :
( c_lessequals(c_Transitive__Closure_Ortrancl(X5,X4),X15,tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Ortrancl(X5,X4),X15,tc_fun(tc_prod(X4,X4),tc_bool)),X5,X4,X4,X4),X15,tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_lessequals(c_Relation_OId(X4),X15,tc_fun(tc_prod(X4,X4),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_643,plain,
! [X15,X5,X4] :
( c_lessequals(c_Transitive__Closure_Otrancl(X5,X4),X15,tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Otrancl(X5,X4),X15,tc_fun(tc_prod(X4,X4),tc_bool)),X5,X4,X4,X4),X15,tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_lessequals(X5,X15,tc_fun(tc_prod(X4,X4),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_644,plain,
! [X7,X8,X20,X21,X36] :
( c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X36,X7),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X36,X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X7,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X21,X20,X8,X7)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X8,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X21,X20,X8,X7)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X7,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_OIIA(X36) ),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_645,plain,
! [X7,X8,X20,X21,X36] :
( c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X36,X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X36,X7),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X7,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X21,X20,X8,X7)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X8,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X21,X20,X8,X7)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X7,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_OIIA(X36) ),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_646,plain,
! [X20,X21,X50,X10] :
( c_in(c_Pair(X20,X21,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X50),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X20,X21,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X50,v_sko__local__X3__1(X10,X50,X21,X20)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X10,v_sko__local__X3__1(X10,X50,X21,X20)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X50,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X10,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X21 = X20 ),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_647,plain,
! [X20,X21,X50,X10] :
( c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X10),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X20,X21,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X50),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X20,X21,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X50,v_sko__local__X3__1(X10,X50,X21,X20)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X10,v_sko__local__X3__1(X10,X50,X21,X20)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X50,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X10,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X21 = X20 ),
inference(fof_simplification,[status(thm)],[c_0_37]) ).
fof(c_0_648,axiom,
! [X53,X8,X54,X28,X55,X29,X56,X48,X17,X6,X4] :
( hAPP(X29,hAPP(X28,X8)) != hAPP(X55,hAPP(X54,X53))
| hAPP(c_Fun_Ocomp(X29,X28,X6,X4,X17),X8) = hAPP(c_Fun_Ocomp(X55,X54,X48,X4,X56),X53) ),
c_0_38 ).
fof(c_0_649,plain,
! [X15,X5,X30,X20,X21,X17,X6,X4] :
( c_in(c_Pair(X21,X30,X4,X17),c_Relation_Orel__comp(X5,X15,X4,X6,X17),tc_prod(X4,X17))
| ~ c_in(c_Pair(X20,X30,X6,X17),X15,tc_prod(X6,X17))
| ~ c_in(c_Pair(X21,X20,X4,X6),X5,tc_prod(X4,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_650,plain,
! [X19,X8,X5,X28,X29,X6,X4] :
( c_Recdef_Ocut(X29,X5,X8,X4,X6) != c_Recdef_Ocut(X28,X5,X8,X4,X6)
| hAPP(X29,X19) = hAPP(X28,X19)
| ~ c_in(c_Pair(X19,X8,X4,X4),X5,tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_651,plain,
! [X13,X12,X4] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X12,X13,tc_fun(tc_prod(X4,X4),tc_bool)),X4)
| ~ c_lessequals(c_Relation_Orel__comp(X12,X13,X4,X4,X4),X12,tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_Wellfounded_Owf(X13,X4)
| ~ c_Wellfounded_Owf(X12,X4) ),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_652,axiom,
! [X57,X32,X30,X20,X21,X48,X17,X6,X4] :
( c_Fun_Ocomp(X21,X20,X17,X6,X4) != c_Fun_Ocomp(X30,X32,X48,X6,X4)
| hAPP(X21,hAPP(X20,X57)) = hAPP(X30,hAPP(X32,X57)) ),
c_0_42 ).
fof(c_0_653,plain,
! [X12,X4] :
( c_Wellfounded_Owf(X12,X4)
| ~ c_Wellfounded_Owf(c_Relation_Orel__comp(X12,X12,X4,X4,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_654,axiom,
! [X15,X5,X17,X6,X4] : hAPP(c_Relation_Oconverse(X6,X4),c_Relation_Orel__comp(X5,X15,X6,X17,X4)) = c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X17,X4),X15),hAPP(c_Relation_Oconverse(X6,X17),X5),X4,X17,X6),
c_0_44 ).
fof(c_0_655,plain,
! [X5,X20,X21,X3,X4] :
( c_in(c_Pair(X21,X20,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(X20,X3,X4)
| ~ c_lessequals(c_Relation_OImage(X5,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4),c_Relation_OImage(X5,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4),tc_fun(X4,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_656,plain,
! [X5,X20,X21,X10,X4] :
( hBOOL(hAPP(X10,X20))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X10,X21,X5,X4),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X10,X21,X5,X4),X4,X4),X5,tc_prod(X4,X4))
| ~ hBOOL(hAPP(X10,X21))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_657,plain,
! [X5,X20,X21,X10,X4] :
( hBOOL(hAPP(X10,X21))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X10,X20,X5,X4),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X10,X20,X5,X4),X4,X4),X5,tc_prod(X4,X4))
| ~ hBOOL(hAPP(X10,X20))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_47]) ).
fof(c_0_658,plain,
! [X30,X2,X3,X6,X4] :
( c_in(c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1(X3,X2,X30,X4,X6),X3,X4)
| ~ c_in(X30,c_Product__Type_OSigma(X3,X2,X4,X6),tc_prod(X4,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_659,plain,
! [X8,X29,X21,X12,X6,X4] :
( hAPP(c_Recdef_Ocut(X29,X12,X21,X4,X6),X8) = hAPP(X29,X8)
| ~ c_in(c_Pair(X8,X21,X4,X4),X12,tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_660,plain,
! [X8,X5,X29,X21,X6,X4] :
( hAPP(c_Recdef_Ocut(X29,X5,X21,X4,X6),X8) = hAPP(X29,X8)
| ~ c_in(c_Pair(X8,X21,X4,X4),X5,tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_661,plain,
! [X5,X20,X3,X6,X4] :
( c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X3,X20,X5,X6,X4),X3,X6)
| ~ c_in(X20,c_Relation_OImage(X5,X3,X6,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_662,plain,
! [X5,X20,X3,X6,X4] :
( c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X3,X20,X5,X6,X4),X3,X6)
| ~ c_in(X20,c_Relation_OImage(X5,X3,X6,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_52]) ).
fof(c_0_663,plain,
! [X18,X19,X8,X5,X4] :
( c_in(c_Pair(X18,X19,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| c_in(c_Pair(X19,X18,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X8,X18,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_Relation_Osingle__valued(X5,X4,X4) ),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_664,plain,
! [X5,X20,X21,X4] :
( c_in(c_Pair(X21,c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X21,X20,X5,X4),X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4))
| c_in(c_Pair(X21,X20,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_665,plain,
! [X18,X8,X5,X4] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X5,X8,X18,X4),X18,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4))
| c_in(c_Pair(X8,X18,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(c_Pair(X8,X18,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_666,plain,
! [X18,X8,X5,X4] :
( c_in(c_Pair(X8,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X5,X8,X18,X4),X4,X4),X5,tc_prod(X4,X4))
| c_in(c_Pair(X8,X18,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(c_Pair(X8,X18,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_667,plain,
! [X5,X20,X21,X4] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X21,X20,X5,X4),X20,X4,X4),X5,tc_prod(X4,X4))
| c_in(c_Pair(X21,X20,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_57]) ).
fof(c_0_668,axiom,
! [X29,X2,X3,X6,X4] :
( c_in(X29,c_FuncSet_OPi(X3,X2,X4,X6),tc_fun(X4,X6))
| c_in(c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X3,X2,X29,X4,X6),X3,X4) ),
c_0_58 ).
fof(c_0_669,axiom,
! [X29,X2,X3,X6,X4] :
( c_in(X29,c_FuncSet_OPi(X3,X2,X4,X6),tc_fun(X4,X6))
| c_in(c_FuncSet_Osko__FuncSet__XPi__I__1__1(X3,X2,X29,X4,X6),X3,X4) ),
c_0_59 ).
fof(c_0_670,axiom,
! [X12,X2,X3,X6,X4] : c_lessequals(c_Relation_OImage(X12,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X6,tc_bool)),X6,X4),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X12,X3,X6,X4),c_Relation_OImage(X12,X2,X6,X4),tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
c_0_60 ).
fof(c_0_671,plain,
! [X5,X20,X21,X3,X4] :
( c_lessequals(c_Relation_OImage(X5,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4),c_Relation_OImage(X5,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4),tc_fun(X4,tc_bool))
| ~ c_in(c_Pair(X21,X20,X4,X4),X5,tc_prod(X4,X4))
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_672,axiom,
c_in(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
c_0_62 ).
fof(c_0_673,plain,
! [X8,X1,X2,X3,X6,X4] :
( c_lessequals(X3,X2,tc_fun(X6,tc_bool))
| ~ c_lessequals(c_Product__Type_OSigma(X3,c_COMBK(X1,tc_fun(X4,tc_bool),X6),X6,X4),c_Product__Type_OSigma(X2,c_COMBK(X1,tc_fun(X4,tc_bool),X6),X6,X4),tc_fun(tc_prod(X6,X4),tc_bool))
| ~ c_in(X8,X1,X4) ),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_674,plain,
! [X5,X3,X4] :
( c_lessequals(X5,c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X4,X4),X5),X5,X4,X4,X4),tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_Relation_Orefl__on(X3,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_675,plain,
! [X19,X8,X5,X4] :
( ~ c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X19,X8,X4,X4),X5,tc_prod(X4,X4)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_65]) ).
fof(c_0_676,plain,
! [X19,X8,X5,X4] :
( ~ c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X19,X8,X4,X4),X5,tc_prod(X4,X4)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_677,plain,
! [X15,X5,X17,X6,X4] :
( c_Relation_Osingle__valued(c_Relation_Orel__comp(X5,X15,X4,X6,X17),X4,X17)
| ~ c_Relation_Osingle__valued(X15,X6,X17)
| ~ c_Relation_Osingle__valued(X5,X4,X6) ),
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_678,plain,
! [X5,X20,X21,X10,X4] :
( hBOOL(hAPP(X10,X21))
| ~ hBOOL(hAPP(X10,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X10,X20,X5,X4)))
| ~ hBOOL(hAPP(X10,X20))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_68]) ).
fof(c_0_679,plain,
! [X5,X20,X21,X10,X4] :
( hBOOL(hAPP(X10,X20))
| ~ hBOOL(hAPP(X10,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X10,X21,X5,X4)))
| ~ hBOOL(hAPP(X10,X21))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_69]) ).
fof(c_0_680,axiom,
! [X5,X4] : c_Transitive__Closure_Ortrancl(X5,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X4),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X5,X4),X5,X4,X4,X4),tc_fun(tc_prod(X4,X4),tc_bool)),
c_0_70 ).
fof(c_0_681,plain,
! [X5,X20,X21,X10,X4] :
( hBOOL(hAPP(X10,X20))
| c_in(c_Pair(X21,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X10,X21,X5,X4),X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ hBOOL(hAPP(X10,X21))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_71]) ).
fof(c_0_682,plain,
! [X5,X20,X21,X10,X4] :
( hBOOL(hAPP(X10,X21))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X10,X20,X5,X4),X20,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ hBOOL(hAPP(X10,X20))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_683,axiom,
! [X5,X4] : c_Transitive__Closure_Otrancl(X5,X4) = c_Lattices_Oupper__semilattice__class_Osup(X5,c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X5,X4),X5,X4,X4,X4),tc_fun(tc_prod(X4,X4),tc_bool)),
c_0_73 ).
fof(c_0_684,plain,
! [X5,X20,X21,X4] :
( c_in(c_Pair(X21,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X21,X20,X5,X4),X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| X21 = X20
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_74]) ).
fof(c_0_685,plain,
! [X18,X8,X5,X4] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X5,X8,X18,X4),X18,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| X8 = X18
| ~ c_in(c_Pair(X8,X18,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_75]) ).
fof(c_0_686,plain,
! [X19,X8,X12,X4] :
( c_in(c_Pair(X8,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X12,X8,X19,X4),X4,X4),c_Transitive__Closure_Ortrancl(X12,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Otrancl(X12,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_76]) ).
fof(c_0_687,plain,
! [X19,X8,X12,X4] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X12,X8,X19,X4),X19,X4,X4),c_Transitive__Closure_Ortrancl(X12,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Otrancl(X12,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_77]) ).
fof(c_0_688,plain,
! [X18,X8,X5,X4] :
( c_in(c_Pair(X8,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X5,X8,X18,X4),X4,X4),X5,tc_prod(X4,X4))
| X8 = X18
| ~ c_in(c_Pair(X8,X18,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_78]) ).
fof(c_0_689,plain,
! [X5,X20,X21,X4] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X21,X20,X5,X4),X20,X4,X4),X5,tc_prod(X4,X4))
| X21 = X20
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_79]) ).
fof(c_0_690,plain,
! [X19,X8,X12,X4] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X12,X8,X19,X4),X19,X4,X4),X12,tc_prod(X4,X4))
| ~ c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Otrancl(X12,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_80]) ).
fof(c_0_691,plain,
! [X19,X8,X12,X4] :
( c_in(c_Pair(X8,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X12,X8,X19,X4),X4,X4),X12,tc_prod(X4,X4))
| ~ c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Otrancl(X12,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_692,plain,
! [X5,X30,X20,X21,X4] :
( c_in(c_Pair(X21,X30,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X20,X30,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_693,plain,
! [X5,X30,X20,X21,X4] :
( c_in(c_Pair(X21,X30,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X20,X30,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_694,plain,
! [X18,X19,X8,X5,X4] :
( c_in(c_Pair(X8,X18,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X19,X18,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_695,plain,
! [X5,X30,X20,X21,X4] :
( c_in(c_Pair(X21,X30,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X20,X30,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_696,axiom,
! [X8,X28,X29,X17,X6,X4] : hAPP(c_Fun_Ocomp(X29,X28,X6,X4,X17),X8) = hAPP(X29,hAPP(X28,X8)),
c_0_86 ).
fof(c_0_697,axiom,
! [X57,X20,X21,X17,X6,X4] : hAPP(X21,hAPP(X20,X57)) = hAPP(c_Fun_Ocomp(X21,X20,X17,X6,X4),X57),
c_0_87 ).
fof(c_0_698,axiom,
! [X5,X4] : c_Relation_Orel__comp(X5,c_Transitive__Closure_Ortrancl(X5,X4),X4,X4,X4) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X5,X4),X5,X4,X4,X4),
c_0_88 ).
fof(c_0_699,plain,
! [X5,X20,X21,X3,X4] :
( c_in(X21,X3,X4)
| X21 = X20
| ~ c_lessequals(X5,c_Product__Type_OSigma(X3,c_COMBK(X3,tc_fun(X4,tc_bool),X4),X4,X4),tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_700,plain,
! [X5,X30,X20,X21,X4] :
( c_in(c_Pair(X21,X30,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X20,X30,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X20,X4,X4),X5,tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_701,plain,
! [X5,X30,X20,X21,X4] :
( c_in(c_Pair(X21,X30,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X20,X30,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_702,plain,
! [X5,X30,X20,X21,X4] :
( c_in(c_Pair(X21,X30,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X20,X30,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X20,X4,X4),X5,tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_703,plain,
! [X5,X30,X20,X21,X4] :
( c_in(c_Pair(X21,X30,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X20,X30,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_704,plain,
! [X5,X30,X20,X21,X4] :
( c_in(c_Pair(X21,X30,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X20,X30,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X20,X4,X4),X5,tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_94]) ).
fof(c_0_705,plain,
! [X5,X30,X20,X21,X4] :
( c_in(c_Pair(X21,X30,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X20,X30,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_95]) ).
fof(c_0_706,plain,
! [X12,X4] :
( c_Wellfounded_Owf(c_Relation_Orel__comp(X12,X12,X4,X4,X4),X4)
| ~ c_Wellfounded_Owf(X12,X4) ),
inference(fof_simplification,[status(thm)],[c_0_96]) ).
fof(c_0_707,plain,
! [X5,X3,X4] :
( c_lessequals(c_Transitive__Closure_Otrancl(X5,X4),c_Product__Type_OSigma(X3,c_COMBK(X3,tc_fun(X4,tc_bool),X4),X4,X4),tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_lessequals(X5,c_Product__Type_OSigma(X3,c_COMBK(X3,tc_fun(X4,tc_bool),X4),X4,X4),tc_fun(tc_prod(X4,X4),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_97]) ).
fof(c_0_708,plain,
! [X30,X20,X21,X12,X4] :
( c_in(c_Pair(X21,X30,X4,X4),c_Transitive__Closure_Otrancl(X12,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X20,X30,X4,X4),X12,tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X20,X4,X4),X12,tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_709,plain,
! [X19,X8,X5,X29,X6,X4] :
( c_in(c_Pair(hAPP(X29,X8),hAPP(X29,X19),X6,X6),X5,tc_prod(X6,X6))
| ~ c_in(c_Pair(X8,X19,X4,X4),c_Relation_Oinv__image(X5,X29,X6,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_99]) ).
fof(c_0_710,axiom,
! [X1,X2,X3,X6,X4] : c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),c_COMBK(X1,tc_fun(X6,tc_bool),X4),X4,X6) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X3,c_COMBK(X1,tc_fun(X6,tc_bool),X4),X4,X6),c_Product__Type_OSigma(X2,c_COMBK(X1,tc_fun(X6,tc_bool),X4),X4,X6),tc_fun(tc_prod(X4,X6),tc_bool)),
c_0_100 ).
fof(c_0_711,axiom,
! [X1,X2,X3,X6,X4] : c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),c_COMBK(X1,tc_fun(X6,tc_bool),X4),X4,X6) = c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(X3,c_COMBK(X1,tc_fun(X6,tc_bool),X4),X4,X6),c_Product__Type_OSigma(X2,c_COMBK(X1,tc_fun(X6,tc_bool),X4),X4,X6),tc_fun(tc_prod(X4,X6),tc_bool)),
c_0_101 ).
fof(c_0_712,plain,
! [X5,X38,X39] :
( c_in(c_Pair(X39,v_sko__Transitive__Closure__Xtrancl__Xcases__1(X39,X38,X5),t_a,t_a),c_Transitive__Closure_Otrancl(X5,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(X39,X38,t_a,t_a),X5,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X39,X38,t_a,t_a),c_Transitive__Closure_Otrancl(X5,t_a),tc_prod(t_a,t_a)) ),
inference(fof_simplification,[status(thm)],[c_0_102]) ).
fof(c_0_713,plain,
! [X19,X8,X5,X3,X4] :
( c_Relation_OImage(X5,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4) != c_Relation_OImage(X5,c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4)
| ~ c_in(X19,X3,X4)
| ~ c_in(X8,X3,X4)
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4)
| c_in(c_Pair(X8,X19,X4,X4),X5,tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_714,plain,
! [X19,X8,X5,X3,X4] :
( c_Relation_OImage(X5,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4) != c_Relation_OImage(X5,c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4)
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4)
| c_in(c_Pair(X8,X19,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(X19,X3,X4)
| ~ c_in(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_715,plain,
! [X5,X38,X39] :
( c_in(c_Pair(v_sko__Transitive__Closure__Xtrancl__Xcases__1(X39,X38,X5),X38,t_a,t_a),X5,tc_prod(t_a,t_a))
| c_in(c_Pair(X39,X38,t_a,t_a),X5,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X39,X38,t_a,t_a),c_Transitive__Closure_Otrancl(X5,t_a),tc_prod(t_a,t_a)) ),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_716,plain,
! [X5,X20,X21,X3,X4] :
( c_Relation_OImage(X5,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4) != c_Relation_OImage(X5,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4)
| c_in(c_Pair(X21,X20,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(X20,X3,X4)
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_717,axiom,
! [X5,X4] :
( c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X4,X4),X5),X5,X4,X4,X4) != X5
| c_Equiv__Relations_Oequiv(c_Relation_ODomain(X5,X4,X4),X5,X4) ),
c_0_107 ).
fof(c_0_718,plain,
! [X8,X20,X21,X36] :
( c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X36,X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X8,v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1(X21,X20,X8)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_Ounanimity(X36) ),
inference(fof_simplification,[status(thm)],[c_0_108]) ).
fof(c_0_719,plain,
! [X19,X8,X5,X29,X6,X4] :
( c_in(c_Pair(X8,X19,X4,X4),c_Relation_Oinv__image(X5,X29,X6,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(hAPP(X29,X8),hAPP(X29,X19),X6,X6),X5,tc_prod(X6,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_109]) ).
fof(c_0_720,plain,
! [X5,X20,X21,X6,X4] :
( c_in(c_Pair(X21,X20,X6,X4),X5,tc_prod(X6,X4))
| ~ c_in(X20,c_Relation_OImage(X5,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X6),X6,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_110]) ).
fof(c_0_721,plain,
! [X19,X8,X5,X3,X4] :
( c_Relation_OImage(X5,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4) = c_Relation_OImage(X5,c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4)
| ~ c_in(c_Pair(X8,X19,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(X19,X3,X4)
| ~ c_in(X8,X3,X4)
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_722,plain,
! [X5,X20,X21,X10,X4] :
( hBOOL(hAPP(X10,X20))
| hBOOL(hAPP(X10,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X10,X21,X5,X4)))
| ~ hBOOL(hAPP(X10,X21))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_112]) ).
fof(c_0_723,plain,
! [X5,X20,X21,X10,X4] :
( hBOOL(hAPP(X10,X21))
| hBOOL(hAPP(X10,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X10,X20,X5,X4)))
| ~ hBOOL(hAPP(X10,X20))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_113]) ).
fof(c_0_724,axiom,
! [X12,X4] :
( c_Relation_Orel__comp(X12,X12,X4,X4,X4) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool))
| c_Wellfounded_Owf(X12,X4) ),
c_0_114 ).
fof(c_0_725,plain,
! [X5,X1,X2,X3,X6,X4] :
( c_lessequals(c_Relation_OImage(X5,X1,X4,X6),X2,tc_fun(X6,tc_bool))
| ~ c_lessequals(X5,c_Product__Type_OSigma(X3,c_COMBK(X2,tc_fun(X6,tc_bool),X4),X4,X6),tc_fun(tc_prod(X4,X6),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_115]) ).
fof(c_0_726,axiom,
! [X1,X2,X3,X4] : 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)),
c_0_116 ).
fof(c_0_727,plain,
! [X36] :
( c_Arrow__Order__Mirabelle_OIIA(X36)
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X36),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X36),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X36,v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X36)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X36),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X36),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X36,v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X36)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[c_0_117]) ).
fof(c_0_728,plain,
! [X8,X1,X2,X3,X6,X4] :
( c_lessequals(c_Product__Type_OSigma(X3,c_COMBK(X1,tc_fun(X4,tc_bool),X6),X6,X4),c_Product__Type_OSigma(X2,c_COMBK(X1,tc_fun(X4,tc_bool),X6),X6,X4),tc_fun(tc_prod(X6,X4),tc_bool))
| ~ c_lessequals(X3,X2,tc_fun(X6,tc_bool))
| ~ c_in(X8,X1,X4) ),
inference(fof_simplification,[status(thm)],[c_0_118]) ).
fof(c_0_729,plain,
! [X5,X20,X21,X3,X4] :
( c_Relation_OImage(X5,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4) = c_Relation_OImage(X5,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4)
| ~ c_in(c_Pair(X21,X20,X4,X4),X5,tc_prod(X4,X4))
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_119]) ).
fof(c_0_730,plain,
! [X19,X8,X5,X3,X4] :
( c_Relation_OImage(X5,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4) = c_Relation_OImage(X5,c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4)
| ~ c_in(c_Pair(X8,X19,X4,X4),X5,tc_prod(X4,X4))
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_120]) ).
fof(c_0_731,plain,
! [X18,X19,X8,X5,X6,X4] :
( X19 = X18
| ~ c_in(c_Pair(X8,X18,X4,X6),X5,tc_prod(X4,X6))
| ~ c_in(c_Pair(X8,X19,X4,X6),X5,tc_prod(X4,X6))
| ~ c_Relation_Osingle__valued(X5,X4,X6) ),
inference(fof_simplification,[status(thm)],[c_0_121]) ).
fof(c_0_732,plain,
! [X19,X8,X5,X4] :
( c_in(c_Pair(X8,X19,X4,X4),hAPP(c_Relation_Oconverse(X4,X4),c_Transitive__Closure_Otrancl(X5,X4)),tc_prod(X4,X4))
| ~ c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Otrancl(hAPP(c_Relation_Oconverse(X4,X4),X5),X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_122]) ).
fof(c_0_733,plain,
! [X5,X20,X21,X6,X4] :
( c_in(X20,c_Relation_OImage(X5,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X6),X6,X4),X4)
| ~ c_in(c_Pair(X21,X20,X6,X4),X5,tc_prod(X6,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_123]) ).
fof(c_0_734,plain,
! [X19,X8,X5,X4] :
( c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Otrancl(hAPP(c_Relation_Oconverse(X4,X4),X5),X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X8,X19,X4,X4),hAPP(c_Relation_Oconverse(X4,X4),c_Transitive__Closure_Otrancl(X5,X4)),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_124]) ).
fof(c_0_735,plain,
! [X5,X20,X21,X4] :
( c_Relation_OImage(X5,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4) != c_Relation_OImage(X5,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4)
| ~ c_in(X20,c_Relation_OField(X5,X4),X4)
| ~ c_in(X21,c_Relation_OField(X5,X4),X4)
| ~ c_Relation_Oantisym(X5,X4)
| ~ c_Relation_Orefl__on(c_Relation_OField(X5,X4),X5,X4)
| X21 = X20 ),
inference(fof_simplification,[status(thm)],[c_0_125]) ).
fof(c_0_736,plain,
! [X19,X8,X5,X4] :
( c_Wellfounded_Owf(X5,X4)
| ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X19,X8,X4,X4),X5,tc_prod(X4,X4)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_126]) ).
fof(c_0_737,plain,
! [X19,X8,X5,X4] :
( c_Wellfounded_Oacyclic(X5,X4)
| ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X19,X8,X4,X4),X5,tc_prod(X4,X4)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_127]) ).
fof(c_0_738,plain,
! [X5,X20,X21,X4] :
( X21 = X20
| ~ c_in(c_Pair(X20,X21,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X20,X4,X4),X5,tc_prod(X4,X4))
| ~ c_Relation_Oantisym(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_128]) ).
fof(c_0_739,plain,
! [X19,X8,X5,X4] :
( X8 = X19
| ~ c_in(c_Pair(X19,X8,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(c_Pair(X8,X19,X4,X4),X5,tc_prod(X4,X4))
| ~ c_Relation_Oantisym(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_129]) ).
fof(c_0_740,plain,
! [X8,X5,X21,X4] :
( ~ c_in(c_Pair(X8,X21,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X8,X4,X4),X5,tc_prod(X4,X4))
| ~ c_Wellfounded_Owf(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_130]) ).
fof(c_0_741,plain,
! [X5,X20,X6,X4] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X20,X5,X4,X6),X20,X6,X4),X5,tc_prod(X6,X4))
| ~ c_in(X20,c_Relation_ORange(X5,X6,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_131]) ).
fof(c_0_742,plain,
! [X5,X21,X6,X4] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X21,X5,X4,X6),X21,X6,X4),X5,tc_prod(X6,X4))
| ~ c_in(X21,c_Relation_ORange(X5,X6,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_132]) ).
fof(c_0_743,plain,
! [X5,X21,X6,X4] :
( c_in(c_Pair(X21,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X21,X5,X4,X6),X4,X6),X5,tc_prod(X4,X6))
| ~ c_in(X21,c_Relation_ODomain(X5,X4,X6),X4) ),
inference(fof_simplification,[status(thm)],[c_0_133]) ).
fof(c_0_744,plain,
! [X5,X21,X6,X4] :
( c_in(c_Pair(X21,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X21,X5,X4,X6),X4,X6),X5,tc_prod(X4,X6))
| ~ c_in(X21,c_Relation_ODomain(X5,X4,X6),X4) ),
inference(fof_simplification,[status(thm)],[c_0_134]) ).
fof(c_0_745,axiom,
! [X5,X20,X21,X4] : c_Relation_OField(c_Set_Oinsert(c_Pair(X21,X20,X4,X4),X5,tc_prod(X4,X4)),X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X21,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4),c_Relation_OField(X5,X4),tc_fun(X4,tc_bool)),
c_0_135 ).
fof(c_0_746,plain,
! [X19,X8,X5,X4] :
( c_in(c_Pair(X19,X8,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Ortrancl(hAPP(c_Relation_Oconverse(X4,X4),X5),X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_136]) ).
fof(c_0_747,plain,
! [X19,X8,X5,X4] :
( c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X19,X8,X4,X4),X5,tc_prod(X4,X4)),X4)
| c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_Wellfounded_Owf(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_137]) ).
fof(c_0_748,plain,
! [X19,X8,X5,X4] :
( c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X19,X8,X4,X4),X5,tc_prod(X4,X4)),X4)
| c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_Wellfounded_Oacyclic(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_138]) ).
fof(c_0_749,plain,
! [X20,X21,X2,X3,X6,X4] :
( c_in(X20,hAPP(X2,X21),X6)
| ~ c_in(c_Pair(X21,X20,X4,X6),c_Product__Type_OSigma(X3,X2,X4,X6),tc_prod(X4,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_139]) ).
fof(c_0_750,plain,
! [X20,X21,X2,X3,X6,X4] :
( c_in(X21,X3,X4)
| ~ c_in(c_Pair(X21,X20,X4,X6),c_Product__Type_OSigma(X3,X2,X4,X6),tc_prod(X4,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_140]) ).
fof(c_0_751,plain,
! [X5,X38,X39] :
( c_in(c_Pair(X39,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X39,X38,X5),t_a,t_a),c_Transitive__Closure_Ortrancl(X5,t_a),tc_prod(t_a,t_a))
| X38 = X39
| ~ c_in(c_Pair(X39,X38,t_a,t_a),c_Transitive__Closure_Ortrancl(X5,t_a),tc_prod(t_a,t_a)) ),
inference(fof_simplification,[status(thm)],[c_0_141]) ).
fof(c_0_752,plain,
! [X19,X8,X5,X4] :
( c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Ortrancl(hAPP(c_Relation_Oconverse(X4,X4),X5),X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X19,X8,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_142]) ).
fof(c_0_753,plain,
! [X5,X38,X39] :
( c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X39,X38,X5),X38,t_a,t_a),X5,tc_prod(t_a,t_a))
| X38 = X39
| ~ c_in(c_Pair(X39,X38,t_a,t_a),c_Transitive__Closure_Ortrancl(X5,t_a),tc_prod(t_a,t_a)) ),
inference(fof_simplification,[status(thm)],[c_0_143]) ).
fof(c_0_754,plain,
! [X19,X8,X5,X3,X4] :
( c_Equiv__Relations_Oquotient(c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X5,X4) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X5,X4)
| ~ c_in(c_Pair(X8,X19,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(X19,X3,X4)
| ~ c_in(X8,X3,X4)
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_144]) ).
fof(c_0_755,plain,
! [X12,X2,X3,X6,X4] :
( c_Relation_OImage(X12,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X6,tc_bool)),X6,X4) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X12,X3,X6,X4),c_Relation_OImage(X12,X2,X6,X4),tc_fun(X4,tc_bool))
| ~ c_Relation_Osingle__valued(hAPP(c_Relation_Oconverse(X6,X4),X12),X4,X6) ),
inference(fof_simplification,[status(thm)],[c_0_145]) ).
fof(c_0_756,plain,
! [X19,X8,X5,X3,X4] :
( c_Equiv__Relations_Oquotient(c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X5,X4) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(X19,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X5,X4)
| ~ c_in(X19,X3,X4)
| ~ c_in(X8,X3,X4)
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4)
| c_in(c_Pair(X8,X19,X4,X4),X5,tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_146]) ).
fof(c_0_757,plain,
! [X37,X36] :
( c_Arrow__Order__Mirabelle_OIIA(X36)
| c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X36),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X36),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X36),X37),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X36),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X36),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X36),X37),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[c_0_147]) ).
fof(c_0_758,plain,
! [X37,X36] :
( c_Arrow__Order__Mirabelle_OIIA(X36)
| c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X36),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X36),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X36),X37),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X36),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X36),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X36),X37),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[c_0_148]) ).
fof(c_0_759,plain,
! [X8,X5,X4] :
( ~ c_in(c_Pair(X8,X8,X4,X4),X5,tc_prod(X4,X4))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X5,X4),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X5,X4),X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_149]) ).
fof(c_0_760,plain,
! [X5,X20,X21,X6,X4] :
( c_in(c_Pair(X20,X21,X6,X4),X5,tc_prod(X6,X4))
| ~ c_in(c_Pair(X21,X20,X4,X6),hAPP(c_Relation_Oconverse(X6,X4),X5),tc_prod(X4,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_150]) ).
fof(c_0_761,axiom,
! [X13,X12,X3,X6,X4] : c_Relation_OImage(c_Lattices_Oupper__semilattice__class_Osup(X12,X13,tc_fun(tc_prod(X6,X4),tc_bool)),X3,X6,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X12,X3,X6,X4),c_Relation_OImage(X13,X3,X6,X4),tc_fun(X4,tc_bool)),
c_0_151 ).
fof(c_0_762,plain,
! [X5,X20,X21,X6,X4] :
( c_in(c_Pair(X20,X21,X6,X4),hAPP(c_Relation_Oconverse(X4,X6),X5),tc_prod(X6,X4))
| ~ c_in(c_Pair(X21,X20,X4,X6),X5,tc_prod(X4,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_152]) ).
fof(c_0_763,plain,
! [X5,X20,X21,X6,X4] :
( c_in(c_Pair(X21,X20,X4,X6),hAPP(c_Relation_Oconverse(X6,X4),X5),tc_prod(X4,X6))
| ~ c_in(c_Pair(X20,X21,X6,X4),X5,tc_prod(X6,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_153]) ).
fof(c_0_764,plain,
! [X8,X29,X2,X3,X6,X4] :
( c_in(hAPP(X29,X8),X2,X6)
| ~ c_in(X8,X3,X4)
| ~ c_in(X29,c_FuncSet_OPi(X3,c_COMBK(X2,tc_fun(X6,tc_bool),X4),X4,X6),tc_fun(X4,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_154]) ).
fof(c_0_765,plain,
! [X20,X21,X12,X4] :
( c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Otrancl(X12,X4),tc_prod(X4,X4))
| X21 = X20
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Ortrancl(X12,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_155]) ).
fof(c_0_766,plain,
! [X19,X8,X12,X4] :
( c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Otrancl(X12,X4),tc_prod(X4,X4))
| X8 = X19
| ~ c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Ortrancl(X12,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_156]) ).
fof(c_0_767,plain,
! [X19,X8,X12,X4] :
( c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Ortrancl(X12,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Otrancl(X12,X4),tc_prod(X4,X4))
| X8 = X19 ),
inference(fof_simplification,[status(thm)],[c_0_157]) ).
fof(c_0_768,plain,
! [X5,X20,X21,X4] :
( c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_158]) ).
fof(c_0_769,plain,
! [X8,X5,X20,X3,X6,X4] :
( c_in(X20,c_Relation_OImage(X5,X3,X6,X4),X4)
| ~ c_in(c_Pair(X8,X20,X6,X4),X5,tc_prod(X6,X4))
| ~ c_in(X8,X3,X6) ),
inference(fof_simplification,[status(thm)],[c_0_159]) ).
fof(c_0_770,plain,
! [X5,X20,X21,X3,X6,X4] :
( c_in(X20,c_Relation_OImage(X5,X3,X4,X6),X6)
| ~ c_in(c_Pair(X21,X20,X4,X6),X5,tc_prod(X4,X6))
| ~ c_in(X21,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_160]) ).
fof(c_0_771,axiom,
! [X22,X23,X1,X6,X4] : c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(X23,X22,tc_fun(X4,tc_bool)),X1,X4,X6) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X23,X1,X4,X6),c_Product__Type_OSigma(X22,X1,X4,X6),tc_fun(tc_prod(X4,X6),tc_bool)),
c_0_161 ).
fof(c_0_772,axiom,
! [X22,X23,X1,X6,X4] : c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(X23,X22,tc_fun(X4,tc_bool)),X1,X4,X6) = c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(X23,X1,X4,X6),c_Product__Type_OSigma(X22,X1,X4,X6),tc_fun(tc_prod(X4,X6),tc_bool)),
c_0_162 ).
fof(c_0_773,plain,
! [X5,X20,X21,X4] :
( c_in(c_Pair(X21,X20,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X20,X4,X4),X5,tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_163]) ).
fof(c_0_774,plain,
! [X5,X20,X21,X4] :
( c_in(c_Pair(X20,X21,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(c_Pair(X21,X20,X4,X4),X5,tc_prod(X4,X4))
| ~ c_Relation_Osym(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_164]) ).
fof(c_0_775,plain,
! [X19,X8,X5,X4] :
( c_in(c_Pair(X19,X8,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(c_Pair(X8,X19,X4,X4),X5,tc_prod(X4,X4))
| ~ c_Relation_Osym(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_165]) ).
fof(c_0_776,plain,
! [X37] :
( c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X37),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X37),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[c_0_166]) ).
fof(c_0_777,plain,
! [X37] :
( c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X37),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X37),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[c_0_167]) ).
fof(c_0_778,plain,
! [X18,X19,X8,X49] :
( c_in(c_Pair(X8,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X49,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X8 = X18
| ~ c_in(c_Pair(X8,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X49,X18),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[c_0_168]) ).
fof(c_0_779,plain,
! [X18,X19,X8,X49] :
( c_in(c_Pair(X8,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X49,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X19 = X18
| ~ c_in(c_Pair(X8,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X49,X18),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[c_0_169]) ).
fof(c_0_780,plain,
! [X18,X19,X8,X49] :
( c_in(c_Pair(X8,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X49,X18),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X8,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X49,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X8 = X18
| X19 = X18 ),
inference(fof_simplification,[status(thm)],[c_0_170]) ).
fof(c_0_781,plain,
! [X18,X19,X8,X49] :
( c_in(c_Pair(X8,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X49,X18),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X8,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X49,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X8 = X19
| X19 = X18 ),
inference(fof_simplification,[status(thm)],[c_0_171]) ).
fof(c_0_782,plain,
! [X18,X19,X8,X49] :
( c_in(c_Pair(X8,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X49,X18),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X8,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X49,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X19 = X18
| X8 = X18 ),
inference(fof_simplification,[status(thm)],[c_0_172]) ).
fof(c_0_783,plain,
! [X18,X19,X8,X49] :
( c_in(c_Pair(X8,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X49,X18),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X8,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X49,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X8 = X19
| X8 = X18 ),
inference(fof_simplification,[status(thm)],[c_0_173]) ).
fof(c_0_784,axiom,
! [X12,X2,X3,X6,X4] : c_Relation_OImage(X12,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X6,tc_bool)),X6,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X12,X3,X6,X4),c_Relation_OImage(X12,X2,X6,X4),tc_fun(X4,tc_bool)),
c_0_174 ).
fof(c_0_785,axiom,
! [X12,X17,X6,X4] : c_Relation_Orel__comp(X12,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X17,X6),tc_bool)),X4,X17,X6) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X6),tc_bool)),
c_0_175 ).
fof(c_0_786,axiom,
! [X12,X17,X6,X4] : c_Relation_Orel__comp(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X17),tc_bool)),X12,X4,X17,X6) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X6),tc_bool)),
c_0_176 ).
fof(c_0_787,plain,
! [X19,X8,X12,X9,X4] :
( ~ c_in(X19,X9,X4)
| ~ c_in(c_Pair(X19,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X9,X12,X4),X4,X4),X12,tc_prod(X4,X4))
| ~ c_in(X8,X9,X4)
| ~ c_Wellfounded_Owf(X12,X4) ),
inference(fof_simplification,[status(thm)],[c_0_177]) ).
fof(c_0_788,plain,
! [X19,X7,X5,X9,X4] :
( ~ c_in(X19,X9,X4)
| ~ c_in(c_Pair(X19,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X9,X5,X4),X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(X7,X9,X4)
| ~ c_Wellfounded_Owf(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_178]) ).
fof(c_0_789,plain,
! [X8,X5,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Relation_Oconverse(X4,X4),X5),c_Transitive__Closure_Ortrancl(X5,X4),tc_fun(tc_prod(X4,X4),tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_in(c_Pair(X8,X8,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_179]) ).
fof(c_0_790,plain,
! [X19,X5,X21,X10,X4] :
( hBOOL(hAPP(X10,X21))
| hBOOL(hAPP(X10,X19))
| ~ c_in(c_Pair(X19,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X10,X5,X4),X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(X21,c_Wellfounded_Oacc(X5,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_180]) ).
fof(c_0_791,plain,
! [X19,X5,X21,X10,X4] :
( hBOOL(hAPP(X10,X21))
| hBOOL(hAPP(X10,X19))
| ~ c_in(c_Pair(X19,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X10,X5,X4),X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(X21,c_Wellfounded_Oacc(X5,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_181]) ).
fof(c_0_792,plain,
! [X7,X8,X5,X3,X4] :
( c_in(c_Pair(X7,X8,X4,X4),X5,tc_prod(X4,X4))
| c_in(c_Pair(X8,X7,X4,X4),X5,tc_prod(X4,X4))
| X8 = X7
| ~ c_in(X7,X3,X4)
| ~ c_in(X8,X3,X4)
| ~ c_Relation_Ototal__on(X3,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_182]) ).
fof(c_0_793,plain,
! [X16,X5,X35,X3,X6,X4] :
( c_lessequals(c_Relation_OImage(X16,X35,X4,X6),c_Relation_OImage(X5,X3,X4,X6),tc_fun(X6,tc_bool))
| ~ c_lessequals(X35,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X16,X5,tc_fun(tc_prod(X4,X6),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_183]) ).
fof(c_0_794,plain,
! [X5,X3,X4] :
( c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X4,X4),X5),X5,X4,X4,X4) = X5
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_184]) ).
fof(c_0_795,axiom,
! [X5,X20,X21,X6,X4] : c_Relation_ORange(c_Set_Oinsert(c_Pair(X21,X20,X6,X4),X5,tc_prod(X6,X4)),X6,X4) = c_Set_Oinsert(X20,c_Relation_ORange(X5,X6,X4),X4),
c_0_185 ).
fof(c_0_796,axiom,
! [X5,X20,X21,X6,X4] : c_Relation_ODomain(c_Set_Oinsert(c_Pair(X21,X20,X4,X6),X5,tc_prod(X4,X6)),X4,X6) = c_Set_Oinsert(X21,c_Relation_ODomain(X5,X4,X6),X4),
c_0_186 ).
fof(c_0_797,plain,
! [X8,X1,X2,X3,X6,X4] :
( c_Product__Type_OSigma(X3,c_COMBK(X1,tc_fun(X4,tc_bool),X6),X6,X4) != c_Product__Type_OSigma(X2,c_COMBK(X1,tc_fun(X4,tc_bool),X6),X6,X4)
| ~ c_in(X8,X1,X4)
| X3 = X2 ),
inference(fof_simplification,[status(thm)],[c_0_187]) ).
fof(c_0_798,plain,
! [X19,X5,X21,X10,X4] :
( hBOOL(hAPP(X10,X21))
| hBOOL(hAPP(X10,X19))
| ~ c_in(c_Pair(X19,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X10,X5,X4),X4,X4),X5,tc_prod(X4,X4))
| ~ c_Wellfounded_Owf(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_188]) ).
fof(c_0_799,plain,
! [X19,X40,X12,X10,X4] :
( hBOOL(hAPP(X10,X40))
| hBOOL(hAPP(X10,X19))
| ~ c_in(c_Pair(X19,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X10,X12,X4),X4,X4),X12,tc_prod(X4,X4))
| ~ c_Wellfounded_Owf(X12,X4) ),
inference(fof_simplification,[status(thm)],[c_0_189]) ).
fof(c_0_800,plain,
! [X19,X7,X5,X10,X4] :
( hBOOL(hAPP(X10,X7))
| hBOOL(hAPP(X10,X19))
| ~ c_in(c_Pair(X19,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X10,X5,X4),X4,X4),X5,tc_prod(X4,X4))
| ~ c_Wellfounded_Owf(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_190]) ).
fof(c_0_801,plain,
! [X19,X5,X21,X10,X4] :
( hBOOL(hAPP(X10,X21))
| hBOOL(hAPP(X10,X19))
| ~ c_in(c_Pair(X19,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X10,X5,X4),X4,X4),X5,tc_prod(X4,X4))
| ~ c_Wellfounded_Owf(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_191]) ).
fof(c_0_802,plain,
! [X18,X19,X5,X29,X6,X4] :
( hAPP(X29,X19) = hAPP(X29,X18)
| ~ c_in(c_Pair(X19,X18,X4,X4),X5,tc_prod(X4,X4))
| ~ c_Equiv__Relations_Ocongruent(X5,X29,X4,X6) ),
inference(fof_simplification,[status(thm)],[c_0_192]) ).
fof(c_0_803,plain,
! [X20,X21,X2,X3,X6,X4] :
( c_in(c_Pair(X21,X20,X4,X6),c_Product__Type_OSigma(X3,X2,X4,X6),tc_prod(X4,X6))
| ~ c_in(X20,hAPP(X2,X21),X6)
| ~ c_in(X21,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_193]) ).
fof(c_0_804,plain,
! [X20,X21,X2,X3,X6,X4] :
( c_in(c_Pair(X21,X20,X4,X6),c_Product__Type_OSigma(X3,X2,X4,X6),tc_prod(X4,X6))
| ~ c_in(X20,hAPP(X2,X21),X6)
| ~ c_in(X21,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_194]) ).
fof(c_0_805,axiom,
! [X2,X3,X6,X4] : c_lessequals(c_Relation_ORange(c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(tc_prod(X6,X4),tc_bool)),X6,X4),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(X3,X6,X4),c_Relation_ORange(X2,X6,X4),tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
c_0_195 ).
fof(c_0_806,axiom,
! [X2,X3,X6,X4] : c_lessequals(c_Relation_ODomain(c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(tc_prod(X4,X6),tc_bool)),X4,X6),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X3,X4,X6),c_Relation_ODomain(X2,X4,X6),tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
c_0_196 ).
fof(c_0_807,axiom,
! [X12,X4] : c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X12,X4),c_Transitive__Closure_Ortrancl(X12,X4),X4,X4,X4) = c_Transitive__Closure_Ortrancl(X12,X4),
c_0_197 ).
fof(c_0_808,axiom,
! [X36] :
( c_Arrow__Order__Mirabelle_OIIA(X36)
| c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X36),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X36),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X36,v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X36)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X36),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X36),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X36,v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X36)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_198 ).
fof(c_0_809,axiom,
! [X5,X4] : c_Transitive__Closure_Otrancl(X5,X4) = c_Relation_Orel__comp(X5,c_Transitive__Closure_Ortrancl(X5,X4),X4,X4,X4),
c_0_199 ).
fof(c_0_810,axiom,
! [X5,X4] : c_Transitive__Closure_Otrancl(X5,X4) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X5,X4),X5,X4,X4,X4),
c_0_200 ).
fof(c_0_811,axiom,
! [X12,X6,X4] : c_Relation_Orel__comp(X12,c_Relation_OId(X6),X4,X6,X6) = X12,
c_0_201 ).
fof(c_0_812,axiom,
! [X12,X6,X4] : c_Relation_Orel__comp(c_Relation_OId(X4),X12,X4,X4,X6) = X12,
c_0_202 ).
fof(c_0_813,plain,
! [X47,X8,X5,X10] :
( hBOOL(hAPP(X10,X8))
| c_in(X47,c_Wellfounded_Oacc(X5,t_a),t_a)
| ~ c_in(c_Pair(X47,v_sko__Wellfounded__Xacc__Xinducts__1(X10,X5),t_a,t_a),X5,tc_prod(t_a,t_a))
| ~ c_in(X8,c_Wellfounded_Oacc(X5,t_a),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_203]) ).
fof(c_0_814,plain,
! [X47,X8,X5,X10] :
( hBOOL(hAPP(X10,X8))
| c_in(X47,c_Wellfounded_Oacc(X5,t_a),t_a)
| ~ c_in(c_Pair(X47,v_sko__Wellfounded__Xacc__Xinduct__1(X10,X5),t_a,t_a),X5,tc_prod(t_a,t_a))
| ~ c_in(X8,c_Wellfounded_Oacc(X5,t_a),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_204]) ).
fof(c_0_815,plain,
! [X5,X20,X21,X4] :
( c_in(X20,c_Wellfounded_Oacc(X5,X4),X4)
| ~ c_in(X21,c_Wellfounded_Oacc(X5,X4),X4)
| ~ c_in(c_Pair(X20,X21,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_205]) ).
fof(c_0_816,plain,
! [X5,X20,X21,X4] :
( c_in(X20,c_Wellfounded_Oacc(X5,X4),X4)
| ~ c_in(c_Pair(X20,X21,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(X21,c_Wellfounded_Oacc(X5,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_206]) ).
fof(c_0_817,plain,
! [X19,X8,X5,X10] :
( hBOOL(hAPP(X10,X8))
| hBOOL(hAPP(X10,X19))
| ~ c_in(c_Pair(X19,v_sko__Wellfounded__Xacc__Xinduct__1(X10,X5),t_a,t_a),X5,tc_prod(t_a,t_a))
| ~ c_in(X8,c_Wellfounded_Oacc(X5,t_a),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_207]) ).
fof(c_0_818,plain,
! [X19,X8,X5,X10] :
( hBOOL(hAPP(X10,X8))
| hBOOL(hAPP(X10,X19))
| ~ c_in(c_Pair(X19,v_sko__Wellfounded__Xacc__Xinducts__1(X10,X5),t_a,t_a),X5,tc_prod(t_a,t_a))
| ~ c_in(X8,c_Wellfounded_Oacc(X5,t_a),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_208]) ).
fof(c_0_819,plain,
! [X5,X21,X3,X4] :
( c_in(X21,c_Relation_OImage(X5,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4),X4)
| ~ c_in(X21,X3,X4)
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_209]) ).
fof(c_0_820,plain,
! [X19,X5,X21,X4] :
( c_in(X19,c_Wellfounded_Oacc(X5,X4),X4)
| ~ c_in(c_Pair(X19,X21,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(X21,c_Wellfounded_Oacc(X5,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_210]) ).
fof(c_0_821,plain,
! [X5,X20,X21,X4] :
( c_in(X21,c_Wellfounded_Oacc(X5,X4),X4)
| ~ c_in(c_Pair(X21,X20,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(X20,c_Wellfounded_Oacc(X5,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_211]) ).
fof(c_0_822,axiom,
! [X5,X4] : c_lessequals(c_Transitive__Closure_Otrancl(X5,X4),c_Product__Type_OSigma(c_Relation_OField(X5,X4),c_COMBK(c_Relation_OField(X5,X4),tc_fun(X4,tc_bool),X4),X4,X4),tc_fun(tc_prod(X4,X4),tc_bool)),
c_0_212 ).
fof(c_0_823,plain,
! [X19,X8,X12,X4] :
( X8 = X19
| ~ c_in(c_Pair(X8,X19,X4,X4),c_Transitive__Closure_Ortrancl(X12,X4),tc_prod(X4,X4))
| c_in(X8,c_Relation_ODomain(X12,X4,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_213]) ).
fof(c_0_824,plain,
! [X8,X29,X2,X3,X6,X4] :
( ~ c_in(X8,X3,X4)
| c_in(hAPP(X29,X8),hAPP(X2,X8),X6)
| ~ c_in(X29,c_FuncSet_OPi(X3,X2,X4,X6),tc_fun(X4,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_214]) ).
fof(c_0_825,plain,
! [X8,X29,X2,X3,X6,X4] :
( c_in(hAPP(X29,X8),hAPP(X2,X8),X6)
| ~ c_in(X8,X3,X4)
| ~ c_in(X29,c_FuncSet_OPi(X3,X2,X4,X6),tc_fun(X4,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_215]) ).
fof(c_0_826,plain,
! [X5,X4] :
( c_Nitpick_Orefl_H(X5,X4)
| ~ c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X5,X4),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X5,X4),X4,X4),X5,tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_216]) ).
fof(c_0_827,plain,
! [X5,X20,X21,X6,X4] :
( c_in(X21,c_Relation_ODomain(X5,X4,X6),X4)
| ~ c_in(c_Pair(X21,X20,X4,X6),X5,tc_prod(X4,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_217]) ).
fof(c_0_828,plain,
! [X8,X5,X21,X6,X4] :
( c_in(X21,c_Relation_ODomain(X5,X4,X6),X4)
| ~ c_in(c_Pair(X21,X8,X4,X6),X5,tc_prod(X4,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_218]) ).
fof(c_0_829,plain,
! [X5,X20,X21,X6,X4] :
( c_in(X20,c_Relation_ORange(X5,X4,X6),X6)
| ~ c_in(c_Pair(X21,X20,X4,X6),X5,tc_prod(X4,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_219]) ).
fof(c_0_830,plain,
! [X8,X5,X21,X6,X4] :
( c_in(X21,c_Relation_ORange(X5,X6,X4),X4)
| ~ c_in(c_Pair(X8,X21,X6,X4),X5,tc_prod(X6,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_220]) ).
fof(c_0_831,plain,
! [X19,X8,X5,X3,X4] :
( c_in(X8,X3,X4)
| ~ c_in(c_Pair(X8,X19,X4,X4),X5,tc_prod(X4,X4))
| ~ c_Relation_Orefl__on(X3,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_221]) ).
fof(c_0_832,plain,
! [X19,X8,X5,X3,X4] :
( c_in(X19,X3,X4)
| ~ c_in(c_Pair(X8,X19,X4,X4),X5,tc_prod(X4,X4))
| ~ c_Relation_Orefl__on(X3,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_222]) ).
fof(c_0_833,plain,
! [X19,X8,X5,X3,X4] :
( c_in(X8,X3,X4)
| ~ c_in(c_Pair(X8,X19,X4,X4),X5,tc_prod(X4,X4))
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_223]) ).
fof(c_0_834,plain,
! [X19,X8,X5,X3,X4] :
( c_in(X19,X3,X4)
| ~ c_in(c_Pair(X8,X19,X4,X4),X5,tc_prod(X4,X4))
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_224]) ).
fof(c_0_835,axiom,
! [X13,X12,X4] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X12,X4),c_Transitive__Closure_Ortrancl(X13,X4),tc_fun(tc_prod(X4,X4),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X12,X13,tc_fun(tc_prod(X4,X4),tc_bool)),X4),tc_fun(tc_prod(X4,X4),tc_bool)),
c_0_225 ).
fof(c_0_836,plain,
! [X5,X3,X4] :
( c_lessequals(X5,c_Product__Type_OSigma(X3,c_COMBK(X3,tc_fun(X4,tc_bool),X4),X4,X4),tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_226]) ).
fof(c_0_837,plain,
! [X5,X3,X4] :
( c_lessequals(X5,c_Product__Type_OSigma(X3,c_COMBK(X3,tc_fun(X4,tc_bool),X4),X4,X4),tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_Relation_Orefl__on(X3,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_227]) ).
fof(c_0_838,plain,
! [X19,X8,X3,X4] :
( c_in(X8,X3,X4)
| ~ c_in(c_Pair(X8,X19,X4,X4),c_Relation_OId__on(X3,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_228]) ).
fof(c_0_839,plain,
! [X36] :
( c_Arrow__Order__Mirabelle_Ounanimity(X36)
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3(X36),v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4(X36),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X36,v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2(X36)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[c_0_229]) ).
fof(c_0_840,plain,
! [X8,X5,X4] :
( ~ c_in(c_Pair(X8,X8,X4,X4),c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4))
| ~ c_Wellfounded_Oacyclic(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_230]) ).
fof(c_0_841,axiom,
! [X3,X4] : c_lessequals(c_Relation_OId__on(X3,X4),c_Product__Type_OSigma(X3,c_COMBK(X3,tc_fun(X4,tc_bool),X4),X4,X4),tc_fun(tc_prod(X4,X4),tc_bool)),
c_0_231 ).
fof(c_0_842,plain,
! [X12,X3,X4] :
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ c_lessequals(X3,c_Relation_OImage(X12,X3,X4,X4),tc_fun(X4,tc_bool))
| ~ c_Wellfounded_Owf(X12,X4) ),
inference(fof_simplification,[status(thm)],[c_0_232]) ).
fof(c_0_843,plain,
! [X19,X8,X3,X4] :
( X8 = X19
| ~ c_in(c_Pair(X8,X19,X4,X4),c_Relation_OId__on(X3,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_233]) ).
fof(c_0_844,plain,
! [X5,X21,X4] :
( ~ c_in(c_Pair(X21,X21,X4,X4),X5,tc_prod(X4,X4))
| ~ c_Wellfounded_Owf(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_234]) ).
fof(c_0_845,plain,
! [X7,X8,X49] : ~ c_in(c_Pair(X7,X8,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X49,X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(fof_simplification,[status(thm)],[c_0_235]) ).
fof(c_0_846,plain,
! [X8,X49] : ~ c_in(c_Pair(X8,X8,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X49,X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(fof_simplification,[status(thm)],[c_0_236]) ).
fof(c_0_847,plain,
! [X19,X8,X49] : ~ c_in(c_Pair(X8,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X49,X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(fof_simplification,[status(thm)],[c_0_237]) ).
fof(c_0_848,plain,
! [X8,X49] : ~ c_in(c_Pair(X8,X8,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X49,X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(fof_simplification,[status(thm)],[c_0_238]) ).
fof(c_0_849,plain,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Olattice(X4)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4),c_Lattices_Olower__semilattice__class_Oinf(X8,X18,X4),X4),c_Lattices_Olower__semilattice__class_Oinf(X8,c_Lattices_Oupper__semilattice__class_Osup(X19,X18,X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_239]) ).
fof(c_0_850,plain,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Olattice(X4)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Lattices_Olower__semilattice__class_Oinf(X19,X18,X4),X4),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4),c_Lattices_Oupper__semilattice__class_Osup(X8,X18,X4),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_240]) ).
fof(c_0_851,plain,
! [X20,X21,X4] :
( X21 = X20
| ~ c_in(c_Pair(X21,X20,X4,X4),c_Relation_OId(X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_241]) ).
fof(c_0_852,axiom,
! [X8,X12,X4] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X12,X8,X4),X8,X4,X4),X12,tc_prod(X4,X4))
| c_in(X8,c_Wellfounded_Oacc(X12,X4),X4) ),
c_0_242 ).
fof(c_0_853,axiom,
! [X8,X5,X4] :
( c_in(X8,c_Wellfounded_Oacc(X5,X4),X4)
| c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X5,X8,X4),X8,X4,X4),X5,tc_prod(X4,X4)) ),
c_0_243 ).
fof(c_0_854,axiom,
! [X29,X12,X6,X4] : hAPP(c_Relation_Oconverse(X4,X4),c_Relation_Oinv__image(X12,X29,X6,X4)) = c_Relation_Oinv__image(hAPP(c_Relation_Oconverse(X6,X6),X12),X29,X6,X4),
c_0_244 ).
fof(c_0_855,axiom,
! [X32,X30,X20,X21,X4] :
( c_Set_Oinsert(X21,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X30,c_Set_Oinsert(X32,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)
| X20 = X30
| X20 = X32 ),
c_0_245 ).
fof(c_0_856,axiom,
! [X32,X30,X20,X21,X4] :
( c_Set_Oinsert(X21,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X30,c_Set_Oinsert(X32,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)
| X21 = X32
| X20 = X32 ),
c_0_246 ).
fof(c_0_857,axiom,
! [X32,X30,X20,X21,X4] :
( c_Set_Oinsert(X21,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X30,c_Set_Oinsert(X32,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)
| X20 = X30
| X21 = X30 ),
c_0_247 ).
fof(c_0_858,axiom,
! [X32,X30,X20,X21,X4] :
( c_Set_Oinsert(X21,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X30,c_Set_Oinsert(X32,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)
| X21 = X32
| X21 = X30 ),
c_0_248 ).
fof(c_0_859,plain,
! [X15,X5,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X5,X4,X4),c_Relation_ORange(X15,X4,X4),tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ c_Wellfounded_Owf(X15,X4)
| ~ c_Wellfounded_Owf(X5,X4)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X5,X15,tc_fun(tc_prod(X4,X4),tc_bool)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_249]) ).
fof(c_0_860,axiom,
! [X1,X2,X3,X4] :
( c_Lattices_Oupper__semilattice__class_Osup(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_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
c_0_250 ).
fof(c_0_861,plain,
! [X8,X13,X12,X4] :
( c_in(X8,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X12,X13,tc_fun(tc_prod(X4,X4),tc_bool)),X4),tc_prod(X4,X4))
| ~ c_in(X8,c_Transitive__Closure_Ortrancl(X13,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_251]) ).
fof(c_0_862,plain,
! [X8,X13,X12,X4] :
( c_in(X8,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X12,X13,tc_fun(tc_prod(X4,X4),tc_bool)),X4),tc_prod(X4,X4))
| ~ c_in(X8,c_Transitive__Closure_Ortrancl(X12,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_252]) ).
fof(c_0_863,axiom,
! [X51,X20,X52,X21,X6,X4] :
( c_Pair(X21,X20,X4,X6) != c_Pair(X52,X51,X4,X6)
| X21 = X52 ),
c_0_253 ).
fof(c_0_864,axiom,
! [X51,X20,X52,X21,X6,X4] :
( c_Pair(X21,X20,X4,X6) != c_Pair(X52,X51,X4,X6)
| X20 = X51 ),
c_0_254 ).
fof(c_0_865,axiom,
! [X8,X12,X4] :
( c_in(X8,c_Relation_ODomain(X12,X4,X4),X4)
| c_in(c_Pair(X8,X8,X4,X4),c_Transitive__Closure_Ortrancl(X12,X4),tc_prod(X4,X4)) ),
c_0_255 ).
fof(c_0_866,plain,
! [X5,X21,X3,X4] :
( c_in(c_Pair(X21,X21,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(X21,X3,X4)
| ~ c_Relation_Orefl__on(X3,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_256]) ).
fof(c_0_867,plain,
! [X8,X5,X3,X4] :
( c_in(c_Pair(X8,X8,X4,X4),X5,tc_prod(X4,X4))
| ~ c_in(X8,X3,X4)
| ~ c_Relation_Orefl__on(X3,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_257]) ).
fof(c_0_868,plain,
! [X8,X3,X4] :
( c_in(c_Pair(X8,X8,X4,X4),c_Relation_OId__on(X3,X4),tc_prod(X4,X4))
| ~ c_in(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_258]) ).
fof(c_0_869,axiom,
! [X13,X12,X4] : c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X12,X4),c_Transitive__Closure_Ortrancl(X13,X4),tc_fun(tc_prod(X4,X4),tc_bool)),X4) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X12,X13,tc_fun(tc_prod(X4,X4),tc_bool)),X4),
c_0_259 ).
fof(c_0_870,plain,
! [X15,X5,X2,X3,X4] :
( c_Relation_Orefl__on(c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X5,X15,tc_fun(tc_prod(X4,X4),tc_bool)),X4)
| ~ c_Relation_Orefl__on(X2,X15,X4)
| ~ c_Relation_Orefl__on(X3,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_260]) ).
fof(c_0_871,plain,
! [X15,X5,X2,X3,X4] :
( c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X5,X15,tc_fun(tc_prod(X4,X4),tc_bool)),X4)
| ~ c_Relation_Orefl__on(X2,X15,X4)
| ~ c_Relation_Orefl__on(X3,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_261]) ).
fof(c_0_872,plain,
! [X30,X3,X4] :
( X30 = c_Pair(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X3,X30,X4),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X3,X30,X4),X4,X4)
| ~ c_in(X30,c_Relation_OId__on(X3,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_262]) ).
fof(c_0_873,axiom,
! [X37,X36] :
( c_Arrow__Order__Mirabelle_Ounanimity(X36)
| c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3(X36),v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4(X36),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2(X36),X37),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_263 ).
fof(c_0_874,plain,
! [X33,X1,X2,X3,X4] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X33,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| ~ c_lessequals(X2,X33,tc_fun(X4,tc_bool))
| ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_264]) ).
fof(c_0_875,plain,
! [X33,X1,X2,X3,X4] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X1,X33,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| ~ c_lessequals(X2,X33,tc_fun(X4,tc_bool))
| ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_265]) ).
fof(c_0_876,axiom,
! [X1,X2,X3,X4] : 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)),
c_0_266 ).
fof(c_0_877,axiom,
! [X1,X2,X3,X4] : 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)),
c_0_267 ).
fof(c_0_878,axiom,
! [X1,X2,X3,X4] : 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)),
c_0_268 ).
fof(c_0_879,axiom,
! [X1,X2,X3,X4] : 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)),
c_0_269 ).
fof(c_0_880,axiom,
! [X2,X3,X6,X4] : c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(tc_prod(X6,X4),tc_bool)),X6,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X3,X6,X4),c_Relation_ORange(X2,X6,X4),tc_fun(X4,tc_bool)),
c_0_270 ).
fof(c_0_881,axiom,
! [X2,X3,X6,X4] : c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(tc_prod(X4,X6),tc_bool)),X4,X6) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X3,X4,X6),c_Relation_ODomain(X2,X4,X6),tc_fun(X4,tc_bool)),
c_0_271 ).
fof(c_0_882,axiom,
! [X8,X12,X4] : c_in(c_Pair(X8,X8,X4,X4),c_Transitive__Closure_Ortrancl(X12,X4),tc_prod(X4,X4)),
c_0_272 ).
fof(c_0_883,axiom,
! [X5,X21,X4] : c_in(c_Pair(X21,X21,X4,X4),c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4)),
c_0_273 ).
fof(c_0_884,plain,
! [X8,X5,X4] :
( c_in(c_Pair(X8,X8,X4,X4),X5,tc_prod(X4,X4))
| ~ c_Nitpick_Orefl_H(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_274]) ).
fof(c_0_885,axiom,
! [X7,X8,X49] :
( X7 = X8
| X7 = X8
| c_in(c_Pair(X7,X8,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X49,X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_275 ).
fof(c_0_886,axiom,
! [X19,X8,X49] :
( X8 = X19
| X19 = X8
| c_in(c_Pair(X8,X19,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X49,X8),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_276 ).
fof(c_0_887,axiom,
! [X20,X21] :
( c_in(c_Pair(X21,X20,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X21,X20),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X21 = X20 ),
c_0_277 ).
fof(c_0_888,plain,
! [X8,X3,X4] :
( X3 = c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4)
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ c_lessequals(X3,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_278]) ).
fof(c_0_889,plain,
! [X8,X2,X3,X4] :
( hBOOL(hAPP(X2,X8))
| hBOOL(hAPP(X3,X8))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_279]) ).
fof(c_0_890,axiom,
! [X3,X6,X4] : c_Product__Type_OSigma(X3,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),tc_fun(X6,tc_bool),X4),X4,X6) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X6),tc_bool)),
c_0_280 ).
fof(c_0_891,plain,
! [X1,X2,X3,X4] :
( c_Lattices_Oupper__semilattice__class_Osup(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_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_281]) ).
fof(c_0_892,axiom,
! [X15,X5,X6,X4] : hAPP(c_Relation_Oconverse(X6,X4),c_Lattices_Olower__semilattice__class_Oinf(X5,X15,tc_fun(tc_prod(X6,X4),tc_bool))) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Relation_Oconverse(X6,X4),X5),hAPP(c_Relation_Oconverse(X6,X4),X15),tc_fun(tc_prod(X4,X6),tc_bool)),
c_0_282 ).
fof(c_0_893,axiom,
! [X15,X5,X6,X4] : hAPP(c_Relation_Oconverse(X6,X4),c_Lattices_Oupper__semilattice__class_Osup(X5,X15,tc_fun(tc_prod(X6,X4),tc_bool))) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Relation_Oconverse(X6,X4),X5),hAPP(c_Relation_Oconverse(X6,X4),X15),tc_fun(tc_prod(X4,X6),tc_bool)),
c_0_283 ).
fof(c_0_894,axiom,
! [X21,X4] : c_in(c_Pair(X21,X21,X4,X4),c_Relation_OId(X4),tc_prod(X4,X4)),
c_0_284 ).
fof(c_0_895,axiom,
! [X8,X4] : c_in(c_Pair(X8,X8,X4,X4),c_Relation_OId(X4),tc_prod(X4,X4)),
c_0_285 ).
fof(c_0_896,plain,
! [X8,X2,X3,X4] :
( hBOOL(hAPP(X3,X8))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_286]) ).
fof(c_0_897,plain,
! [X8,X2,X3,X4] :
( hBOOL(hAPP(X2,X8))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_287]) ).
fof(c_0_898,plain,
! [X5,X21,X10,X4] :
( hBOOL(hAPP(X10,X21))
| ~ hBOOL(hAPP(X10,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X10,X5,X4)))
| ~ c_in(X21,c_Wellfounded_Oacc(X5,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_288]) ).
fof(c_0_899,plain,
! [X5,X21,X10,X4] :
( hBOOL(hAPP(X10,X21))
| ~ hBOOL(hAPP(X10,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X10,X5,X4)))
| ~ c_in(X21,c_Wellfounded_Oacc(X5,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_289]) ).
fof(c_0_900,axiom,
! [X7,X8,X4] : c_Set_Oinsert(X7,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) = c_Set_Oinsert(X8,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4),
c_0_290 ).
fof(c_0_901,plain,
! [X5,X29,X6,X4] :
( c_Relation_Osym(c_Relation_Oinv__image(X5,X29,X4,X6),X6)
| ~ c_Relation_Osym(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_291]) ).
fof(c_0_902,plain,
! [X5,X29,X6,X4] :
( c_Wellfounded_Owf(c_Relation_Oinv__image(X5,X29,X4,X6),X6)
| ~ c_Wellfounded_Owf(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_292]) ).
fof(c_0_903,axiom,
! [X21,X2,X3,X4] : c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X21,X3,X4),c_Set_Oinsert(X21,X2,X4),tc_fun(X4,tc_bool)) = c_Set_Oinsert(X21,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),X4),
c_0_293 ).
fof(c_0_904,plain,
! [X15,X5,X6,X4] :
( c_lessequals(c_Relation_ODomain(X5,X4,X6),c_Relation_ODomain(X15,X4,X6),tc_fun(X4,tc_bool))
| ~ c_lessequals(X5,X15,tc_fun(tc_prod(X4,X6),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_294]) ).
fof(c_0_905,plain,
! [X15,X5,X34,X4] :
( c_in(X34,c_Transitive__Closure_Otrancl(X15,X4),tc_prod(X4,X4))
| ~ c_lessequals(X5,X15,tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_in(X34,c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_295]) ).
fof(c_0_906,plain,
! [X21,X2,X3,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(X3,c_Set_Oinsert(X21,X2,X4),tc_fun(X4,tc_bool)) = c_Set_Oinsert(X21,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),X4)
| ~ c_in(X21,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_296]) ).
fof(c_0_907,plain,
! [X21,X1,X2,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X21,X2,X4),X1,tc_fun(X4,tc_bool)) = c_Set_Oinsert(X21,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X4,tc_bool)),X4)
| ~ c_in(X21,X1,X4) ),
inference(fof_simplification,[status(thm)],[c_0_297]) ).
fof(c_0_908,plain,
! [X13,X12,X4] :
( c_Transitive__Closure_Ortrancl(X13,X4) = c_Transitive__Closure_Ortrancl(X12,X4)
| ~ c_lessequals(X13,c_Transitive__Closure_Ortrancl(X12,X4),tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_lessequals(X12,X13,tc_fun(tc_prod(X4,X4),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_298]) ).
fof(c_0_909,plain,
! [X1,X2,X3,X4] :
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_299]) ).
fof(c_0_910,plain,
! [X1,X2,X3,X4] :
( c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,X2,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_300]) ).
fof(c_0_911,plain,
! [X1,X2,X3,X4] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X1,tc_fun(X4,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X4,tc_bool))
| ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_301]) ).
fof(c_0_912,plain,
! [X1,X2,X3,X4] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X1,tc_fun(X4,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X4,tc_bool))
| ~ c_lessequals(X3,X1,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_302]) ).
fof(c_0_913,axiom,
! [X1,X2,X3,X4] : 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)),
c_0_303 ).
fof(c_0_914,axiom,
! [X1,X2,X3,X4] : 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)),
c_0_304 ).
fof(c_0_915,axiom,
! [X1,X2,X3,X4] : 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)),
c_0_305 ).
fof(c_0_916,axiom,
! [X1,X2,X3,X4] : 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)),
c_0_306 ).
fof(c_0_917,plain,
! [X5,X4] :
( c_Relation_Oantisym(X5,X4)
| ~ c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X5,c_Relation_OId(X4),tc_fun(tc_prod(X4,X4),tc_bool)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_307]) ).
fof(c_0_918,plain,
! [X1,X2,X3,X4] :
( c_lessequals(X2,X1,tc_fun(X4,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X1,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_308]) ).
fof(c_0_919,plain,
! [X1,X2,X3,X4] :
( c_lessequals(X3,X1,tc_fun(X4,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X1,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_309]) ).
fof(c_0_920,plain,
! [X1,X2,X3,X4] :
( c_lessequals(X1,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_310]) ).
fof(c_0_921,plain,
! [X1,X2,X3,X4] :
( c_lessequals(X1,X2,tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_311]) ).
fof(c_0_922,plain,
! [X34,X4] :
( X34 = c_Pair(c_ATP__Linkup_Osko__Relation__XIdE__1__1(X34,X4),c_ATP__Linkup_Osko__Relation__XIdE__1__1(X34,X4),X4,X4)
| ~ c_in(X34,c_Relation_OId(X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_312]) ).
fof(c_0_923,plain,
! [X5,X21,X10,X4] :
( hBOOL(hAPP(X10,X21))
| ~ hBOOL(hAPP(X10,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X10,X5,X4)))
| ~ c_Wellfounded_Owf(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_313]) ).
fof(c_0_924,plain,
! [X24,X5,X10,X4] :
( hBOOL(hAPP(X10,X24))
| ~ hBOOL(hAPP(X10,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X10,X5,X4)))
| ~ c_Wellfounded_Owf(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_314]) ).
fof(c_0_925,plain,
! [X5,X21,X10,X4] :
( hBOOL(hAPP(X10,X21))
| ~ hBOOL(hAPP(X10,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X10,X5,X4)))
| ~ c_Wellfounded_Owf(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_315]) ).
fof(c_0_926,plain,
! [X11,X12,X10,X4] :
( hBOOL(hAPP(X10,X11))
| ~ hBOOL(hAPP(X10,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X10,X12,X4)))
| ~ c_Wellfounded_Owf(X12,X4) ),
inference(fof_simplification,[status(thm)],[c_0_316]) ).
fof(c_0_927,plain,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Odistrib__lattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X8,c_Lattices_Olower__semilattice__class_Oinf(X19,X18,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4),c_Lattices_Oupper__semilattice__class_Osup(X8,X18,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_317]) ).
fof(c_0_928,plain,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Odistrib__lattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X19,X18,X4),X8,X4) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X19,X8,X4),c_Lattices_Oupper__semilattice__class_Osup(X18,X8,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_318]) ).
fof(c_0_929,plain,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Odistrib__lattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X8,c_Lattices_Oupper__semilattice__class_Osup(X19,X18,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4),c_Lattices_Olower__semilattice__class_Oinf(X8,X18,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_319]) ).
fof(c_0_930,plain,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Odistrib__lattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X19,X18,X4),X8,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X19,X8,X4),c_Lattices_Olower__semilattice__class_Oinf(X18,X8,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_320]) ).
fof(c_0_931,plain,
! [X30,X2,X3,X4] :
( c_in(X30,X2,X4)
| c_in(X30,X3,X4)
| ~ c_in(X30,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_321]) ).
fof(c_0_932,plain,
! [X8,X2,X3,X4] :
( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),X8))
| ~ hBOOL(hAPP(X2,X8))
| ~ hBOOL(hAPP(X3,X8)) ),
inference(fof_simplification,[status(thm)],[c_0_322]) ).
fof(c_0_933,axiom,
! [X5,X4] : c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X5,hAPP(c_Relation_Oconverse(X4,X4),X5),tc_fun(tc_prod(X4,X4),tc_bool)),X4),
c_0_323 ).
fof(c_0_934,axiom,
! [X5,X4] : c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X5,hAPP(c_Relation_Oconverse(X4,X4),X5),tc_fun(tc_prod(X4,X4),tc_bool)),X4),
c_0_324 ).
fof(c_0_935,plain,
! [X15,X5,X4] :
( c_lessequals(c_Transitive__Closure_Ortrancl(X5,X4),c_Transitive__Closure_Ortrancl(X15,X4),tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_lessequals(X5,c_Transitive__Closure_Ortrancl(X15,X4),tc_fun(tc_prod(X4,X4),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_325]) ).
fof(c_0_936,plain,
! [X8,X2,X3,X4] :
( c_lessequals(X3,X2,tc_fun(X4,tc_bool))
| ~ c_lessequals(X3,c_Set_Oinsert(X8,X2,X4),tc_fun(X4,tc_bool))
| c_in(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_326]) ).
fof(c_0_937,plain,
! [X8,X2,X3,X4] :
( c_lessequals(X3,X2,tc_fun(X4,tc_bool))
| c_in(X8,X3,X4)
| ~ c_lessequals(X3,c_Set_Oinsert(X8,X2,X4),tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_327]) ).
fof(c_0_938,plain,
! [X20,X21,X4] :
( X20 = X21
| ~ c_in(X20,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_328]) ).
fof(c_0_939,plain,
! [X19,X8,X3,X4] :
( hBOOL(hAPP(X3,X8))
| X19 = X8
| ~ hBOOL(hAPP(c_Set_Oinsert(X19,X3,X4),X8)) ),
inference(fof_simplification,[status(thm)],[c_0_329]) ).
fof(c_0_940,plain,
! [X21,X33,X1,X4] :
( c_lessequals(c_Set_Oinsert(X21,X1,X4),c_Set_Oinsert(X21,X33,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X1,X33,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_330]) ).
fof(c_0_941,axiom,
! [X15,X5,X4] : c_Relation_OField(c_Lattices_Oupper__semilattice__class_Osup(X5,X15,tc_fun(tc_prod(X4,X4),tc_bool)),X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OField(X5,X4),c_Relation_OField(X15,X4),tc_fun(X4,tc_bool)),
c_0_331 ).
fof(c_0_942,plain,
! [X8,X2,X3,X4] :
( c_lessequals(c_Set_Oinsert(X8,X3,X4),X2,tc_fun(X4,tc_bool))
| ~ c_lessequals(X3,X2,tc_fun(X4,tc_bool))
| ~ c_in(X8,X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_332]) ).
fof(c_0_943,axiom,
! [X21,X2,X3,X4] : c_Lattices_Oupper__semilattice__class_Osup(X3,c_Set_Oinsert(X21,X2,X4),tc_fun(X4,tc_bool)) = c_Set_Oinsert(X21,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X4),
c_0_333 ).
fof(c_0_944,axiom,
! [X21,X1,X2,X4] : c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X21,X2,X4),X1,tc_fun(X4,tc_bool)) = c_Set_Oinsert(X21,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X4,tc_bool)),X4),
c_0_334 ).
fof(c_0_945,plain,
! [X15,X5,X4] :
( c_lessequals(c_Transitive__Closure_Ortrancl(X5,X4),c_Transitive__Closure_Ortrancl(X15,X4),tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_lessequals(X5,X15,tc_fun(tc_prod(X4,X4),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_335]) ).
fof(c_0_946,plain,
! [X8,X2,X3,X4] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X8))
| ~ hBOOL(hAPP(X3,X8)) ),
inference(fof_simplification,[status(thm)],[c_0_336]) ).
fof(c_0_947,plain,
! [X8,X2,X3,X4] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X8))
| ~ hBOOL(hAPP(X2,X8)) ),
inference(fof_simplification,[status(thm)],[c_0_337]) ).
fof(c_0_948,plain,
! [X30,X2,X3,X4] :
( c_in(X30,X3,X4)
| ~ c_in(X30,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_338]) ).
fof(c_0_949,plain,
! [X30,X2,X3,X4] :
( c_in(X30,X2,X4)
| ~ c_in(X30,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_339]) ).
fof(c_0_950,plain,
! [X30,X2,X3,X4] :
( c_in(X30,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),X4)
| ~ c_in(X30,X2,X4)
| ~ c_in(X30,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_340]) ).
fof(c_0_951,plain,
! [X30,X2,X3,X4] :
( c_in(X30,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),X4)
| ~ c_in(X30,X2,X4)
| ~ c_in(X30,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_341]) ).
fof(c_0_952,axiom,
! [X2,X6,X4] : c_Product__Type_OSigma(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X2,X4,X6) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X6),tc_bool)),
c_0_342 ).
fof(c_0_953,plain,
! [X8,X12,X4] :
( ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X12,X8,X4),c_Wellfounded_Oacc(X12,X4),X4)
| c_in(X8,c_Wellfounded_Oacc(X12,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_343]) ).
fof(c_0_954,plain,
! [X8,X5,X4] :
( c_in(X8,c_Wellfounded_Oacc(X5,X4),X4)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X5,X8,X4),c_Wellfounded_Oacc(X5,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_344]) ).
fof(c_0_955,plain,
! [X8,X2,X3,X4] :
( c_lessequals(X3,X2,tc_fun(X4,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X8,X3,X4),X2,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_345]) ).
fof(c_0_956,plain,
! [X8,X37,X36] :
( hAPP(X36,X8) = hAPP(X8,X37)
| ~ c_in(X8,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_Odictator(X36,X37) ),
inference(fof_simplification,[status(thm)],[c_0_346]) ).
fof(c_0_957,plain,
! [X8,X2,X3,X4] :
( c_lessequals(X3,c_Set_Oinsert(X8,X2,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X3,X2,tc_fun(X4,tc_bool))
| c_in(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_347]) ).
fof(c_0_958,plain,
! [X8,X2,X3,X4] :
( c_lessequals(X3,c_Set_Oinsert(X8,X2,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X3,X2,tc_fun(X4,tc_bool))
| c_in(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_348]) ).
fof(c_0_959,axiom,
! [X2,X3,X4] : c_Relation_OImage(c_Relation_OId__on(X3,X4),X2,X4,X4) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),
c_0_349 ).
fof(c_0_960,plain,
! [X5,X21,X10,X4] :
( hBOOL(hAPP(X10,X21))
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X10,X5,X4),c_Wellfounded_Oacc(X5,X4),X4)
| ~ c_in(X21,c_Wellfounded_Oacc(X5,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_350]) ).
fof(c_0_961,plain,
! [X5,X21,X10,X4] :
( hBOOL(hAPP(X10,X21))
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X10,X5,X4),c_Wellfounded_Oacc(X5,X4),X4)
| ~ c_in(X21,c_Wellfounded_Oacc(X5,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_351]) ).
fof(c_0_962,plain,
! [X15,X5,X6,X4] :
( c_Relation_Osingle__valued(X5,X4,X6)
| ~ c_Relation_Osingle__valued(X15,X4,X6)
| ~ c_lessequals(X5,X15,tc_fun(tc_prod(X4,X6),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_352]) ).
fof(c_0_963,plain,
! [X8,X2,X3,X4] :
( c_in(X8,X2,X4)
| ~ c_lessequals(c_Set_Oinsert(X8,X3,X4),X2,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_353]) ).
fof(c_0_964,axiom,
! [X21,X3,X4] : c_Set_Oinsert(X21,X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X3,tc_fun(X4,tc_bool)),
c_0_354 ).
fof(c_0_965,plain,
! [X8,X20,X21,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(X8,c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X4),X4)
| ~ c_lessequals(X8,X20,X4)
| ~ c_lessequals(X8,X21,X4) ),
inference(fof_simplification,[status(thm)],[c_0_355]) ).
fof(c_0_966,plain,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(X8,c_Lattices_Olower__semilattice__class_Oinf(X19,X18,X4),X4)
| ~ c_lessequals(X8,X18,X4)
| ~ c_lessequals(X8,X19,X4) ),
inference(fof_simplification,[status(thm)],[c_0_356]) ).
fof(c_0_967,plain,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(X8,c_Lattices_Olower__semilattice__class_Oinf(X19,X18,X4),X4)
| ~ c_lessequals(X8,X18,X4)
| ~ c_lessequals(X8,X19,X4) ),
inference(fof_simplification,[status(thm)],[c_0_357]) ).
fof(c_0_968,plain,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4),X18,X4)
| ~ c_lessequals(X19,X18,X4)
| ~ c_lessequals(X8,X18,X4) ),
inference(fof_simplification,[status(thm)],[c_0_358]) ).
fof(c_0_969,plain,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X19,X18,X4),X8,X4)
| ~ c_lessequals(X18,X8,X4)
| ~ c_lessequals(X19,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_359]) ).
fof(c_0_970,plain,
! [X8,X20,X21,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X4),X8,X4)
| ~ c_lessequals(X20,X8,X4)
| ~ c_lessequals(X21,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_360]) ).
fof(c_0_971,plain,
! [X8,X2,X3,X4] :
( ~ c_in(X8,X2,X4)
| ~ c_in(X8,X3,X4)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_361]) ).
fof(c_0_972,axiom,
! [X20,X21,X4] :
( c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4) != c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4)
| X21 = X20 ),
c_0_362 ).
fof(c_0_973,plain,
! [X15,X5,X4] :
( c_lessequals(c_Relation_OField(X5,X4),c_Relation_OField(X15,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X5,X15,tc_fun(tc_prod(X4,X4),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_363]) ).
fof(c_0_974,plain,
! [X26,X27,X4] :
( c_lessequals(c_Wellfounded_Oacc(X26,X4),c_Wellfounded_Oacc(X27,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X27,X26,tc_fun(tc_prod(X4,X4),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_364]) ).
fof(c_0_975,plain,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4),X18,X4) = c_Lattices_Oupper__semilattice__class_Osup(X8,c_Lattices_Oupper__semilattice__class_Osup(X19,X18,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_365]) ).
fof(c_0_976,plain,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X8,c_Lattices_Oupper__semilattice__class_Osup(X19,X18,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X19,c_Lattices_Oupper__semilattice__class_Osup(X8,X18,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_366]) ).
fof(c_0_977,plain,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X8,c_Lattices_Oupper__semilattice__class_Osup(X19,X18,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X19,c_Lattices_Oupper__semilattice__class_Osup(X8,X18,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_367]) ).
fof(c_0_978,plain,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4),X18,X4) = c_Lattices_Oupper__semilattice__class_Osup(X8,c_Lattices_Oupper__semilattice__class_Osup(X19,X18,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_368]) ).
fof(c_0_979,plain,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4),X18,X4) = c_Lattices_Olower__semilattice__class_Oinf(X8,c_Lattices_Olower__semilattice__class_Oinf(X19,X18,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_369]) ).
fof(c_0_980,plain,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X8,c_Lattices_Olower__semilattice__class_Oinf(X19,X18,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X19,c_Lattices_Olower__semilattice__class_Oinf(X8,X18,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_370]) ).
fof(c_0_981,plain,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X8,c_Lattices_Olower__semilattice__class_Oinf(X19,X18,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X19,c_Lattices_Olower__semilattice__class_Oinf(X8,X18,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_371]) ).
fof(c_0_982,plain,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4),X18,X4) = c_Lattices_Olower__semilattice__class_Oinf(X8,c_Lattices_Olower__semilattice__class_Oinf(X19,X18,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_372]) ).
fof(c_0_983,plain,
! [X30,X3,X4] :
( c_in(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X3,X30,X4),X3,X4)
| ~ c_in(X30,c_Relation_OId__on(X3,X4),tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_373]) ).
fof(c_0_984,axiom,
! [X12,X6,X4] : c_Relation_OImage(X12,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X6,X4) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
c_0_374 ).
fof(c_0_985,axiom,
! [X19,X8,X3,X4] : c_Set_Oinsert(X8,c_Set_Oinsert(X19,X3,X4),X4) = c_Set_Oinsert(X19,c_Set_Oinsert(X8,X3,X4),X4),
c_0_375 ).
fof(c_0_986,plain,
! [X1,X2,X3,X4] :
( c_lessequals(X3,X1,tc_fun(X4,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X4,tc_bool))
| ~ c_lessequals(X3,X2,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_376]) ).
fof(c_0_987,axiom,
! [X21,X1,X2,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X21,X2,X4),X1,tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X4,tc_bool))
| c_in(X21,X1,X4) ),
c_0_377 ).
fof(c_0_988,axiom,
! [X21,X2,X3,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(X3,c_Set_Oinsert(X21,X2,X4),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool))
| c_in(X21,X3,X4) ),
c_0_378 ).
fof(c_0_989,plain,
! [X15,X5,X4] :
( c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X5,X15,tc_fun(tc_prod(X4,X4),tc_bool)),X4)
| ~ c_Relation_Osym(X15,X4)
| ~ c_Relation_Osym(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_379]) ).
fof(c_0_990,plain,
! [X15,X5,X4] :
( c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X5,X15,tc_fun(tc_prod(X4,X4),tc_bool)),X4)
| ~ c_Relation_Osym(X15,X4)
| ~ c_Relation_Osym(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_380]) ).
fof(c_0_991,plain,
! [X8,X20,X21,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_lessequals(X21,X8,X4)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_381]) ).
fof(c_0_992,plain,
! [X8,X20,X21,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_lessequals(X20,X8,X4)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_382]) ).
fof(c_0_993,plain,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_lessequals(X8,X18,X4)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4),X18,X4) ),
inference(fof_simplification,[status(thm)],[c_0_383]) ).
fof(c_0_994,plain,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_lessequals(X19,X18,X4)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4),X18,X4) ),
inference(fof_simplification,[status(thm)],[c_0_384]) ).
fof(c_0_995,plain,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(X8,X18,X4)
| ~ c_lessequals(X8,c_Lattices_Olower__semilattice__class_Oinf(X19,X18,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_385]) ).
fof(c_0_996,plain,
! [X18,X19,X8,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(X8,X19,X4)
| ~ c_lessequals(X8,c_Lattices_Olower__semilattice__class_Oinf(X19,X18,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_386]) ).
fof(c_0_997,plain,
! [X8,X20,X21,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(X8,X20,X4)
| ~ c_lessequals(X8,c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_387]) ).
fof(c_0_998,plain,
! [X8,X20,X21,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(X8,X21,X4)
| ~ c_lessequals(X8,c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_388]) ).
fof(c_0_999,plain,
! [X20,X21,X3,X4] :
( c_in(X21,X3,X4)
| X21 = X20
| ~ c_in(X21,c_Set_Oinsert(X20,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_389]) ).
fof(c_0_1000,axiom,
! [X2,X3,X4] : c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),
c_0_390 ).
fof(c_0_1001,axiom,
! [X2,X3,X4] : c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),
c_0_391 ).
fof(c_0_1002,plain,
! [X20,X2,X3,X4] :
( c_lessequals(X3,c_Set_Oinsert(X20,X2,X4),tc_fun(X4,tc_bool))
| ~ c_lessequals(X3,X2,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_392]) ).
fof(c_0_1003,plain,
! [X5,X4] :
( c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X5,c_Relation_OId(X4),tc_fun(tc_prod(X4,X4),tc_bool)),X4)
| ~ c_Relation_Oantisym(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_393]) ).
fof(c_0_1004,axiom,
! [X5,X4] : c_Relation_OField(X5,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X5,X4,X4),c_Relation_ORange(X5,X4,X4),tc_fun(X4,tc_bool)),
c_0_394 ).
fof(c_0_1005,axiom,
! [X5,X4] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X5,c_Relation_OId(X4),tc_fun(tc_prod(X4,X4),tc_bool)),X4) = c_Transitive__Closure_Ortrancl(X5,X4),
c_0_395 ).
fof(c_0_1006,axiom,
! [X12,X4] : c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X12,c_Relation_OId(X4),tc_fun(tc_prod(X4,X4),tc_bool)),X4) = c_Transitive__Closure_Ortrancl(X12,X4),
c_0_396 ).
fof(c_0_1007,plain,
! [X30,X2,X3,X4] :
( c_in(X30,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X4)
| ~ c_in(X30,X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_397]) ).
fof(c_0_1008,plain,
! [X30,X2,X3,X4] :
( c_in(X30,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),X4)
| ~ c_in(X30,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_398]) ).
fof(c_0_1009,plain,
! [X16,X5,X4] :
( c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X16,X5,tc_fun(tc_prod(X4,X4),tc_bool)),X4)
| ~ c_Wellfounded_Owf(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_399]) ).
fof(c_0_1010,plain,
! [X16,X5,X4] :
( c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X5,X16,tc_fun(tc_prod(X4,X4),tc_bool)),X4)
| ~ c_Wellfounded_Owf(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_400]) ).
fof(c_0_1011,plain,
! [X19,X8,X3,X4] :
( hBOOL(hAPP(c_Set_Oinsert(X19,X3,X4),X8))
| ~ hBOOL(hAPP(X3,X8)) ),
inference(fof_simplification,[status(thm)],[c_0_401]) ).
fof(c_0_1012,plain,
! [X5,X4] :
( c_Wellfounded_Owf(hAPP(c_Relation_Oconverse(X4,X4),c_Transitive__Closure_Otrancl(X5,X4)),X4)
| ~ c_Wellfounded_Owf(hAPP(c_Relation_Oconverse(X4,X4),X5),X4) ),
inference(fof_simplification,[status(thm)],[c_0_402]) ).
fof(c_0_1013,axiom,
! [X2,X4] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool)),X2,tc_fun(tc_prod(X4,X4),tc_bool)),
c_0_403 ).
fof(c_0_1014,axiom,
! [X8,X2,X3,X4] :
( c_Set_Oinsert(X8,X3,X4) != c_Set_Oinsert(X8,X2,X4)
| c_in(X8,X2,X4)
| c_in(X8,X3,X4)
| X3 = X2 ),
c_0_404 ).
fof(c_0_1015,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)),
c_0_405 ).
fof(c_0_1016,plain,
! [X8,X5,X10] :
( hBOOL(hAPP(X10,X8))
| ~ hBOOL(hAPP(X10,v_sko__Wellfounded__Xacc__Xinducts__1(X10,X5)))
| ~ c_in(X8,c_Wellfounded_Oacc(X5,t_a),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_406]) ).
fof(c_0_1017,plain,
! [X8,X5,X10] :
( hBOOL(hAPP(X10,X8))
| ~ hBOOL(hAPP(X10,v_sko__Wellfounded__Xacc__Xinduct__1(X10,X5)))
| ~ c_in(X8,c_Wellfounded_Oacc(X5,t_a),t_a) ),
inference(fof_simplification,[status(thm)],[c_0_407]) ).
fof(c_0_1018,plain,
! [X7,X5,X9,X4] :
( c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X9,X5,X4),X9,X4)
| ~ c_in(X7,X9,X4)
| ~ c_Wellfounded_Owf(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_408]) ).
fof(c_0_1019,plain,
! [X8,X12,X9,X4] :
( c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X9,X12,X4),X9,X4)
| ~ c_in(X8,X9,X4)
| ~ c_Wellfounded_Owf(X12,X4) ),
inference(fof_simplification,[status(thm)],[c_0_409]) ).
fof(c_0_1020,axiom,
! [X8,X4] : c_in(X8,c_Set_Oinsert(X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4),
c_0_410 ).
fof(c_0_1021,plain,
! [X5,X3,X4] :
( c_Relation_Ototal__on(X3,X5,X4)
| ~ c_Relation_Ototal__on(X3,hAPP(c_Relation_Oconverse(X4,X4),X5),X4) ),
inference(fof_simplification,[status(thm)],[c_0_411]) ).
fof(c_0_1022,plain,
! [X5,X3,X4] :
( c_Relation_Orefl__on(X3,X5,X4)
| ~ c_Relation_Orefl__on(X3,hAPP(c_Relation_Oconverse(X4,X4),X5),X4) ),
inference(fof_simplification,[status(thm)],[c_0_412]) ).
fof(c_0_1023,plain,
! [X8,X2,X3,X4] :
( c_in(X8,X2,X4)
| ~ c_in(X8,X3,X4)
| ~ c_lessequals(X3,X2,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_413]) ).
fof(c_0_1024,plain,
! [X30,X2,X3,X4] :
( c_in(X30,X2,X4)
| ~ c_in(X30,X3,X4)
| ~ c_lessequals(X3,X2,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_414]) ).
fof(c_0_1025,plain,
! [X8,X2,X3,X4] :
( c_in(X8,X2,X4)
| ~ c_lessequals(X3,X2,tc_fun(X4,tc_bool))
| ~ c_in(X8,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_415]) ).
fof(c_0_1026,plain,
! [X31,X2,X3,X4] :
( c_in(X31,X2,X4)
| ~ c_in(X31,X3,X4)
| ~ c_lessequals(X3,X2,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_416]) ).
fof(c_0_1027,axiom,
! [X4] : c_Relation_Orefl__on(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool)),X4),
c_0_417 ).
fof(c_0_1028,plain,
! [X8,X20,X21,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_lessequals(X8,c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X4),X4)
| ~ c_lessequals(X8,X21,X4) ),
inference(fof_simplification,[status(thm)],[c_0_418]) ).
fof(c_0_1029,plain,
! [X8,X20,X21,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_lessequals(X8,c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X4),X4)
| ~ c_lessequals(X8,X20,X4) ),
inference(fof_simplification,[status(thm)],[c_0_419]) ).
fof(c_0_1030,plain,
! [X8,X20,X21,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X4),X8,X4)
| ~ c_lessequals(X20,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_420]) ).
fof(c_0_1031,plain,
! [X8,X20,X21,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X4),X8,X4)
| ~ c_lessequals(X21,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_421]) ).
fof(c_0_1032,axiom,
! [X3,X4] : c_Relation_OImage(c_Relation_OId(X4),X3,X4,X4) = X3,
c_0_422 ).
fof(c_0_1033,axiom,
! [X4] : c_Transitive__Closure_Otrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool)),X4) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool)),
c_0_423 ).
fof(c_0_1034,plain,
! [X20,X21,X2,X4] :
( c_in(X21,c_Set_Oinsert(X20,X2,X4),X4)
| ~ c_in(X21,X2,X4) ),
inference(fof_simplification,[status(thm)],[c_0_424]) ).
fof(c_0_1035,plain,
! [X20,X21,X3,X4] :
( c_in(X21,c_Set_Oinsert(X20,X3,X4),X4)
| ~ c_in(X21,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_425]) ).
fof(c_0_1036,plain,
! [X2,X3,X4] :
( X3 = X2
| ~ c_lessequals(X2,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X3,X2,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_426]) ).
fof(c_0_1037,plain,
! [X2,X3,X4] :
( X3 = X2
| ~ c_lessequals(X2,X3,tc_fun(X4,tc_bool))
| ~ c_lessequals(X3,X2,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_427]) ).
fof(c_0_1038,axiom,
! [X8,X3,X4] : hBOOL(hAPP(c_Set_Oinsert(X8,X3,X4),X8)),
c_0_428 ).
fof(c_0_1039,axiom,
! [X37,X36] :
( c_Arrow__Order__Mirabelle_Odictator(X36,X37)
| c_in(v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(X36,X37),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
c_0_429 ).
fof(c_0_1040,plain,
! [X15,X5,X4] :
( c_Wellfounded_Oacyclic(X5,X4)
| ~ c_lessequals(X5,X15,tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_Wellfounded_Oacyclic(X15,X4) ),
inference(fof_simplification,[status(thm)],[c_0_430]) ).
fof(c_0_1041,plain,
! [X15,X5,X4] :
( c_Relation_Oantisym(X5,X4)
| ~ c_Relation_Oantisym(X15,X4)
| ~ c_lessequals(X5,X15,tc_fun(tc_prod(X4,X4),tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_431]) ).
fof(c_0_1042,plain,
! [X5,X34,X4] :
( c_Wellfounded_Owf(X34,X4)
| ~ c_lessequals(X34,X5,tc_fun(tc_prod(X4,X4),tc_bool))
| ~ c_Wellfounded_Owf(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_432]) ).
fof(c_0_1043,plain,
! [X8,X28,X29,X6,X4] :
( ~ class_HOL_Oord(X6)
| c_lessequals(hAPP(X29,X8),hAPP(X28,X8),X6)
| ~ c_lessequals(X29,X28,tc_fun(X4,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_433]) ).
fof(c_0_1044,axiom,
! [X6,X4] : c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X6,X4),tc_bool)),X6,X4) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
c_0_434 ).
fof(c_0_1045,axiom,
! [X6,X4] : c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X6),tc_bool)),X4,X6) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
c_0_435 ).
fof(c_0_1046,plain,
! [X18,X19,X8,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_lessequals(X8,X18,X4)
| ~ c_lessequals(X19,X18,X4)
| ~ c_lessequals(X8,X19,X4) ),
inference(fof_simplification,[status(thm)],[c_0_436]) ).
fof(c_0_1047,plain,
! [X18,X19,X8,X4] :
( ~ class_Orderings_Oorder(X4)
| c_lessequals(X18,X8,X4)
| ~ c_lessequals(X18,X19,X4)
| ~ c_lessequals(X19,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_437]) ).
fof(c_0_1048,plain,
! [X5,X34,X4] :
( c_in(X34,c_Transitive__Closure_Otrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(X34,X5,tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_438]) ).
fof(c_0_1049,plain,
! [X5,X34,X4] :
( c_in(X34,c_Transitive__Closure_Ortrancl(X5,X4),tc_prod(X4,X4))
| ~ c_in(X34,X5,tc_prod(X4,X4)) ),
inference(fof_simplification,[status(thm)],[c_0_439]) ).
fof(c_0_1050,plain,
! [X3,X4] :
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ c_lessequals(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_440]) ).
fof(c_0_1051,axiom,
! [X2,X3,X4] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),X2,tc_fun(X4,tc_bool)),
c_0_441 ).
fof(c_0_1052,axiom,
! [X2,X3,X4] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)),
c_0_442 ).
fof(c_0_1053,axiom,
! [X2,X3,X4] : c_lessequals(X3,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
c_0_443 ).
fof(c_0_1054,axiom,
! [X2,X3,X4] : c_lessequals(X2,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
c_0_444 ).
fof(c_0_1055,plain,
! [X19,X8,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X8,c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4) ),
inference(fof_simplification,[status(thm)],[c_0_445]) ).
fof(c_0_1056,plain,
! [X19,X8,X4] :
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X8,c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4),X4) = c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4) ),
inference(fof_simplification,[status(thm)],[c_0_446]) ).
fof(c_0_1057,plain,
! [X19,X8,X4] :
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X8,c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4) ),
inference(fof_simplification,[status(thm)],[c_0_447]) ).
fof(c_0_1058,plain,
! [X19,X8,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X8,c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4),X4) = c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4) ),
inference(fof_simplification,[status(thm)],[c_0_448]) ).
fof(c_0_1059,plain,
! [X5,X3,X4] :
( c_Relation_Ototal__on(X3,hAPP(c_Relation_Oconverse(X4,X4),X5),X4)
| ~ c_Relation_Ototal__on(X3,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_449]) ).
fof(c_0_1060,plain,
! [X5,X3,X4] :
( c_Relation_Orefl__on(X3,hAPP(c_Relation_Oconverse(X4,X4),X5),X4)
| ~ c_Relation_Orefl__on(X3,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_450]) ).
fof(c_0_1061,axiom,
! [X8,X3,X4] : c_Set_Oinsert(X8,c_Set_Oinsert(X8,X3,X4),X4) = c_Set_Oinsert(X8,X3,X4),
c_0_451 ).
fof(c_0_1062,plain,
! [X8,X10,X4] :
( ~ hBOOL(hAPP(X10,X8))
| ~ c_in(X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_452]) ).
fof(c_0_1063,axiom,
! [X36] :
( c_Arrow__Order__Mirabelle_Ounanimity(X36)
| c_in(v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2(X36),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
c_0_453 ).
fof(c_0_1064,axiom,
! [X36] :
( c_Arrow__Order__Mirabelle_OIIA(X36)
| c_in(v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X36),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
c_0_454 ).
fof(c_0_1065,axiom,
! [X36] :
( c_Arrow__Order__Mirabelle_OIIA(X36)
| c_in(v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X36),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
c_0_455 ).
fof(c_0_1066,plain,
! [X8,X4] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X8)),
inference(fof_simplification,[status(thm)],[c_0_456]) ).
fof(c_0_1067,axiom,
! [X5,X6,X4] :
( c_Relation_ORange(X5,X6,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| X5 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X6,X4),tc_bool)) ),
c_0_457 ).
fof(c_0_1068,axiom,
! [X5,X6,X4] :
( c_Relation_ODomain(X5,X4,X6) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| X5 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X6),tc_bool)) ),
c_0_458 ).
fof(c_0_1069,axiom,
! [X4] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
c_0_459 ).
fof(c_0_1070,axiom,
! [X2,X3,X4] :
( c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)) != X2
| c_lessequals(X3,X2,tc_fun(X4,tc_bool)) ),
c_0_460 ).
fof(c_0_1071,plain,
! [X2,X3,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)) = X2
| ~ c_lessequals(X2,X3,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_461]) ).
fof(c_0_1072,plain,
! [X2,X3,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)) = X3
| ~ c_lessequals(X3,X2,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_462]) ).
fof(c_0_1073,plain,
! [X2,X3,X4] :
( c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)) = X3
| ~ c_lessequals(X2,X3,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_463]) ).
fof(c_0_1074,plain,
! [X2,X3,X4] :
( c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)) = X2
| ~ c_lessequals(X3,X2,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_464]) ).
fof(c_0_1075,plain,
! [X8,X9,X10,X4] :
( hBOOL(hAPP(X9,X8))
| ~ c_lessequals(X10,X9,tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(X10,X8)) ),
inference(fof_simplification,[status(thm)],[c_0_465]) ).
fof(c_0_1076,plain,
! [X8,X9,X10,X4] :
( hBOOL(hAPP(X9,X8))
| ~ hBOOL(hAPP(X10,X8))
| ~ c_lessequals(X10,X9,tc_fun(X4,tc_bool)) ),
inference(fof_simplification,[status(thm)],[c_0_466]) ).
fof(c_0_1077,axiom,
c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
c_0_467 ).
fof(c_0_1078,axiom,
c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
c_0_468 ).
fof(c_0_1079,plain,
! [X8,X10,X4] :
( hBOOL(hAPP(X10,X8))
| ~ c_in(X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4) ),
inference(fof_simplification,[status(thm)],[c_0_469]) ).
fof(c_0_1080,axiom,
! [X4] : c_Relation_OField(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool)),X4) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
c_0_470 ).
fof(c_0_1081,axiom,
! [X2,X3,X4] :
( c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
c_0_471 ).
fof(c_0_1082,axiom,
! [X2,X3,X4] :
( c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
c_0_472 ).
fof(c_0_1083,axiom,
! [X5,X6,X4] : c_Relation_ORange(X5,X6,X4) = c_Relation_ODomain(hAPP(c_Relation_Oconverse(X6,X4),X5),X4,X6),
c_0_473 ).
fof(c_0_1084,axiom,
! [X5,X6,X4] : c_Relation_ODomain(hAPP(c_Relation_Oconverse(X6,X4),X5),X4,X6) = c_Relation_ORange(X5,X6,X4),
c_0_474 ).
fof(c_0_1085,axiom,
! [X5,X6,X4] : c_Relation_ORange(hAPP(c_Relation_Oconverse(X4,X6),X5),X6,X4) = c_Relation_ODomain(X5,X4,X6),
c_0_475 ).
fof(c_0_1086,axiom,
! [X21,X2,X4] : c_lessequals(X2,c_Set_Oinsert(X21,X2,X4),tc_fun(X4,tc_bool)),
c_0_476 ).
fof(c_0_1087,axiom,
! [X7,X8,X4] :
( c_Set_Oinsert(X8,X7,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| c_in(X8,X7,X4) ),
c_0_477 ).
fof(c_0_1088,plain,
! [X5,X4] :
( c_Wellfounded_Owf(X5,X4)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X5,X4),c_Wellfounded_Oacc(X5,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_478]) ).
fof(c_0_1089,plain,
! [X5,X4] :
( c_Wellfounded_Owf(X5,X4)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X5,X4),c_Wellfounded_Oacc(X5,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_479]) ).
fof(c_0_1090,plain,
! [X19,X8,X4] :
( ~ class_Orderings_Oorder(X4)
| X8 = X19
| ~ c_lessequals(X8,X19,X4)
| ~ c_lessequals(X19,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_480]) ).
fof(c_0_1091,plain,
! [X19,X8,X4] :
( ~ class_Orderings_Oorder(X4)
| X8 = X19
| ~ c_lessequals(X19,X8,X4)
| ~ c_lessequals(X8,X19,X4) ),
inference(fof_simplification,[status(thm)],[c_0_481]) ).
fof(c_0_1092,plain,
! [X19,X8,X4] :
( ~ class_Orderings_Oorder(X4)
| X8 = X19
| ~ c_lessequals(X19,X8,X4)
| ~ c_lessequals(X8,X19,X4) ),
inference(fof_simplification,[status(thm)],[c_0_482]) ).
fof(c_0_1093,axiom,
! [X4] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
c_0_483 ).
fof(c_0_1094,axiom,
! [X5,X4] : c_Transitive__Closure_Ortrancl(X5,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X5,X4),c_Relation_OId(X4),tc_fun(tc_prod(X4,X4),tc_bool)),
c_0_484 ).
fof(c_0_1095,axiom,
! [X5,X4] : c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X5,X4),c_Relation_OId(X4),tc_fun(tc_prod(X4,X4),tc_bool)) = c_Transitive__Closure_Ortrancl(X5,X4),
c_0_485 ).
fof(c_0_1096,axiom,
! [X12,X4] : c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X12,X4),c_Relation_OId(X4),tc_fun(tc_prod(X4,X4),tc_bool)) = c_Transitive__Closure_Ortrancl(X12,X4),
c_0_486 ).
fof(c_0_1097,axiom,
! [X4] : c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool)),X4) = c_Relation_OId(X4),
c_0_487 ).
fof(c_0_1098,axiom,
! [X4] : c_Relation_Oantisym(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool)),X4),
c_0_488 ).
fof(c_0_1099,axiom,
! [X4] : c_Wellfounded_Owf(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool)),X4),
c_0_489 ).
fof(c_0_1100,plain,
! [X19,X8,X4] :
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X8,c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4),X4) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_490]) ).
fof(c_0_1101,plain,
! [X19,X8,X4] :
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X8,c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4),X4) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_491]) ).
fof(c_0_1102,plain,
! [X19,X8,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_492]) ).
fof(c_0_1103,plain,
! [X19,X8,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4),X19,X4) ),
inference(fof_simplification,[status(thm)],[c_0_493]) ).
fof(c_0_1104,plain,
! [X19,X8,X4] :
( ~ class_Lattices_Olattice(X4)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4),X19,X4) ),
inference(fof_simplification,[status(thm)],[c_0_494]) ).
fof(c_0_1105,plain,
! [X19,X8,X4] :
( ~ class_Lattices_Olattice(X4)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_495]) ).
fof(c_0_1106,plain,
! [X19,X8,X4] :
( ~ class_Lattices_Olattice(X4)
| c_lessequals(X8,c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_496]) ).
fof(c_0_1107,plain,
! [X19,X8,X4] :
( ~ class_Lattices_Olattice(X4)
| c_lessequals(X19,c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_497]) ).
fof(c_0_1108,plain,
! [X19,X8,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_lessequals(X19,c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_498]) ).
fof(c_0_1109,plain,
! [X19,X8,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_lessequals(X8,c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_499]) ).
fof(c_0_1110,plain,
! [X21,X4] : ~ c_in(X21,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),
inference(fof_simplification,[status(thm)],[c_0_500]) ).
fof(c_0_1111,plain,
! [X30,X4] : ~ c_in(X30,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),
inference(fof_simplification,[status(thm)],[c_0_501]) ).
fof(c_0_1112,plain,
! [X8,X4] : ~ c_in(X8,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),
inference(fof_simplification,[status(thm)],[c_0_502]) ).
fof(c_0_1113,axiom,
c_Relation_ORange(v_r,t_a,t_b) = c_Relation_ODomain(hAPP(c_Relation_Oconverse(t_a,t_b),v_r),t_b,t_a),
c_0_503 ).
fof(c_0_1114,axiom,
! [X8,X2,X4] : c_in(X8,c_Set_Oinsert(X8,X2,X4),X4),
c_0_504 ).
fof(c_0_1115,axiom,
! [X21,X2,X4] : c_in(X21,c_Set_Oinsert(X21,X2,X4),X4),
c_0_505 ).
fof(c_0_1116,axiom,
! [X8,X3,X4] : c_in(X8,c_Set_Oinsert(X8,X3,X4),X4),
c_0_506 ).
fof(c_0_1117,plain,
! [X5,X4] :
( c_Relation_Oantisym(X5,X4)
| ~ c_Relation_Oantisym(hAPP(c_Relation_Oconverse(X4,X4),X5),X4) ),
inference(fof_simplification,[status(thm)],[c_0_507]) ).
fof(c_0_1118,plain,
! [X5,X4] :
( c_Relation_Osym(X5,X4)
| ~ c_Relation_Osym(hAPP(c_Relation_Oconverse(X4,X4),X5),X4) ),
inference(fof_simplification,[status(thm)],[c_0_508]) ).
fof(c_0_1119,plain,
! [X5,X4] :
( c_Wellfounded_Oacyclic(X5,X4)
| ~ c_Wellfounded_Oacyclic(hAPP(c_Relation_Oconverse(X4,X4),X5),X4) ),
inference(fof_simplification,[status(thm)],[c_0_509]) ).
fof(c_0_1120,axiom,
! [X5,X4] : c_Transitive__Closure_Ortrancl(hAPP(c_Relation_Oconverse(X4,X4),X5),X4) = hAPP(c_Relation_Oconverse(X4,X4),c_Transitive__Closure_Ortrancl(X5,X4)),
c_0_510 ).
fof(c_0_1121,axiom,
! [X5,X4] : c_Transitive__Closure_Otrancl(hAPP(c_Relation_Oconverse(X4,X4),X5),X4) = hAPP(c_Relation_Oconverse(X4,X4),c_Transitive__Closure_Otrancl(X5,X4)),
c_0_511 ).
fof(c_0_1122,axiom,
! [X3,X4] : c_Lattices_Olower__semilattice__class_Oinf(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
c_0_512 ).
fof(c_0_1123,axiom,
! [X2,X4] : c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X2,tc_fun(X4,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
c_0_513 ).
fof(c_0_1124,axiom,
! [X2,X3,X4] : c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),
c_0_514 ).
fof(c_0_1125,axiom,
! [X2,X3,X4] : c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),
c_0_515 ).
fof(c_0_1126,plain,
! [X19,X8,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4) != X8
| c_lessequals(X8,X19,X4) ),
inference(fof_simplification,[status(thm)],[c_0_516]) ).
fof(c_0_1127,plain,
! [X19,X8,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4) != X19
| c_lessequals(X8,X19,X4) ),
inference(fof_simplification,[status(thm)],[c_0_517]) ).
fof(c_0_1128,plain,
! [X19,X8,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4) = X19
| ~ c_lessequals(X19,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_518]) ).
fof(c_0_1129,plain,
! [X19,X8,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4) = X8
| ~ c_lessequals(X8,X19,X4) ),
inference(fof_simplification,[status(thm)],[c_0_519]) ).
fof(c_0_1130,plain,
! [X19,X8,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4) = X19
| ~ c_lessequals(X8,X19,X4) ),
inference(fof_simplification,[status(thm)],[c_0_520]) ).
fof(c_0_1131,plain,
! [X19,X8,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4) = X8
| ~ c_lessequals(X19,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_521]) ).
fof(c_0_1132,axiom,
! [X4] : c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool)),
c_0_522 ).
fof(c_0_1133,plain,
! [X21,X3,X4] :
( c_Set_Oinsert(X21,X3,X4) = X3
| ~ c_in(X21,X3,X4) ),
inference(fof_simplification,[status(thm)],[c_0_523]) ).
fof(c_0_1134,plain,
! [X5,X3,X4] :
( c_Relation_Orefl__on(X3,X5,X4)
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_524]) ).
fof(c_0_1135,axiom,
! [X37,X36] :
( hAPP(X36,v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(X36,X37)) != hAPP(v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(X36,X37),X37)
| c_Arrow__Order__Mirabelle_Odictator(X36,X37) ),
c_0_525 ).
fof(c_0_1136,axiom,
! [X5,X4] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X5,X4),X4,X4) = c_Relation_ORange(X5,X4,X4),
c_0_526 ).
fof(c_0_1137,axiom,
! [X5,X4] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X5,X4),X4,X4) = c_Relation_ODomain(X5,X4,X4),
c_0_527 ).
fof(c_0_1138,axiom,
! [X3,X4] : c_Lattices_Oupper__semilattice__class_Osup(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = X3,
c_0_528 ).
fof(c_0_1139,axiom,
! [X2,X4] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X2,tc_fun(X4,tc_bool)) = X2,
c_0_529 ).
fof(c_0_1140,axiom,
! [X3,X4] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X3,tc_fun(X4,tc_bool)),
c_0_530 ).
fof(c_0_1141,axiom,
! [X21,X3,X4] : c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) != c_Set_Oinsert(X21,X3,X4),
c_0_531 ).
fof(c_0_1142,axiom,
! [X21,X3,X4] : c_Set_Oinsert(X21,X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
c_0_532 ).
fof(c_0_1143,axiom,
! [X9,X10,X6,X4] : hAPP(c_COMBK(X10,X4,X6),X9) = X10,
c_0_533 ).
fof(c_0_1144,axiom,
! [X5,X6,X4] : hAPP(c_Relation_Oconverse(X6,X4),hAPP(c_Relation_Oconverse(X4,X6),X5)) = X5,
c_0_534 ).
fof(c_0_1145,plain,
! [X19,X8,X4] :
( ~ class_Orderings_Olinorder(X4)
| c_lessequals(X19,X8,X4)
| c_lessequals(X8,X19,X4) ),
inference(fof_simplification,[status(thm)],[c_0_535]) ).
fof(c_0_1146,plain,
! [X8,X13,X4] :
( hBOOL(hAPP(X13,X8))
| ~ c_in(X8,X13,X4) ),
inference(fof_simplification,[status(thm)],[c_0_536]) ).
fof(c_0_1147,plain,
! [X19,X8,X4] :
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4) = c_Lattices_Oupper__semilattice__class_Osup(X19,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_537]) ).
fof(c_0_1148,plain,
! [X19,X8,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X8,X19,X4) = c_Lattices_Oupper__semilattice__class_Osup(X19,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_538]) ).
fof(c_0_1149,plain,
! [X19,X8,X4] :
( ~ class_Lattices_Olattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4) = c_Lattices_Olower__semilattice__class_Oinf(X19,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_539]) ).
fof(c_0_1150,plain,
! [X19,X8,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X8,X19,X4) = c_Lattices_Olower__semilattice__class_Oinf(X19,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_540]) ).
fof(c_0_1151,plain,
! [X5,X4] :
( c_Relation_Oantisym(hAPP(c_Relation_Oconverse(X4,X4),X5),X4)
| ~ c_Relation_Oantisym(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_541]) ).
fof(c_0_1152,plain,
! [X5,X4] :
( c_Relation_Osym(hAPP(c_Relation_Oconverse(X4,X4),X5),X4)
| ~ c_Relation_Osym(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_542]) ).
fof(c_0_1153,plain,
! [X5,X4] :
( c_Wellfounded_Oacyclic(hAPP(c_Relation_Oconverse(X4,X4),X5),X4)
| ~ c_Wellfounded_Oacyclic(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_543]) ).
fof(c_0_1154,axiom,
! [X5,X4] : c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X5,X4),
c_0_544 ).
fof(c_0_1155,axiom,
! [X5,X4] : c_Relation_OField(hAPP(c_Relation_Oconverse(X4,X4),X5),X4) = c_Relation_OField(X5,X4),
c_0_545 ).
fof(c_0_1156,plain,
! [X2,X3,X4] :
( ~ class_Lattices_Obounded__lattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X4) != c_Orderings_Obot__class_Obot(X4)
| X2 = c_Orderings_Obot__class_Obot(X4) ),
inference(fof_simplification,[status(thm)],[c_0_546]) ).
fof(c_0_1157,plain,
! [X2,X3,X4] :
( ~ class_Lattices_Obounded__lattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X4) != c_Orderings_Obot__class_Obot(X4)
| X3 = c_Orderings_Obot__class_Obot(X4) ),
inference(fof_simplification,[status(thm)],[c_0_547]) ).
fof(c_0_1158,plain,
! [X8,X5,X4] :
( c_in(X8,c_Wellfounded_Oacc(X5,X4),X4)
| ~ c_Wellfounded_Owf(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_548]) ).
fof(c_0_1159,plain,
! [X8,X13,X4] :
( c_in(X8,X13,X4)
| ~ hBOOL(hAPP(X13,X8)) ),
inference(fof_simplification,[status(thm)],[c_0_549]) ).
fof(c_0_1160,plain,
! [X5,X3,X4] :
( c_Relation_Osym(X5,X4)
| ~ c_Equiv__Relations_Oequiv(X3,X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_550]) ).
fof(c_0_1161,plain,
! [X61,X62,X4] :
( X62 = X61
| ~ c_fequal(X62,X61,X4) ),
inference(fof_simplification,[status(thm)],[c_0_551]) ).
fof(c_0_1162,axiom,
! [X3,X4] : c_Relation_ORange(c_Relation_OId__on(X3,X4),X4,X4) = X3,
c_0_552 ).
fof(c_0_1163,axiom,
! [X3,X4] : c_Relation_ODomain(c_Relation_OId__on(X3,X4),X4,X4) = X3,
c_0_553 ).
fof(c_0_1164,axiom,
! [X3,X4] : c_Relation_Orefl__on(X3,c_Relation_OId__on(X3,X4),X4),
c_0_554 ).
fof(c_0_1165,axiom,
! [X3,X4] : c_Relation_Osingle__valued(c_Relation_OId__on(X3,X4),X4,X4),
c_0_555 ).
fof(c_0_1166,axiom,
! [X3,X4] : hAPP(c_Relation_Oconverse(X4,X4),c_Relation_OId__on(X3,X4)) = c_Relation_OId__on(X3,X4),
c_0_556 ).
fof(c_0_1167,axiom,
! [X5,X4] :
( hAPP(c_Relation_Oconverse(X4,X4),X5) != X5
| c_Relation_Osym(X5,X4) ),
c_0_557 ).
fof(c_0_1168,axiom,
! [X3,X4] : c_Lattices_Olower__semilattice__class_Oinf(X3,X3,tc_fun(X4,tc_bool)) = X3,
c_0_558 ).
fof(c_0_1169,axiom,
! [X3,X4] : c_Lattices_Oupper__semilattice__class_Osup(X3,X3,tc_fun(X4,tc_bool)) = X3,
c_0_559 ).
fof(c_0_1170,axiom,
! [X3,X4] : c_lessequals(X3,X3,tc_fun(X4,tc_bool)),
c_0_560 ).
fof(c_0_1171,axiom,
! [X8,X4] : c_lessequals(X8,X8,tc_fun(X4,tc_bool)),
c_0_561 ).
fof(c_0_1172,plain,
! [X8,X4] :
( ~ class_Lattices_Obounded__lattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X4),X8,X4) = c_Orderings_Obot__class_Obot(X4) ),
inference(fof_simplification,[status(thm)],[c_0_562]) ).
fof(c_0_1173,plain,
! [X8,X4] :
( ~ class_Lattices_Obounded__lattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X8,c_Orderings_Obot__class_Obot(X4),X4) = c_Orderings_Obot__class_Obot(X4) ),
inference(fof_simplification,[status(thm)],[c_0_563]) ).
fof(c_0_1174,plain,
! [X8,X4] :
( ~ class_Lattices_Obounded__lattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X4),X8,X4) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_564]) ).
fof(c_0_1175,plain,
! [X8,X4] :
( ~ class_Lattices_Obounded__lattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X8,c_Orderings_Obot__class_Obot(X4),X4) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_565]) ).
fof(c_0_1176,plain,
! [X8,X4] :
( ~ class_Orderings_Obot(X4)
| c_lessequals(c_Orderings_Obot__class_Obot(X4),X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_566]) ).
fof(c_0_1177,plain,
! [X5,X4] :
( hAPP(c_Relation_Oconverse(X4,X4),X5) = X5
| ~ c_Relation_Osym(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_567]) ).
fof(c_0_1178,plain,
! [X5,X4] :
( c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X5,X4),X4)
| ~ c_Wellfounded_Owf(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_568]) ).
fof(c_0_1179,plain,
! [X5,X4] :
( c_Relation_Osym(c_Transitive__Closure_Ortrancl(X5,X4),X4)
| ~ c_Relation_Osym(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_569]) ).
fof(c_0_1180,plain,
! [X5,X4] :
( c_Relation_Osym(c_Transitive__Closure_Otrancl(X5,X4),X4)
| ~ c_Relation_Osym(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_570]) ).
fof(c_0_1181,plain,
! [X5,X4] :
( c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X5,X4),X4)
| ~ c_Wellfounded_Oacyclic(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_571]) ).
fof(c_0_1182,plain,
! [X8,X4] :
( ~ class_Lattices_Olower__semilattice(X4)
| c_Lattices_Olower__semilattice__class_Oinf(X8,X8,X4) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_572]) ).
fof(c_0_1183,plain,
! [X8,X4] :
( ~ class_Lattices_Oupper__semilattice(X4)
| c_Lattices_Oupper__semilattice__class_Osup(X8,X8,X4) = X8 ),
inference(fof_simplification,[status(thm)],[c_0_573]) ).
fof(c_0_1184,plain,
! [X8,X4] :
( ~ class_Orderings_Opreorder(X4)
| c_lessequals(X8,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_574]) ).
fof(c_0_1185,plain,
! [X8,X4] :
( ~ class_Orderings_Oorder(X4)
| c_lessequals(X8,X8,X4) ),
inference(fof_simplification,[status(thm)],[c_0_575]) ).
fof(c_0_1186,axiom,
! [X4] : c_Relation_Osingle__valued(c_Relation_OId(X4),X4,X4),
c_0_576 ).
fof(c_0_1187,axiom,
! [X8,X4] : c_fequal(X8,X8,X4),
c_0_577 ).
fof(c_0_1188,axiom,
! [X5,X4] : c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X5,X4),X4) = c_Transitive__Closure_Ortrancl(X5,X4),
c_0_578 ).
fof(c_0_1189,axiom,
! [X12,X4] : c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X12,X4),X4) = c_Transitive__Closure_Ortrancl(X12,X4),
c_0_579 ).
fof(c_0_1190,axiom,
! [X12,X4] : c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X12,X4),X4) = c_Transitive__Closure_Ortrancl(X12,X4),
c_0_580 ).
fof(c_0_1191,axiom,
! [X4] : hAPP(c_Relation_Oconverse(X4,X4),c_Relation_OId(X4)) = c_Relation_OId(X4),
c_0_581 ).
fof(c_0_1192,axiom,
! [X3,X4] : c_Relation_Osym(c_Relation_OId__on(X3,X4),X4),
c_0_582 ).
fof(c_0_1193,axiom,
! [X3,X4] : c_Relation_Oantisym(c_Relation_OId__on(X3,X4),X4),
c_0_583 ).
fof(c_0_1194,plain,
! [X59,X60] :
( class_HOL_Oord(tc_fun(X59,X60))
| ~ class_HOL_Oord(X60) ),
inference(fof_simplification,[status(thm)],[c_0_584]) ).
fof(c_0_1195,plain,
! [X59,X60] :
( class_Orderings_Obot(tc_fun(X59,X60))
| ~ class_Orderings_Obot(X60) ),
inference(fof_simplification,[status(thm)],[c_0_585]) ).
fof(c_0_1196,plain,
! [X59,X60] :
( class_Orderings_Oorder(tc_fun(X59,X60))
| ~ class_Orderings_Oorder(X60) ),
inference(fof_simplification,[status(thm)],[c_0_586]) ).
fof(c_0_1197,plain,
! [X59,X60] :
( class_Lattices_Olattice(tc_fun(X59,X60))
| ~ class_Lattices_Olattice(X60) ),
inference(fof_simplification,[status(thm)],[c_0_587]) ).
fof(c_0_1198,plain,
! [X59,X60] :
( class_Orderings_Opreorder(tc_fun(X59,X60))
| ~ class_Orderings_Opreorder(X60) ),
inference(fof_simplification,[status(thm)],[c_0_588]) ).
fof(c_0_1199,plain,
! [X59,X60] :
( class_Lattices_Obounded__lattice(tc_fun(X59,X60))
| ~ class_Lattices_Obounded__lattice(X60) ),
inference(fof_simplification,[status(thm)],[c_0_589]) ).
fof(c_0_1200,plain,
! [X59,X60] :
( class_Lattices_Odistrib__lattice(tc_fun(X59,X60))
| ~ class_Lattices_Odistrib__lattice(X60) ),
inference(fof_simplification,[status(thm)],[c_0_590]) ).
fof(c_0_1201,plain,
! [X59,X60] :
( class_Lattices_Olower__semilattice(tc_fun(X59,X60))
| ~ class_Lattices_Olattice(X60) ),
inference(fof_simplification,[status(thm)],[c_0_591]) ).
fof(c_0_1202,plain,
! [X59,X60] :
( class_Lattices_Oupper__semilattice(tc_fun(X59,X60))
| ~ class_Lattices_Olattice(X60) ),
inference(fof_simplification,[status(thm)],[c_0_592]) ).
fof(c_0_1203,plain,
! [X5,X4] :
( c_Wellfounded_Oacyclic(X5,X4)
| ~ c_Wellfounded_Owf(X5,X4) ),
inference(fof_simplification,[status(thm)],[c_0_593]) ).
fof(c_0_1204,axiom,
! [X4] : c_Relation_Oantisym(c_Relation_OId(X4),X4),
c_0_594 ).
fof(c_0_1205,axiom,
! [X4] : c_Relation_Osym(c_Relation_OId(X4),X4),
c_0_595 ).
fof(c_0_1206,axiom,
class_HOL_Oord(tc_bool),
c_0_596 ).
fof(c_0_1207,axiom,
class_Orderings_Obot(tc_bool),
c_0_597 ).
fof(c_0_1208,axiom,
class_Orderings_Oorder(tc_bool),
c_0_598 ).
fof(c_0_1209,axiom,
class_Lattices_Olattice(tc_bool),
c_0_599 ).
fof(c_0_1210,axiom,
class_Orderings_Opreorder(tc_bool),
c_0_600 ).
fof(c_0_1211,axiom,
class_Lattices_Obounded__lattice(tc_bool),
c_0_601 ).
fof(c_0_1212,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
c_0_602 ).
fof(c_0_1213,axiom,
class_Lattices_Olower__semilattice(tc_bool),
c_0_603 ).
fof(c_0_1214,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
c_0_604 ).
fof(c_0_1215,axiom,
c_Arrow__Order__Mirabelle_OIIA(v_F),
c_0_605 ).
fof(c_0_1216,axiom,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
c_0_606 ).
fof(c_0_1217,axiom,
v_a____ != v_c____,
c_0_607 ).
fof(c_0_1218,axiom,
v_b____ != v_c____,
c_0_608 ).
fof(c_0_1219,axiom,
v_a____ != v_b____,
c_0_609 ).
fof(c_0_1220,plain,
! [X31,X32,X33,X34,X35,X36,X37] :
( c_in(c_Pair(X34,c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X34,X33,X32,X31,X37,X36,X35),X37,X35),X32,tc_prod(X37,X35))
| ~ c_in(c_Pair(X34,X33,X37,X36),c_Relation_Orel__comp(X32,X31,X37,X35,X36),tc_prod(X37,X36)) ),
inference(variable_rename,[status(thm)],[c_0_610]) ).
fof(c_0_1221,plain,
! [X31,X32,X33,X34,X35,X36,X37] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X34,X33,X32,X31,X37,X36,X35),X33,X35,X36),X31,tc_prod(X35,X36))
| ~ c_in(c_Pair(X34,X33,X37,X36),c_Relation_Orel__comp(X32,X31,X37,X35,X36),tc_prod(X37,X36)) ),
inference(variable_rename,[status(thm)],[c_0_611]) ).
fof(c_0_1222,plain,
! [X53,X54,X55,X56,X57,X58] :
( c_in(c_Pair(X55,X53,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X57),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X56,X54,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X58),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X55,X53,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X57,v_sko__local__X1__1(X58,X57,X56,X55,X54,X53)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X56,X54,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X58,v_sko__local__X1__1(X58,X57,X56,X55,X54,X53)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X57,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X58,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X54 = X55
| X56 = X53
| X55 = X53
| X56 = X54 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_612])])]) ).
fof(c_0_1223,plain,
! [X53,X54,X55,X56,X57,X58] :
( c_in(c_Pair(X55,X53,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X57),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X56,X54,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X58),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X55,X53,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X57,v_sko__local__X2__1(X58,X57,X56,X55,X54,X53)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X56,X54,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X58,v_sko__local__X2__1(X58,X57,X56,X55,X54,X53)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X57,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X58,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X54 = X55
| X56 = X53
| X55 = X53
| X56 = X54 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_613])])]) ).
fof(c_0_1224,plain,
! [X53,X54,X55,X56,X57,X58] :
( c_in(c_Pair(X56,X54,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X58),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X55,X53,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X57),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X55,X53,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X57,v_sko__local__X2__1(X58,X57,X56,X55,X54,X53)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X56,X54,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X58,v_sko__local__X2__1(X58,X57,X56,X55,X54,X53)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X57,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X58,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X54 = X55
| X56 = X53
| X55 = X53
| X56 = X54 ),
inference(variable_rename,[status(thm)],[c_0_614]) ).
fof(c_0_1225,plain,
! [X53,X54,X55,X56,X57,X58] :
( c_in(c_Pair(X55,X53,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X57),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X56,X54,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X58),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X55,X53,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X57,v_sko__local__X1__1(X58,X57,X56,X55,X54,X53)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X56,X54,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X58,v_sko__local__X1__1(X58,X57,X56,X55,X54,X53)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X57,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X58,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X54 = X55
| X56 = X53
| X55 = X53
| X56 = X54 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_615])])]) ).
fof(c_0_1226,plain,
! [X53,X54,X55,X56,X57,X58] :
( c_in(c_Pair(X55,X53,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X57),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X56,X54,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X58),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X55,X53,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X57,v_sko__local__X2__1(X58,X57,X56,X55,X54,X53)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X56,X54,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X58,v_sko__local__X2__1(X58,X57,X56,X55,X54,X53)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X57,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X58,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X54 = X55
| X56 = X53
| X55 = X53
| X56 = X54 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_616])])]) ).
fof(c_0_1227,plain,
! [X53,X54,X55,X56,X57,X58] :
( c_in(c_Pair(X56,X54,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X58),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X55,X53,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X57),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X55,X53,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X57,v_sko__local__X2__1(X58,X57,X56,X55,X54,X53)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X56,X54,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X58,v_sko__local__X2__1(X58,X57,X56,X55,X54,X53)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X57,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X58,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X54 = X55
| X56 = X53
| X55 = X53
| X56 = X54 ),
inference(variable_rename,[status(thm)],[c_0_617]) ).
fof(c_0_1228,plain,
! [X30,X31,X32,X33,X34,X35] :
( hAPP(X33,c_List_Osko__Recdef__Xcuts__eq__1__1(X33,X32,X31,X30,X35,X34)) != hAPP(X32,c_List_Osko__Recdef__Xcuts__eq__1__1(X33,X32,X31,X30,X35,X34))
| c_Recdef_Ocut(X33,X31,X30,X35,X34) = c_Recdef_Ocut(X32,X31,X30,X35,X34) ),
inference(variable_rename,[status(thm)],[c_0_618]) ).
fof(c_0_1229,plain,
! [X14,X15,X16] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X15,X14,tc_fun(tc_prod(X16,X16),tc_bool)),X16)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X15,X15,X16,X16,X16),c_Relation_Orel__comp(X14,X15,X16,X16,X16),tc_fun(tc_prod(X16,X16),tc_bool)),X14,tc_fun(tc_prod(X16,X16),tc_bool)),X16) ),
inference(variable_rename,[status(thm)],[c_0_619]) ).
fof(c_0_1230,plain,
! [X30,X31,X32,X33,X34,X35] :
( c_Recdef_Ocut(X33,X31,X30,X35,X34) = c_Recdef_Ocut(X32,X31,X30,X35,X34)
| c_in(c_Pair(c_List_Osko__Recdef__Xcuts__eq__1__1(X33,X32,X31,X30,X35,X34),X30,X35,X35),X31,tc_prod(X35,X35)) ),
inference(variable_rename,[status(thm)],[c_0_620]) ).
fof(c_0_1231,plain,
! [X14,X15,X16] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X15,X15,X16,X16,X16),c_Relation_Orel__comp(X14,X15,X16,X16,X16),tc_fun(tc_prod(X16,X16),tc_bool)),X14,tc_fun(tc_prod(X16,X16),tc_bool)),X16)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X15,X14,tc_fun(tc_prod(X16,X16),tc_bool)),X16) ),
inference(variable_rename,[status(thm)],[c_0_621]) ).
fof(c_0_1232,plain,
! [X30,X31,X32,X33,X34] :
( c_in(X30,c_FuncSet_OPi(X32,X31,X34,X33),tc_fun(X34,X33))
| ~ c_in(hAPP(X30,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X32,X31,X30,X34,X33)),hAPP(X31,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X32,X31,X30,X34,X33)),X33) ),
inference(variable_rename,[status(thm)],[c_0_622]) ).
fof(c_0_1233,plain,
! [X30,X31,X32,X33,X34] :
( c_in(X30,c_FuncSet_OPi(X32,X31,X34,X33),tc_fun(X34,X33))
| ~ c_in(hAPP(X30,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X32,X31,X30,X34,X33)),hAPP(X31,c_FuncSet_Osko__FuncSet__XPi__I__1__1(X32,X31,X30,X34,X33)),X33) ),
inference(variable_rename,[status(thm)],[c_0_623]) ).
fof(c_0_1234,plain,
! [X47,X48,X49,X50,X51,X52,X53,X54,X55,X56] :
( hAPP(hAPP(X53,X50),X49) = hAPP(hAPP(X53,X48),X47)
| ~ c_in(c_Pair(X49,X47,X55,X55),X51,tc_prod(X55,X55))
| ~ c_in(c_Pair(X50,X48,X56,X56),X52,tc_prod(X56,X56))
| ~ c_Equiv__Relations_Ocongruent2(X52,X51,X53,X56,X55,X54) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_624])])]) ).
fof(c_0_1235,plain,
! [X47,X48,X49,X50,X51,X52,X53,X54] :
( c_Equiv__Relations_Ocongruent(X47,hAPP(X49,X50),X53,X52)
| ~ c_in(X50,X51,X54)
| ~ c_Equiv__Relations_Ocongruent2(X48,X47,X49,X54,X53,X52)
| ~ c_Equiv__Relations_Oequiv(X51,X48,X54) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_625])])]) ).
fof(c_0_1236,plain,
! [X59,X60,X61,X62,X63,X64,X65] : c_Fun_Ocomp(X61,c_Fun_Ocomp(X60,X59,X62,X63,X65),X63,X64,X65) = c_Fun_Ocomp(c_Fun_Ocomp(X61,X60,X63,X64,X62),X59,X62,X64,X65),
inference(variable_rename,[status(thm)],[c_0_626]) ).
fof(c_0_1237,plain,
! [X49,X50,X51,X52,X53,X54,X55] : c_Relation_Orel__comp(c_Relation_Orel__comp(X51,X50,X55,X52,X53),X49,X55,X53,X54) = c_Relation_Orel__comp(X51,c_Relation_Orel__comp(X50,X49,X52,X53,X54),X55,X52,X54),
inference(variable_rename,[status(thm)],[c_0_627]) ).
fof(c_0_1238,plain,
! [X37,X38,X39,X40,X41] :
( c_in(c_Pair(X40,X39,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X41,X37),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X40,X39,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X41,X38),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X40,X39,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X37,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X40,X39,X38,X37)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X40,X39,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X38,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X40,X39,X38,X37)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X37,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X38,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_OIIA(X41) ),
inference(variable_rename,[status(thm)],[c_0_628]) ).
fof(c_0_1239,plain,
! [X37,X38,X39,X40,X41] :
( c_in(c_Pair(X40,X39,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X41,X38),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X40,X39,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X41,X37),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X40,X39,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X37,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X40,X39,X38,X37)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X40,X39,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X38,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X40,X39,X38,X37)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X37,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X38,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_OIIA(X41) ),
inference(variable_rename,[status(thm)],[c_0_629]) ).
fof(c_0_1240,plain,
! [X51,X52,X53,X54] :
( c_in(c_Pair(X51,X52,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X53),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X54),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X51,X52,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X53,v_sko__local__X3__1(X54,X53,X52,X51)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X54,v_sko__local__X3__1(X54,X53,X52,X51)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X53,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X54,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X52 = X51 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_630])])]) ).
fof(c_0_1241,plain,
! [X51,X52,X53,X54] :
( c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X54),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X51,X52,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X53),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X51,X52,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X53,v_sko__local__X3__1(X54,X53,X52,X51)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X54,v_sko__local__X3__1(X54,X53,X52,X51)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X53,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X54,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X52 = X51 ),
inference(variable_rename,[status(thm)],[c_0_631]) ).
fof(c_0_1242,plain,
! [X22,X23,X24,X25,X26,X27] :
( c_in(c_Pair(X25,X24,X27,X27),X23,tc_prod(X27,X27))
| ~ c_in(X22,c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X23,c_Set_Oinsert(X25,c_Orderings_Obot__class_Obot(tc_fun(X27,tc_bool)),X27),X27,X27),c_Relation_OImage(X23,c_Set_Oinsert(X24,c_Orderings_Obot__class_Obot(tc_fun(X27,tc_bool)),X27),X27,X27),tc_fun(X27,tc_bool)),X27)
| ~ c_Equiv__Relations_Oequiv(X26,X23,X27) ),
inference(variable_rename,[status(thm)],[c_0_632]) ).
fof(c_0_1243,plain,
! [X26,X27,X28,X29,X30,X31] : c_Relation_Orel__comp(X28,c_Lattices_Oupper__semilattice__class_Osup(X27,X26,tc_fun(tc_prod(X29,X30),tc_bool)),X31,X29,X30) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X28,X27,X31,X29,X30),c_Relation_Orel__comp(X28,X26,X31,X29,X30),tc_fun(tc_prod(X31,X30),tc_bool)),
inference(variable_rename,[status(thm)],[c_0_633]) ).
fof(c_0_1244,plain,
! [X26,X27,X28,X29,X30,X31] : c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X27,X26,tc_fun(tc_prod(X31,X29),tc_bool)),X28,X31,X29,X30) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X27,X28,X31,X29,X30),c_Relation_Orel__comp(X26,X28,X31,X29,X30),tc_fun(tc_prod(X31,X30),tc_bool)),
inference(variable_rename,[status(thm)],[c_0_634]) ).
fof(c_0_1245,plain,
! [X18,X19,X20,X21,X22,X23,X24,X25] :
( c_lessequals(c_Relation_Orel__comp(X19,X18,X25,X24,X23),c_Product__Type_OSigma(X22,c_COMBK(X20,tc_fun(X23,tc_bool),X25),X25,X23),tc_fun(tc_prod(X25,X23),tc_bool))
| ~ c_lessequals(X18,c_Product__Type_OSigma(X21,c_COMBK(X20,tc_fun(X23,tc_bool),X24),X24,X23),tc_fun(tc_prod(X24,X23),tc_bool))
| ~ c_lessequals(X19,c_Product__Type_OSigma(X22,c_COMBK(X21,tc_fun(X24,tc_bool),X25),X25,X24),tc_fun(tc_prod(X25,X24),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_635]) ).
fof(c_0_1246,plain,
! [X21,X22,X23,X24,X25] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X23,X22,X21,X24,X25),X22,X24,X25),X21,tc_prod(X24,X25))
| ~ c_in(X22,c_Relation_OImage(X21,X23,X24,X25),X25) ),
inference(variable_rename,[status(thm)],[c_0_636]) ).
fof(c_0_1247,plain,
! [X21,X22,X23,X24,X25] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X23,X22,X21,X24,X25),X22,X24,X25),X21,tc_prod(X24,X25))
| ~ c_in(X22,c_Relation_OImage(X21,X23,X24,X25),X25) ),
inference(variable_rename,[status(thm)],[c_0_637]) ).
fof(c_0_1248,plain,
! [X22,X23,X24,X25,X26,X27] : c_Product__Type_OSigma(c_Set_Oinsert(X23,X25,X27),c_COMBK(c_Set_Oinsert(X22,X24,X26),tc_fun(X26,tc_bool),X27),X27,X26) = c_Set_Oinsert(c_Pair(X23,X22,X27,X26),c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X25,c_COMBK(c_Set_Oinsert(X22,X24,X26),tc_fun(X26,tc_bool),X27),X27,X26),c_Product__Type_OSigma(c_Set_Oinsert(X23,X25,X27),c_COMBK(X24,tc_fun(X26,tc_bool),X27),X27,X26),tc_fun(tc_prod(X27,X26),tc_bool)),tc_prod(X27,X26)),
inference(variable_rename,[status(thm)],[c_0_638]) ).
fof(c_0_1249,plain,
! [X5,X6,X7,X8] :
( c_Relation_Orel__comp(X7,X5,X8,X8,X8) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X8,X8),tc_bool))
| c_Relation_Orel__comp(X7,X6,X8,X8,X8) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X8,X8),tc_bool))
| c_Relation_Orel__comp(X7,c_Lattices_Oupper__semilattice__class_Osup(X6,X5,tc_fun(tc_prod(X8,X8),tc_bool)),X8,X8,X8) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X8,X8),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_639]) ).
fof(c_0_1250,plain,
! [X5,X6,X7,X8] :
( c_Relation_Orel__comp(X6,X5,X8,X8,X8) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X8,X8),tc_bool))
| c_Relation_Orel__comp(X7,X5,X8,X8,X8) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X8,X8),tc_bool))
| c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X7,X6,tc_fun(tc_prod(X8,X8),tc_bool)),X5,X8,X8,X8) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X8,X8),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_640]) ).
fof(c_0_1251,plain,
! [X18,X19,X20,X21,X22,X23,X24] :
( c_lessequals(c_Relation_Orel__comp(X20,X18,X24,X23,X22),c_Relation_Orel__comp(X21,X19,X24,X23,X22),tc_fun(tc_prod(X24,X22),tc_bool))
| ~ c_lessequals(X18,X19,tc_fun(tc_prod(X23,X22),tc_bool))
| ~ c_lessequals(X20,X21,tc_fun(tc_prod(X24,X23),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_641]) ).
fof(c_0_1252,plain,
! [X16,X17,X18] :
( c_lessequals(c_Transitive__Closure_Ortrancl(X17,X18),X16,tc_fun(tc_prod(X18,X18),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Ortrancl(X17,X18),X16,tc_fun(tc_prod(X18,X18),tc_bool)),X17,X18,X18,X18),X16,tc_fun(tc_prod(X18,X18),tc_bool))
| ~ c_lessequals(c_Relation_OId(X18),X16,tc_fun(tc_prod(X18,X18),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_642]) ).
fof(c_0_1253,plain,
! [X16,X17,X18] :
( c_lessequals(c_Transitive__Closure_Otrancl(X17,X18),X16,tc_fun(tc_prod(X18,X18),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(c_Lattices_Olower__semilattice__class_Oinf(c_Transitive__Closure_Otrancl(X17,X18),X16,tc_fun(tc_prod(X18,X18),tc_bool)),X17,X18,X18,X18),X16,tc_fun(tc_prod(X18,X18),tc_bool))
| ~ c_lessequals(X17,X16,tc_fun(tc_prod(X18,X18),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_643]) ).
fof(c_0_1254,plain,
! [X37,X38,X39,X40,X41] :
( c_in(c_Pair(X40,X39,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X41,X37),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X40,X39,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X41,X38),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X40,X39,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X37,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X40,X39,X38,X37)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X40,X39,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X38,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X40,X39,X38,X37)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X37,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X38,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_OIIA(X41) ),
inference(variable_rename,[status(thm)],[c_0_644]) ).
fof(c_0_1255,plain,
! [X37,X38,X39,X40,X41] :
( c_in(c_Pair(X40,X39,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X41,X38),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X40,X39,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X41,X37),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X40,X39,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X37,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X40,X39,X38,X37)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X40,X39,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X38,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X40,X39,X38,X37)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X37,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X38,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_OIIA(X41) ),
inference(variable_rename,[status(thm)],[c_0_645]) ).
fof(c_0_1256,plain,
! [X51,X52,X53,X54] :
( c_in(c_Pair(X51,X52,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X53),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X54),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X51,X52,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X53,v_sko__local__X3__1(X54,X53,X52,X51)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X54,v_sko__local__X3__1(X54,X53,X52,X51)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X53,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X54,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X52 = X51 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_646])])]) ).
fof(c_0_1257,plain,
! [X51,X52,X53,X54] :
( c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X54),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X51,X52,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X53),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X51,X52,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X53,v_sko__local__X3__1(X54,X53,X52,X51)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X54,v_sko__local__X3__1(X54,X53,X52,X51)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X53,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X54,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| X52 = X51 ),
inference(variable_rename,[status(thm)],[c_0_647]) ).
fof(c_0_1258,plain,
! [X57,X58,X59,X60,X61,X62,X63,X64,X65,X66,X67] :
( hAPP(X62,hAPP(X60,X58)) != hAPP(X61,hAPP(X59,X57))
| hAPP(c_Fun_Ocomp(X62,X60,X66,X67,X65),X58) = hAPP(c_Fun_Ocomp(X61,X59,X64,X67,X63),X57) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_648])])]) ).
fof(c_0_1259,plain,
! [X31,X32,X33,X34,X35,X36,X37,X38] :
( c_in(c_Pair(X35,X33,X38,X36),c_Relation_Orel__comp(X32,X31,X38,X37,X36),tc_prod(X38,X36))
| ~ c_in(c_Pair(X34,X33,X37,X36),X31,tc_prod(X37,X36))
| ~ c_in(c_Pair(X35,X34,X38,X37),X32,tc_prod(X38,X37)) ),
inference(variable_rename,[status(thm)],[c_0_649]) ).
fof(c_0_1260,plain,
! [X30,X31,X32,X33,X34,X35,X36] :
( c_Recdef_Ocut(X34,X32,X31,X36,X35) != c_Recdef_Ocut(X33,X32,X31,X36,X35)
| hAPP(X34,X30) = hAPP(X33,X30)
| ~ c_in(c_Pair(X30,X31,X36,X36),X32,tc_prod(X36,X36)) ),
inference(variable_rename,[status(thm)],[c_0_650]) ).
fof(c_0_1261,plain,
! [X14,X15,X16] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X15,X14,tc_fun(tc_prod(X16,X16),tc_bool)),X16)
| ~ c_lessequals(c_Relation_Orel__comp(X15,X14,X16,X16,X16),X15,tc_fun(tc_prod(X16,X16),tc_bool))
| ~ c_Wellfounded_Owf(X14,X16)
| ~ c_Wellfounded_Owf(X15,X16) ),
inference(variable_rename,[status(thm)],[c_0_651]) ).
fof(c_0_1262,plain,
! [X58,X59,X60,X61,X62,X63,X64,X65,X66] :
( c_Fun_Ocomp(X62,X61,X64,X65,X66) != c_Fun_Ocomp(X60,X59,X63,X65,X66)
| hAPP(X62,hAPP(X61,X58)) = hAPP(X60,hAPP(X59,X58)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_652])])]) ).
fof(c_0_1263,plain,
! [X13,X14] :
( c_Wellfounded_Owf(X13,X14)
| ~ c_Wellfounded_Owf(c_Relation_Orel__comp(X13,X13,X14,X14,X14),X14) ),
inference(variable_rename,[status(thm)],[c_0_653]) ).
fof(c_0_1264,plain,
! [X18,X19,X20,X21,X22] : hAPP(c_Relation_Oconverse(X21,X22),c_Relation_Orel__comp(X19,X18,X21,X20,X22)) = c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X20,X22),X18),hAPP(c_Relation_Oconverse(X21,X20),X19),X22,X20,X21),
inference(variable_rename,[status(thm)],[c_0_654]) ).
fof(c_0_1265,plain,
! [X22,X23,X24,X25,X26] :
( c_in(c_Pair(X24,X23,X26,X26),X22,tc_prod(X26,X26))
| ~ c_in(X23,X25,X26)
| ~ c_lessequals(c_Relation_OImage(X22,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X26,tc_bool)),X26),X26,X26),c_Relation_OImage(X22,c_Set_Oinsert(X24,c_Orderings_Obot__class_Obot(tc_fun(X26,tc_bool)),X26),X26,X26),tc_fun(X26,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X25,X22,X26) ),
inference(variable_rename,[status(thm)],[c_0_655]) ).
fof(c_0_1266,plain,
! [X22,X23,X24,X25,X26] :
( hBOOL(hAPP(X25,X23))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X25,X24,X22,X26),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X25,X24,X22,X26),X26,X26),X22,tc_prod(X26,X26))
| ~ hBOOL(hAPP(X25,X24))
| ~ c_in(c_Pair(X24,X23,X26,X26),c_Transitive__Closure_Ortrancl(X22,X26),tc_prod(X26,X26)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_656])])]) ).
fof(c_0_1267,plain,
! [X22,X23,X24,X25,X26] :
( hBOOL(hAPP(X25,X24))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X25,X23,X22,X26),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X25,X23,X22,X26),X26,X26),X22,tc_prod(X26,X26))
| ~ hBOOL(hAPP(X25,X23))
| ~ c_in(c_Pair(X24,X23,X26,X26),c_Transitive__Closure_Ortrancl(X22,X26),tc_prod(X26,X26)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_657])])]) ).
fof(c_0_1268,plain,
! [X31,X32,X33,X34,X35] :
( c_in(c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1(X33,X32,X31,X35,X34),X33,X35)
| ~ c_in(X31,c_Product__Type_OSigma(X33,X32,X35,X34),tc_prod(X35,X34)) ),
inference(variable_rename,[status(thm)],[c_0_658]) ).
fof(c_0_1269,plain,
! [X30,X31,X32,X33,X34,X35] :
( hAPP(c_Recdef_Ocut(X31,X33,X32,X35,X34),X30) = hAPP(X31,X30)
| ~ c_in(c_Pair(X30,X32,X35,X35),X33,tc_prod(X35,X35)) ),
inference(variable_rename,[status(thm)],[c_0_659]) ).
fof(c_0_1270,plain,
! [X30,X31,X32,X33,X34,X35] :
( hAPP(c_Recdef_Ocut(X32,X31,X33,X35,X34),X30) = hAPP(X32,X30)
| ~ c_in(c_Pair(X30,X33,X35,X35),X31,tc_prod(X35,X35)) ),
inference(variable_rename,[status(thm)],[c_0_660]) ).
fof(c_0_1271,plain,
! [X21,X22,X23,X24,X25] :
( c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X23,X22,X21,X24,X25),X23,X24)
| ~ c_in(X22,c_Relation_OImage(X21,X23,X24,X25),X25) ),
inference(variable_rename,[status(thm)],[c_0_661]) ).
fof(c_0_1272,plain,
! [X21,X22,X23,X24,X25] :
( c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X23,X22,X21,X24,X25),X23,X24)
| ~ c_in(X22,c_Relation_OImage(X21,X23,X24,X25),X25) ),
inference(variable_rename,[status(thm)],[c_0_662]) ).
fof(c_0_1273,plain,
! [X20,X21,X22,X23,X24] :
( c_in(c_Pair(X20,X21,X24,X24),c_Transitive__Closure_Ortrancl(X23,X24),tc_prod(X24,X24))
| c_in(c_Pair(X21,X20,X24,X24),c_Transitive__Closure_Ortrancl(X23,X24),tc_prod(X24,X24))
| ~ c_in(c_Pair(X22,X20,X24,X24),c_Transitive__Closure_Ortrancl(X23,X24),tc_prod(X24,X24))
| ~ c_in(c_Pair(X22,X21,X24,X24),c_Transitive__Closure_Ortrancl(X23,X24),tc_prod(X24,X24))
| ~ c_Relation_Osingle__valued(X23,X24,X24) ),
inference(variable_rename,[status(thm)],[c_0_663]) ).
fof(c_0_1274,plain,
! [X22,X23,X24,X25] :
( c_in(c_Pair(X24,c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X24,X23,X22,X25),X25,X25),c_Transitive__Closure_Otrancl(X22,X25),tc_prod(X25,X25))
| c_in(c_Pair(X24,X23,X25,X25),X22,tc_prod(X25,X25))
| ~ c_in(c_Pair(X24,X23,X25,X25),c_Transitive__Closure_Otrancl(X22,X25),tc_prod(X25,X25)) ),
inference(variable_rename,[status(thm)],[c_0_664]) ).
fof(c_0_1275,plain,
! [X19,X20,X21,X22] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X21,X20,X19,X22),X19,X22,X22),c_Transitive__Closure_Otrancl(X21,X22),tc_prod(X22,X22))
| c_in(c_Pair(X20,X19,X22,X22),X21,tc_prod(X22,X22))
| ~ c_in(c_Pair(X20,X19,X22,X22),c_Transitive__Closure_Otrancl(X21,X22),tc_prod(X22,X22)) ),
inference(variable_rename,[status(thm)],[c_0_665]) ).
fof(c_0_1276,plain,
! [X19,X20,X21,X22] :
( c_in(c_Pair(X20,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X21,X20,X19,X22),X22,X22),X21,tc_prod(X22,X22))
| c_in(c_Pair(X20,X19,X22,X22),X21,tc_prod(X22,X22))
| ~ c_in(c_Pair(X20,X19,X22,X22),c_Transitive__Closure_Otrancl(X21,X22),tc_prod(X22,X22)) ),
inference(variable_rename,[status(thm)],[c_0_666]) ).
fof(c_0_1277,plain,
! [X22,X23,X24,X25] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X24,X23,X22,X25),X23,X25,X25),X22,tc_prod(X25,X25))
| c_in(c_Pair(X24,X23,X25,X25),X22,tc_prod(X25,X25))
| ~ c_in(c_Pair(X24,X23,X25,X25),c_Transitive__Closure_Otrancl(X22,X25),tc_prod(X25,X25)) ),
inference(variable_rename,[status(thm)],[c_0_667]) ).
fof(c_0_1278,plain,
! [X30,X31,X32,X33,X34] :
( c_in(X30,c_FuncSet_OPi(X32,X31,X34,X33),tc_fun(X34,X33))
| c_in(c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X32,X31,X30,X34,X33),X32,X34) ),
inference(variable_rename,[status(thm)],[c_0_668]) ).
fof(c_0_1279,plain,
! [X30,X31,X32,X33,X34] :
( c_in(X30,c_FuncSet_OPi(X32,X31,X34,X33),tc_fun(X34,X33))
| c_in(c_FuncSet_Osko__FuncSet__XPi__I__1__1(X32,X31,X30,X34,X33),X32,X34) ),
inference(variable_rename,[status(thm)],[c_0_669]) ).
fof(c_0_1280,plain,
! [X13,X14,X15,X16,X17] : c_lessequals(c_Relation_OImage(X13,c_Lattices_Olower__semilattice__class_Oinf(X15,X14,tc_fun(X16,tc_bool)),X16,X17),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X13,X15,X16,X17),c_Relation_OImage(X13,X14,X16,X17),tc_fun(X17,tc_bool)),tc_fun(X17,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_670]) ).
fof(c_0_1281,plain,
! [X22,X23,X24,X25,X26] :
( c_lessequals(c_Relation_OImage(X22,c_Set_Oinsert(X24,c_Orderings_Obot__class_Obot(tc_fun(X26,tc_bool)),X26),X26,X26),c_Relation_OImage(X22,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X26,tc_bool)),X26),X26,X26),tc_fun(X26,tc_bool))
| ~ c_in(c_Pair(X24,X23,X26,X26),X22,tc_prod(X26,X26))
| ~ c_Equiv__Relations_Oequiv(X25,X22,X26) ),
inference(variable_rename,[status(thm)],[c_0_671]) ).
fof(c_0_1282,axiom,
c_in(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
c_0_672 ).
fof(c_0_1283,plain,
! [X9,X10,X11,X12,X13,X14] :
( c_lessequals(X12,X11,tc_fun(X13,tc_bool))
| ~ c_lessequals(c_Product__Type_OSigma(X12,c_COMBK(X10,tc_fun(X14,tc_bool),X13),X13,X14),c_Product__Type_OSigma(X11,c_COMBK(X10,tc_fun(X14,tc_bool),X13),X13,X14),tc_fun(tc_prod(X13,X14),tc_bool))
| ~ c_in(X9,X10,X14) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_673])])]) ).
fof(c_0_1284,plain,
! [X6,X7,X8] :
( c_lessequals(X6,c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X8,X8),X6),X6,X8,X8,X8),tc_fun(tc_prod(X8,X8),tc_bool))
| ~ c_Relation_Orefl__on(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_674]) ).
fof(c_0_1285,plain,
! [X20,X21,X22,X23] :
( ~ c_in(c_Pair(X21,X20,X23,X23),c_Transitive__Closure_Ortrancl(X22,X23),tc_prod(X23,X23))
| ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X20,X21,X23,X23),X22,tc_prod(X23,X23)),X23) ),
inference(variable_rename,[status(thm)],[c_0_675]) ).
fof(c_0_1286,plain,
! [X20,X21,X22,X23] :
( ~ c_in(c_Pair(X21,X20,X23,X23),c_Transitive__Closure_Ortrancl(X22,X23),tc_prod(X23,X23))
| ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X20,X21,X23,X23),X22,tc_prod(X23,X23)),X23) ),
inference(variable_rename,[status(thm)],[c_0_676]) ).
fof(c_0_1287,plain,
! [X18,X19,X20,X21,X22] :
( c_Relation_Osingle__valued(c_Relation_Orel__comp(X19,X18,X22,X21,X20),X22,X20)
| ~ c_Relation_Osingle__valued(X18,X21,X20)
| ~ c_Relation_Osingle__valued(X19,X22,X21) ),
inference(variable_rename,[status(thm)],[c_0_677]) ).
fof(c_0_1288,plain,
! [X22,X23,X24,X25,X26] :
( hBOOL(hAPP(X25,X24))
| ~ hBOOL(hAPP(X25,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X25,X23,X22,X26)))
| ~ hBOOL(hAPP(X25,X23))
| ~ c_in(c_Pair(X24,X23,X26,X26),c_Transitive__Closure_Ortrancl(X22,X26),tc_prod(X26,X26)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_678])])]) ).
fof(c_0_1289,plain,
! [X22,X23,X24,X25,X26] :
( hBOOL(hAPP(X25,X23))
| ~ hBOOL(hAPP(X25,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X25,X24,X22,X26)))
| ~ hBOOL(hAPP(X25,X24))
| ~ c_in(c_Pair(X24,X23,X26,X26),c_Transitive__Closure_Ortrancl(X22,X26),tc_prod(X26,X26)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_679])])]) ).
fof(c_0_1290,plain,
! [X6,X7] : c_Transitive__Closure_Ortrancl(X6,X7) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X7),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X6,X7),X6,X7,X7,X7),tc_fun(tc_prod(X7,X7),tc_bool)),
inference(variable_rename,[status(thm)],[c_0_680]) ).
fof(c_0_1291,plain,
! [X22,X23,X24,X25,X26] :
( hBOOL(hAPP(X25,X23))
| c_in(c_Pair(X24,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X25,X24,X22,X26),X26,X26),c_Transitive__Closure_Ortrancl(X22,X26),tc_prod(X26,X26))
| ~ hBOOL(hAPP(X25,X24))
| ~ c_in(c_Pair(X24,X23,X26,X26),c_Transitive__Closure_Ortrancl(X22,X26),tc_prod(X26,X26)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_681])])]) ).
fof(c_0_1292,plain,
! [X22,X23,X24,X25,X26] :
( hBOOL(hAPP(X25,X24))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X25,X23,X22,X26),X23,X26,X26),c_Transitive__Closure_Ortrancl(X22,X26),tc_prod(X26,X26))
| ~ hBOOL(hAPP(X25,X23))
| ~ c_in(c_Pair(X24,X23,X26,X26),c_Transitive__Closure_Ortrancl(X22,X26),tc_prod(X26,X26)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_682])])]) ).
fof(c_0_1293,plain,
! [X6,X7] : c_Transitive__Closure_Otrancl(X6,X7) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X6,X7),X6,X7,X7,X7),tc_fun(tc_prod(X7,X7),tc_bool)),
inference(variable_rename,[status(thm)],[c_0_683]) ).
fof(c_0_1294,plain,
! [X22,X23,X24,X25] :
( c_in(c_Pair(X24,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X24,X23,X22,X25),X25,X25),c_Transitive__Closure_Ortrancl(X22,X25),tc_prod(X25,X25))
| X24 = X23
| ~ c_in(c_Pair(X24,X23,X25,X25),c_Transitive__Closure_Ortrancl(X22,X25),tc_prod(X25,X25)) ),
inference(variable_rename,[status(thm)],[c_0_684]) ).
fof(c_0_1295,plain,
! [X19,X20,X21,X22] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X21,X20,X19,X22),X19,X22,X22),c_Transitive__Closure_Ortrancl(X21,X22),tc_prod(X22,X22))
| X20 = X19
| ~ c_in(c_Pair(X20,X19,X22,X22),c_Transitive__Closure_Ortrancl(X21,X22),tc_prod(X22,X22)) ),
inference(variable_rename,[status(thm)],[c_0_685]) ).
fof(c_0_1296,plain,
! [X20,X21,X22,X23] :
( c_in(c_Pair(X21,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X22,X21,X20,X23),X23,X23),c_Transitive__Closure_Ortrancl(X22,X23),tc_prod(X23,X23))
| ~ c_in(c_Pair(X21,X20,X23,X23),c_Transitive__Closure_Otrancl(X22,X23),tc_prod(X23,X23)) ),
inference(variable_rename,[status(thm)],[c_0_686]) ).
fof(c_0_1297,plain,
! [X20,X21,X22,X23] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X22,X21,X20,X23),X20,X23,X23),c_Transitive__Closure_Ortrancl(X22,X23),tc_prod(X23,X23))
| ~ c_in(c_Pair(X21,X20,X23,X23),c_Transitive__Closure_Otrancl(X22,X23),tc_prod(X23,X23)) ),
inference(variable_rename,[status(thm)],[c_0_687]) ).
fof(c_0_1298,plain,
! [X19,X20,X21,X22] :
( c_in(c_Pair(X20,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X21,X20,X19,X22),X22,X22),X21,tc_prod(X22,X22))
| X20 = X19
| ~ c_in(c_Pair(X20,X19,X22,X22),c_Transitive__Closure_Ortrancl(X21,X22),tc_prod(X22,X22)) ),
inference(variable_rename,[status(thm)],[c_0_688]) ).
fof(c_0_1299,plain,
! [X22,X23,X24,X25] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X24,X23,X22,X25),X23,X25,X25),X22,tc_prod(X25,X25))
| X24 = X23
| ~ c_in(c_Pair(X24,X23,X25,X25),c_Transitive__Closure_Ortrancl(X22,X25),tc_prod(X25,X25)) ),
inference(variable_rename,[status(thm)],[c_0_689]) ).
fof(c_0_1300,plain,
! [X20,X21,X22,X23] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X22,X21,X20,X23),X20,X23,X23),X22,tc_prod(X23,X23))
| ~ c_in(c_Pair(X21,X20,X23,X23),c_Transitive__Closure_Otrancl(X22,X23),tc_prod(X23,X23)) ),
inference(variable_rename,[status(thm)],[c_0_690]) ).
fof(c_0_1301,plain,
! [X20,X21,X22,X23] :
( c_in(c_Pair(X21,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X22,X21,X20,X23),X23,X23),X22,tc_prod(X23,X23))
| ~ c_in(c_Pair(X21,X20,X23,X23),c_Transitive__Closure_Otrancl(X22,X23),tc_prod(X23,X23)) ),
inference(variable_rename,[status(thm)],[c_0_691]) ).
fof(c_0_1302,plain,
! [X31,X32,X33,X34,X35] :
( c_in(c_Pair(X34,X32,X35,X35),c_Transitive__Closure_Otrancl(X31,X35),tc_prod(X35,X35))
| ~ c_in(c_Pair(X33,X32,X35,X35),c_Transitive__Closure_Otrancl(X31,X35),tc_prod(X35,X35))
| ~ c_in(c_Pair(X34,X33,X35,X35),c_Transitive__Closure_Otrancl(X31,X35),tc_prod(X35,X35)) ),
inference(variable_rename,[status(thm)],[c_0_692]) ).
fof(c_0_1303,plain,
! [X31,X32,X33,X34,X35] :
( c_in(c_Pair(X34,X32,X35,X35),c_Transitive__Closure_Ortrancl(X31,X35),tc_prod(X35,X35))
| ~ c_in(c_Pair(X33,X32,X35,X35),c_Transitive__Closure_Ortrancl(X31,X35),tc_prod(X35,X35))
| ~ c_in(c_Pair(X34,X33,X35,X35),c_Transitive__Closure_Ortrancl(X31,X35),tc_prod(X35,X35)) ),
inference(variable_rename,[status(thm)],[c_0_693]) ).
fof(c_0_1304,plain,
! [X20,X21,X22,X23,X24] :
( c_in(c_Pair(X22,X20,X24,X24),c_Transitive__Closure_Otrancl(X23,X24),tc_prod(X24,X24))
| ~ c_in(c_Pair(X21,X20,X24,X24),c_Transitive__Closure_Otrancl(X23,X24),tc_prod(X24,X24))
| ~ c_in(c_Pair(X22,X21,X24,X24),c_Transitive__Closure_Ortrancl(X23,X24),tc_prod(X24,X24)) ),
inference(variable_rename,[status(thm)],[c_0_694]) ).
fof(c_0_1305,plain,
! [X31,X32,X33,X34,X35] :
( c_in(c_Pair(X34,X32,X35,X35),c_Transitive__Closure_Otrancl(X31,X35),tc_prod(X35,X35))
| ~ c_in(c_Pair(X33,X32,X35,X35),c_Transitive__Closure_Ortrancl(X31,X35),tc_prod(X35,X35))
| ~ c_in(c_Pair(X34,X33,X35,X35),c_Transitive__Closure_Otrancl(X31,X35),tc_prod(X35,X35)) ),
inference(variable_rename,[status(thm)],[c_0_695]) ).
fof(c_0_1306,plain,
! [X30,X31,X32,X33,X34,X35] : hAPP(c_Fun_Ocomp(X32,X31,X34,X35,X33),X30) = hAPP(X32,hAPP(X31,X30)),
inference(variable_rename,[status(thm)],[c_0_696]) ).
fof(c_0_1307,plain,
! [X58,X59,X60,X61,X62,X63] : hAPP(X60,hAPP(X59,X58)) = hAPP(c_Fun_Ocomp(X60,X59,X61,X62,X63),X58),
inference(variable_rename,[status(thm)],[c_0_697]) ).
fof(c_0_1308,plain,
! [X6,X7] : c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X7),X7,X7,X7) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X6,X7),X6,X7,X7,X7),
inference(variable_rename,[status(thm)],[c_0_698]) ).
fof(c_0_1309,plain,
! [X22,X23,X24,X25,X26] :
( c_in(X24,X25,X26)
| X24 = X23
| ~ c_lessequals(X22,c_Product__Type_OSigma(X25,c_COMBK(X25,tc_fun(X26,tc_bool),X26),X26,X26),tc_fun(tc_prod(X26,X26),tc_bool))
| ~ c_in(c_Pair(X24,X23,X26,X26),c_Transitive__Closure_Ortrancl(X22,X26),tc_prod(X26,X26)) ),
inference(variable_rename,[status(thm)],[c_0_699]) ).
fof(c_0_1310,plain,
! [X31,X32,X33,X34,X35] :
( c_in(c_Pair(X34,X32,X35,X35),c_Transitive__Closure_Ortrancl(X31,X35),tc_prod(X35,X35))
| ~ c_in(c_Pair(X33,X32,X35,X35),c_Transitive__Closure_Ortrancl(X31,X35),tc_prod(X35,X35))
| ~ c_in(c_Pair(X34,X33,X35,X35),X31,tc_prod(X35,X35)) ),
inference(variable_rename,[status(thm)],[c_0_700]) ).
fof(c_0_1311,plain,
! [X31,X32,X33,X34,X35] :
( c_in(c_Pair(X34,X32,X35,X35),c_Transitive__Closure_Otrancl(X31,X35),tc_prod(X35,X35))
| ~ c_in(c_Pair(X33,X32,X35,X35),X31,tc_prod(X35,X35))
| ~ c_in(c_Pair(X34,X33,X35,X35),c_Transitive__Closure_Ortrancl(X31,X35),tc_prod(X35,X35)) ),
inference(variable_rename,[status(thm)],[c_0_701]) ).
fof(c_0_1312,plain,
! [X31,X32,X33,X34,X35] :
( c_in(c_Pair(X34,X32,X35,X35),c_Transitive__Closure_Otrancl(X31,X35),tc_prod(X35,X35))
| ~ c_in(c_Pair(X33,X32,X35,X35),c_Transitive__Closure_Ortrancl(X31,X35),tc_prod(X35,X35))
| ~ c_in(c_Pair(X34,X33,X35,X35),X31,tc_prod(X35,X35)) ),
inference(variable_rename,[status(thm)],[c_0_702]) ).
fof(c_0_1313,plain,
! [X31,X32,X33,X34,X35] :
( c_in(c_Pair(X34,X32,X35,X35),c_Transitive__Closure_Otrancl(X31,X35),tc_prod(X35,X35))
| ~ c_in(c_Pair(X33,X32,X35,X35),X31,tc_prod(X35,X35))
| ~ c_in(c_Pair(X34,X33,X35,X35),c_Transitive__Closure_Otrancl(X31,X35),tc_prod(X35,X35)) ),
inference(variable_rename,[status(thm)],[c_0_703]) ).
fof(c_0_1314,plain,
! [X31,X32,X33,X34,X35] :
( c_in(c_Pair(X34,X32,X35,X35),c_Transitive__Closure_Otrancl(X31,X35),tc_prod(X35,X35))
| ~ c_in(c_Pair(X33,X32,X35,X35),c_Transitive__Closure_Otrancl(X31,X35),tc_prod(X35,X35))
| ~ c_in(c_Pair(X34,X33,X35,X35),X31,tc_prod(X35,X35)) ),
inference(variable_rename,[status(thm)],[c_0_704]) ).
fof(c_0_1315,plain,
! [X31,X32,X33,X34,X35] :
( c_in(c_Pair(X34,X32,X35,X35),c_Transitive__Closure_Ortrancl(X31,X35),tc_prod(X35,X35))
| ~ c_in(c_Pair(X33,X32,X35,X35),X31,tc_prod(X35,X35))
| ~ c_in(c_Pair(X34,X33,X35,X35),c_Transitive__Closure_Ortrancl(X31,X35),tc_prod(X35,X35)) ),
inference(variable_rename,[status(thm)],[c_0_705]) ).
fof(c_0_1316,plain,
! [X13,X14] :
( c_Wellfounded_Owf(c_Relation_Orel__comp(X13,X13,X14,X14,X14),X14)
| ~ c_Wellfounded_Owf(X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_706]) ).
fof(c_0_1317,plain,
! [X6,X7,X8] :
( c_lessequals(c_Transitive__Closure_Otrancl(X6,X8),c_Product__Type_OSigma(X7,c_COMBK(X7,tc_fun(X8,tc_bool),X8),X8,X8),tc_fun(tc_prod(X8,X8),tc_bool))
| ~ c_lessequals(X6,c_Product__Type_OSigma(X7,c_COMBK(X7,tc_fun(X8,tc_bool),X8),X8,X8),tc_fun(tc_prod(X8,X8),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_707]) ).
fof(c_0_1318,plain,
! [X31,X32,X33,X34,X35] :
( c_in(c_Pair(X33,X31,X35,X35),c_Transitive__Closure_Otrancl(X34,X35),tc_prod(X35,X35))
| ~ c_in(c_Pair(X32,X31,X35,X35),X34,tc_prod(X35,X35))
| ~ c_in(c_Pair(X33,X32,X35,X35),X34,tc_prod(X35,X35)) ),
inference(variable_rename,[status(thm)],[c_0_708]) ).
fof(c_0_1319,plain,
! [X30,X31,X32,X33,X34,X35] :
( c_in(c_Pair(hAPP(X33,X31),hAPP(X33,X30),X34,X34),X32,tc_prod(X34,X34))
| ~ c_in(c_Pair(X31,X30,X35,X35),c_Relation_Oinv__image(X32,X33,X34,X35),tc_prod(X35,X35)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_709])])]) ).
fof(c_0_1320,plain,
! [X7,X8,X9,X10,X11] : c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(X9,X8,tc_fun(X11,tc_bool)),c_COMBK(X7,tc_fun(X10,tc_bool),X11),X11,X10) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X9,c_COMBK(X7,tc_fun(X10,tc_bool),X11),X11,X10),c_Product__Type_OSigma(X8,c_COMBK(X7,tc_fun(X10,tc_bool),X11),X11,X10),tc_fun(tc_prod(X11,X10),tc_bool)),
inference(variable_rename,[status(thm)],[c_0_710]) ).
fof(c_0_1321,plain,
! [X7,X8,X9,X10,X11] : c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(X9,X8,tc_fun(X11,tc_bool)),c_COMBK(X7,tc_fun(X10,tc_bool),X11),X11,X10) = c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(X9,c_COMBK(X7,tc_fun(X10,tc_bool),X11),X11,X10),c_Product__Type_OSigma(X8,c_COMBK(X7,tc_fun(X10,tc_bool),X11),X11,X10),tc_fun(tc_prod(X11,X10),tc_bool)),
inference(variable_rename,[status(thm)],[c_0_711]) ).
fof(c_0_1322,plain,
! [X40,X41,X42] :
( c_in(c_Pair(X42,v_sko__Transitive__Closure__Xtrancl__Xcases__1(X42,X41,X40),t_a,t_a),c_Transitive__Closure_Otrancl(X40,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(X42,X41,t_a,t_a),X40,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X42,X41,t_a,t_a),c_Transitive__Closure_Otrancl(X40,t_a),tc_prod(t_a,t_a)) ),
inference(variable_rename,[status(thm)],[c_0_712]) ).
fof(c_0_1323,plain,
! [X20,X21,X22,X23,X24] :
( c_Relation_OImage(X22,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)),X24),X24,X24) != c_Relation_OImage(X22,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)),X24),X24,X24)
| ~ c_in(X20,X23,X24)
| ~ c_in(X21,X23,X24)
| ~ c_Equiv__Relations_Oequiv(X23,X22,X24)
| c_in(c_Pair(X21,X20,X24,X24),X22,tc_prod(X24,X24)) ),
inference(variable_rename,[status(thm)],[c_0_713]) ).
fof(c_0_1324,plain,
! [X20,X21,X22,X23,X24] :
( c_Relation_OImage(X22,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)),X24),X24,X24) != c_Relation_OImage(X22,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)),X24),X24,X24)
| ~ c_Equiv__Relations_Oequiv(X23,X22,X24)
| c_in(c_Pair(X21,X20,X24,X24),X22,tc_prod(X24,X24))
| ~ c_in(X20,X23,X24)
| ~ c_in(X21,X23,X24) ),
inference(variable_rename,[status(thm)],[c_0_714]) ).
fof(c_0_1325,plain,
! [X40,X41,X42] :
( c_in(c_Pair(v_sko__Transitive__Closure__Xtrancl__Xcases__1(X42,X41,X40),X41,t_a,t_a),X40,tc_prod(t_a,t_a))
| c_in(c_Pair(X42,X41,t_a,t_a),X40,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X42,X41,t_a,t_a),c_Transitive__Closure_Otrancl(X40,t_a),tc_prod(t_a,t_a)) ),
inference(variable_rename,[status(thm)],[c_0_715]) ).
fof(c_0_1326,plain,
! [X22,X23,X24,X25,X26] :
( c_Relation_OImage(X22,c_Set_Oinsert(X24,c_Orderings_Obot__class_Obot(tc_fun(X26,tc_bool)),X26),X26,X26) != c_Relation_OImage(X22,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X26,tc_bool)),X26),X26,X26)
| c_in(c_Pair(X24,X23,X26,X26),X22,tc_prod(X26,X26))
| ~ c_in(X23,X25,X26)
| ~ c_Equiv__Relations_Oequiv(X25,X22,X26) ),
inference(variable_rename,[status(thm)],[c_0_716]) ).
fof(c_0_1327,plain,
! [X6,X7] :
( c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X7,X7),X6),X6,X7,X7,X7) != X6
| c_Equiv__Relations_Oequiv(c_Relation_ODomain(X6,X7,X7),X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_717]) ).
fof(c_0_1328,plain,
! [X37,X38,X39,X40] :
( c_in(c_Pair(X39,X38,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X40,X37),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X39,X38,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X37,v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1(X39,X38,X37)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X37,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_Ounanimity(X40) ),
inference(variable_rename,[status(thm)],[c_0_718]) ).
fof(c_0_1329,plain,
! [X30,X31,X32,X33,X34,X35] :
( c_in(c_Pair(X31,X30,X35,X35),c_Relation_Oinv__image(X32,X33,X34,X35),tc_prod(X35,X35))
| ~ c_in(c_Pair(hAPP(X33,X31),hAPP(X33,X30),X34,X34),X32,tc_prod(X34,X34)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_719])])]) ).
fof(c_0_1330,plain,
! [X22,X23,X24,X25,X26] :
( c_in(c_Pair(X24,X23,X25,X26),X22,tc_prod(X25,X26))
| ~ c_in(X23,c_Relation_OImage(X22,c_Set_Oinsert(X24,c_Orderings_Obot__class_Obot(tc_fun(X25,tc_bool)),X25),X25,X26),X26) ),
inference(variable_rename,[status(thm)],[c_0_720]) ).
fof(c_0_1331,plain,
! [X20,X21,X22,X23,X24] :
( c_Relation_OImage(X22,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)),X24),X24,X24) = c_Relation_OImage(X22,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)),X24),X24,X24)
| ~ c_in(c_Pair(X21,X20,X24,X24),X22,tc_prod(X24,X24))
| ~ c_in(X20,X23,X24)
| ~ c_in(X21,X23,X24)
| ~ c_Equiv__Relations_Oequiv(X23,X22,X24) ),
inference(variable_rename,[status(thm)],[c_0_721]) ).
fof(c_0_1332,plain,
! [X22,X23,X24,X25,X26] :
( hBOOL(hAPP(X25,X23))
| hBOOL(hAPP(X25,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X25,X24,X22,X26)))
| ~ hBOOL(hAPP(X25,X24))
| ~ c_in(c_Pair(X24,X23,X26,X26),c_Transitive__Closure_Ortrancl(X22,X26),tc_prod(X26,X26)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_722])])]) ).
fof(c_0_1333,plain,
! [X22,X23,X24,X25,X26] :
( hBOOL(hAPP(X25,X24))
| hBOOL(hAPP(X25,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X25,X23,X22,X26)))
| ~ hBOOL(hAPP(X25,X23))
| ~ c_in(c_Pair(X24,X23,X26,X26),c_Transitive__Closure_Ortrancl(X22,X26),tc_prod(X26,X26)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_723])])]) ).
fof(c_0_1334,plain,
! [X13,X14] :
( c_Relation_Orel__comp(X13,X13,X14,X14,X14) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X14,X14),tc_bool))
| c_Wellfounded_Owf(X13,X14) ),
inference(variable_rename,[status(thm)],[c_0_724]) ).
fof(c_0_1335,plain,
! [X7,X8,X9,X10,X11,X12] :
( c_lessequals(c_Relation_OImage(X7,X8,X12,X11),X9,tc_fun(X11,tc_bool))
| ~ c_lessequals(X7,c_Product__Type_OSigma(X10,c_COMBK(X9,tc_fun(X11,tc_bool),X12),X12,X11),tc_fun(tc_prod(X12,X11),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_725]) ).
fof(c_0_1336,plain,
! [X5,X6,X7,X8] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X8,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X5,tc_fun(X8,tc_bool)),tc_fun(X8,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X5,X7,tc_fun(X8,tc_bool)),tc_fun(X8,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X7,X6,tc_fun(X8,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X6,X5,tc_fun(X8,tc_bool)),tc_fun(X8,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X5,X7,tc_fun(X8,tc_bool)),tc_fun(X8,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_726]) ).
fof(c_0_1337,plain,
! [X37] :
( c_Arrow__Order__Mirabelle_OIIA(X37)
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X37),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X37),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X37,v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X37)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X37),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X37),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X37,v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X37)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(variable_rename,[status(thm)],[c_0_727]) ).
fof(c_0_1338,plain,
! [X9,X10,X11,X12,X13,X14] :
( c_lessequals(c_Product__Type_OSigma(X12,c_COMBK(X10,tc_fun(X14,tc_bool),X13),X13,X14),c_Product__Type_OSigma(X11,c_COMBK(X10,tc_fun(X14,tc_bool),X13),X13,X14),tc_fun(tc_prod(X13,X14),tc_bool))
| ~ c_lessequals(X12,X11,tc_fun(X13,tc_bool))
| ~ c_in(X9,X10,X14) ),
inference(variable_rename,[status(thm)],[c_0_728]) ).
fof(c_0_1339,plain,
! [X22,X23,X24,X25,X26] :
( c_Relation_OImage(X22,c_Set_Oinsert(X24,c_Orderings_Obot__class_Obot(tc_fun(X26,tc_bool)),X26),X26,X26) = c_Relation_OImage(X22,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X26,tc_bool)),X26),X26,X26)
| ~ c_in(c_Pair(X24,X23,X26,X26),X22,tc_prod(X26,X26))
| ~ c_Equiv__Relations_Oequiv(X25,X22,X26) ),
inference(variable_rename,[status(thm)],[c_0_729]) ).
fof(c_0_1340,plain,
! [X20,X21,X22,X23,X24] :
( c_Relation_OImage(X22,c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)),X24),X24,X24) = c_Relation_OImage(X22,c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)),X24),X24,X24)
| ~ c_in(c_Pair(X21,X20,X24,X24),X22,tc_prod(X24,X24))
| ~ c_Equiv__Relations_Oequiv(X23,X22,X24) ),
inference(variable_rename,[status(thm)],[c_0_730]) ).
fof(c_0_1341,plain,
! [X20,X21,X22,X23,X24,X25] :
( X21 = X20
| ~ c_in(c_Pair(X22,X20,X25,X24),X23,tc_prod(X25,X24))
| ~ c_in(c_Pair(X22,X21,X25,X24),X23,tc_prod(X25,X24))
| ~ c_Relation_Osingle__valued(X23,X25,X24) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_731])])]) ).
fof(c_0_1342,plain,
! [X20,X21,X22,X23] :
( c_in(c_Pair(X21,X20,X23,X23),hAPP(c_Relation_Oconverse(X23,X23),c_Transitive__Closure_Otrancl(X22,X23)),tc_prod(X23,X23))
| ~ c_in(c_Pair(X21,X20,X23,X23),c_Transitive__Closure_Otrancl(hAPP(c_Relation_Oconverse(X23,X23),X22),X23),tc_prod(X23,X23)) ),
inference(variable_rename,[status(thm)],[c_0_732]) ).
fof(c_0_1343,plain,
! [X22,X23,X24,X25,X26] :
( c_in(X23,c_Relation_OImage(X22,c_Set_Oinsert(X24,c_Orderings_Obot__class_Obot(tc_fun(X25,tc_bool)),X25),X25,X26),X26)
| ~ c_in(c_Pair(X24,X23,X25,X26),X22,tc_prod(X25,X26)) ),
inference(variable_rename,[status(thm)],[c_0_733]) ).
fof(c_0_1344,plain,
! [X20,X21,X22,X23] :
( c_in(c_Pair(X21,X20,X23,X23),c_Transitive__Closure_Otrancl(hAPP(c_Relation_Oconverse(X23,X23),X22),X23),tc_prod(X23,X23))
| ~ c_in(c_Pair(X21,X20,X23,X23),hAPP(c_Relation_Oconverse(X23,X23),c_Transitive__Closure_Otrancl(X22,X23)),tc_prod(X23,X23)) ),
inference(variable_rename,[status(thm)],[c_0_734]) ).
fof(c_0_1345,plain,
! [X22,X23,X24,X25] :
( c_Relation_OImage(X22,c_Set_Oinsert(X24,c_Orderings_Obot__class_Obot(tc_fun(X25,tc_bool)),X25),X25,X25) != c_Relation_OImage(X22,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X25,tc_bool)),X25),X25,X25)
| ~ c_in(X23,c_Relation_OField(X22,X25),X25)
| ~ c_in(X24,c_Relation_OField(X22,X25),X25)
| ~ c_Relation_Oantisym(X22,X25)
| ~ c_Relation_Orefl__on(c_Relation_OField(X22,X25),X22,X25)
| X24 = X23 ),
inference(variable_rename,[status(thm)],[c_0_735]) ).
fof(c_0_1346,plain,
! [X20,X21,X22,X23] :
( c_Wellfounded_Owf(X22,X23)
| ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X20,X21,X23,X23),X22,tc_prod(X23,X23)),X23) ),
inference(variable_rename,[status(thm)],[c_0_736]) ).
fof(c_0_1347,plain,
! [X20,X21,X22,X23] :
( c_Wellfounded_Oacyclic(X22,X23)
| ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X20,X21,X23,X23),X22,tc_prod(X23,X23)),X23) ),
inference(variable_rename,[status(thm)],[c_0_737]) ).
fof(c_0_1348,plain,
! [X22,X23,X24,X25] :
( X24 = X23
| ~ c_in(c_Pair(X23,X24,X25,X25),X22,tc_prod(X25,X25))
| ~ c_in(c_Pair(X24,X23,X25,X25),X22,tc_prod(X25,X25))
| ~ c_Relation_Oantisym(X22,X25) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_738])])]) ).
fof(c_0_1349,plain,
! [X20,X21,X22,X23] :
( X21 = X20
| ~ c_in(c_Pair(X20,X21,X23,X23),X22,tc_prod(X23,X23))
| ~ c_in(c_Pair(X21,X20,X23,X23),X22,tc_prod(X23,X23))
| ~ c_Relation_Oantisym(X22,X23) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_739])])]) ).
fof(c_0_1350,plain,
! [X22,X23,X24,X25] :
( ~ c_in(c_Pair(X22,X24,X25,X25),X23,tc_prod(X25,X25))
| ~ c_in(c_Pair(X24,X22,X25,X25),X23,tc_prod(X25,X25))
| ~ c_Wellfounded_Owf(X23,X25) ),
inference(variable_rename,[status(thm)],[c_0_740]) ).
fof(c_0_1351,plain,
! [X21,X22,X23,X24] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X22,X21,X24,X23),X22,X23,X24),X21,tc_prod(X23,X24))
| ~ c_in(X22,c_Relation_ORange(X21,X23,X24),X24) ),
inference(variable_rename,[status(thm)],[c_0_741]) ).
fof(c_0_1352,plain,
! [X22,X23,X24,X25] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X23,X22,X25,X24),X23,X24,X25),X22,tc_prod(X24,X25))
| ~ c_in(X23,c_Relation_ORange(X22,X24,X25),X25) ),
inference(variable_rename,[status(thm)],[c_0_742]) ).
fof(c_0_1353,plain,
! [X22,X23,X24,X25] :
( c_in(c_Pair(X23,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X23,X22,X25,X24),X25,X24),X22,tc_prod(X25,X24))
| ~ c_in(X23,c_Relation_ODomain(X22,X25,X24),X25) ),
inference(variable_rename,[status(thm)],[c_0_743]) ).
fof(c_0_1354,plain,
! [X22,X23,X24,X25] :
( c_in(c_Pair(X23,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X23,X22,X25,X24),X25,X24),X22,tc_prod(X25,X24))
| ~ c_in(X23,c_Relation_ODomain(X22,X25,X24),X25) ),
inference(variable_rename,[status(thm)],[c_0_744]) ).
fof(c_0_1355,plain,
! [X22,X23,X24,X25] : c_Relation_OField(c_Set_Oinsert(c_Pair(X24,X23,X25,X25),X22,tc_prod(X25,X25)),X25) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X24,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X25,tc_bool)),X25),X25),c_Relation_OField(X22,X25),tc_fun(X25,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_745]) ).
fof(c_0_1356,plain,
! [X20,X21,X22,X23] :
( c_in(c_Pair(X20,X21,X23,X23),c_Transitive__Closure_Ortrancl(X22,X23),tc_prod(X23,X23))
| ~ c_in(c_Pair(X21,X20,X23,X23),c_Transitive__Closure_Ortrancl(hAPP(c_Relation_Oconverse(X23,X23),X22),X23),tc_prod(X23,X23)) ),
inference(variable_rename,[status(thm)],[c_0_746]) ).
fof(c_0_1357,plain,
! [X20,X21,X22,X23] :
( c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X20,X21,X23,X23),X22,tc_prod(X23,X23)),X23)
| c_in(c_Pair(X21,X20,X23,X23),c_Transitive__Closure_Ortrancl(X22,X23),tc_prod(X23,X23))
| ~ c_Wellfounded_Owf(X22,X23) ),
inference(variable_rename,[status(thm)],[c_0_747]) ).
fof(c_0_1358,plain,
! [X20,X21,X22,X23] :
( c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X20,X21,X23,X23),X22,tc_prod(X23,X23)),X23)
| c_in(c_Pair(X21,X20,X23,X23),c_Transitive__Closure_Ortrancl(X22,X23),tc_prod(X23,X23))
| ~ c_Wellfounded_Oacyclic(X22,X23) ),
inference(variable_rename,[status(thm)],[c_0_748]) ).
fof(c_0_1359,plain,
! [X22,X23,X24,X25,X26,X27] :
( c_in(X22,hAPP(X24,X23),X26)
| ~ c_in(c_Pair(X23,X22,X27,X26),c_Product__Type_OSigma(X25,X24,X27,X26),tc_prod(X27,X26)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_749])])]) ).
fof(c_0_1360,plain,
! [X22,X23,X24,X25,X26,X27] :
( c_in(X23,X25,X27)
| ~ c_in(c_Pair(X23,X22,X27,X26),c_Product__Type_OSigma(X25,X24,X27,X26),tc_prod(X27,X26)) ),
inference(variable_rename,[status(thm)],[c_0_750]) ).
fof(c_0_1361,plain,
! [X40,X41,X42] :
( c_in(c_Pair(X42,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X42,X41,X40),t_a,t_a),c_Transitive__Closure_Ortrancl(X40,t_a),tc_prod(t_a,t_a))
| X41 = X42
| ~ c_in(c_Pair(X42,X41,t_a,t_a),c_Transitive__Closure_Ortrancl(X40,t_a),tc_prod(t_a,t_a)) ),
inference(variable_rename,[status(thm)],[c_0_751]) ).
fof(c_0_1362,plain,
! [X20,X21,X22,X23] :
( c_in(c_Pair(X21,X20,X23,X23),c_Transitive__Closure_Ortrancl(hAPP(c_Relation_Oconverse(X23,X23),X22),X23),tc_prod(X23,X23))
| ~ c_in(c_Pair(X20,X21,X23,X23),c_Transitive__Closure_Ortrancl(X22,X23),tc_prod(X23,X23)) ),
inference(variable_rename,[status(thm)],[c_0_752]) ).
fof(c_0_1363,plain,
! [X40,X41,X42] :
( c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X42,X41,X40),X41,t_a,t_a),X40,tc_prod(t_a,t_a))
| X41 = X42
| ~ c_in(c_Pair(X42,X41,t_a,t_a),c_Transitive__Closure_Ortrancl(X40,t_a),tc_prod(t_a,t_a)) ),
inference(variable_rename,[status(thm)],[c_0_753]) ).
fof(c_0_1364,plain,
! [X20,X21,X22,X23,X24] :
( c_Equiv__Relations_Oquotient(c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)),X24),X22,X24) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)),X24),X22,X24)
| ~ c_in(c_Pair(X21,X20,X24,X24),X22,tc_prod(X24,X24))
| ~ c_in(X20,X23,X24)
| ~ c_in(X21,X23,X24)
| ~ c_Equiv__Relations_Oequiv(X23,X22,X24) ),
inference(variable_rename,[status(thm)],[c_0_754]) ).
fof(c_0_1365,plain,
! [X13,X14,X15,X16,X17] :
( c_Relation_OImage(X13,c_Lattices_Olower__semilattice__class_Oinf(X15,X14,tc_fun(X16,tc_bool)),X16,X17) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X13,X15,X16,X17),c_Relation_OImage(X13,X14,X16,X17),tc_fun(X17,tc_bool))
| ~ c_Relation_Osingle__valued(hAPP(c_Relation_Oconverse(X16,X17),X13),X17,X16) ),
inference(variable_rename,[status(thm)],[c_0_755]) ).
fof(c_0_1366,plain,
! [X20,X21,X22,X23,X24] :
( c_Equiv__Relations_Oquotient(c_Set_Oinsert(X21,c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)),X24),X22,X24) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(X20,c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)),X24),X22,X24)
| ~ c_in(X20,X23,X24)
| ~ c_in(X21,X23,X24)
| ~ c_Equiv__Relations_Oequiv(X23,X22,X24)
| c_in(c_Pair(X21,X20,X24,X24),X22,tc_prod(X24,X24)) ),
inference(variable_rename,[status(thm)],[c_0_756]) ).
fof(c_0_1367,plain,
! [X38,X39] :
( c_Arrow__Order__Mirabelle_OIIA(X39)
| c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X39),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X39),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X39),X38),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X39),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X39),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X39),X38),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(variable_rename,[status(thm)],[c_0_757]) ).
fof(c_0_1368,plain,
! [X38,X39] :
( c_Arrow__Order__Mirabelle_OIIA(X39)
| c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X39),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X39),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X39),X38),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X39),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X39),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X39),X38),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(variable_rename,[status(thm)],[c_0_758]) ).
fof(c_0_1369,plain,
! [X9,X10,X11] :
( ~ c_in(c_Pair(X9,X9,X11,X11),X10,tc_prod(X11,X11))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X10,X11),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X10,X11),X11,X11),c_Transitive__Closure_Otrancl(X10,X11),tc_prod(X11,X11)) ),
inference(variable_rename,[status(thm)],[c_0_759]) ).
fof(c_0_1370,plain,
! [X22,X23,X24,X25,X26] :
( c_in(c_Pair(X23,X24,X25,X26),X22,tc_prod(X25,X26))
| ~ c_in(c_Pair(X24,X23,X26,X25),hAPP(c_Relation_Oconverse(X25,X26),X22),tc_prod(X26,X25)) ),
inference(variable_rename,[status(thm)],[c_0_760]) ).
fof(c_0_1371,plain,
! [X14,X15,X16,X17,X18] : c_Relation_OImage(c_Lattices_Oupper__semilattice__class_Osup(X15,X14,tc_fun(tc_prod(X17,X18),tc_bool)),X16,X17,X18) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X15,X16,X17,X18),c_Relation_OImage(X14,X16,X17,X18),tc_fun(X18,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_761]) ).
fof(c_0_1372,plain,
! [X22,X23,X24,X25,X26] :
( c_in(c_Pair(X23,X24,X25,X26),hAPP(c_Relation_Oconverse(X26,X25),X22),tc_prod(X25,X26))
| ~ c_in(c_Pair(X24,X23,X26,X25),X22,tc_prod(X26,X25)) ),
inference(variable_rename,[status(thm)],[c_0_762]) ).
fof(c_0_1373,plain,
! [X22,X23,X24,X25,X26] :
( c_in(c_Pair(X24,X23,X26,X25),hAPP(c_Relation_Oconverse(X25,X26),X22),tc_prod(X26,X25))
| ~ c_in(c_Pair(X23,X24,X25,X26),X22,tc_prod(X25,X26)) ),
inference(variable_rename,[status(thm)],[c_0_763]) ).
fof(c_0_1374,plain,
! [X30,X31,X32,X33,X34,X35] :
( c_in(hAPP(X31,X30),X32,X34)
| ~ c_in(X30,X33,X35)
| ~ c_in(X31,c_FuncSet_OPi(X33,c_COMBK(X32,tc_fun(X34,tc_bool),X35),X35,X34),tc_fun(X35,X34)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_764])])]) ).
fof(c_0_1375,plain,
! [X22,X23,X24,X25] :
( c_in(c_Pair(X23,X22,X25,X25),c_Transitive__Closure_Otrancl(X24,X25),tc_prod(X25,X25))
| X23 = X22
| ~ 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_765]) ).
fof(c_0_1376,plain,
! [X20,X21,X22,X23] :
( c_in(c_Pair(X21,X20,X23,X23),c_Transitive__Closure_Otrancl(X22,X23),tc_prod(X23,X23))
| X21 = X20
| ~ c_in(c_Pair(X21,X20,X23,X23),c_Transitive__Closure_Ortrancl(X22,X23),tc_prod(X23,X23)) ),
inference(variable_rename,[status(thm)],[c_0_766]) ).
fof(c_0_1377,plain,
! [X20,X21,X22,X23] :
( c_in(c_Pair(X21,X20,X23,X23),c_Transitive__Closure_Ortrancl(X22,X23),tc_prod(X23,X23))
| ~ c_in(c_Pair(X21,X20,X23,X23),c_Transitive__Closure_Otrancl(X22,X23),tc_prod(X23,X23))
| X21 = X20 ),
inference(variable_rename,[status(thm)],[c_0_767]) ).
fof(c_0_1378,plain,
! [X22,X23,X24,X25] :
( c_in(c_Pair(X24,X23,X25,X25),c_Transitive__Closure_Ortrancl(X22,X25),tc_prod(X25,X25))
| ~ c_in(c_Pair(X24,X23,X25,X25),c_Transitive__Closure_Otrancl(X22,X25),tc_prod(X25,X25)) ),
inference(variable_rename,[status(thm)],[c_0_768]) ).
fof(c_0_1379,plain,
! [X21,X22,X23,X24,X25,X26] :
( c_in(X23,c_Relation_OImage(X22,X24,X25,X26),X26)
| ~ c_in(c_Pair(X21,X23,X25,X26),X22,tc_prod(X25,X26))
| ~ c_in(X21,X24,X25) ),
inference(variable_rename,[status(thm)],[c_0_769]) ).
fof(c_0_1380,plain,
! [X22,X23,X24,X25,X26,X27] :
( c_in(X23,c_Relation_OImage(X22,X25,X27,X26),X26)
| ~ c_in(c_Pair(X24,X23,X27,X26),X22,tc_prod(X27,X26))
| ~ c_in(X24,X25,X27) ),
inference(variable_rename,[status(thm)],[c_0_770]) ).
fof(c_0_1381,plain,
! [X24,X25,X26,X27,X28] : c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(X25,X24,tc_fun(X28,tc_bool)),X26,X28,X27) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X25,X26,X28,X27),c_Product__Type_OSigma(X24,X26,X28,X27),tc_fun(tc_prod(X28,X27),tc_bool)),
inference(variable_rename,[status(thm)],[c_0_771]) ).
fof(c_0_1382,plain,
! [X24,X25,X26,X27,X28] : c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(X25,X24,tc_fun(X28,tc_bool)),X26,X28,X27) = c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(X25,X26,X28,X27),c_Product__Type_OSigma(X24,X26,X28,X27),tc_fun(tc_prod(X28,X27),tc_bool)),
inference(variable_rename,[status(thm)],[c_0_772]) ).
fof(c_0_1383,plain,
! [X22,X23,X24,X25] :
( c_in(c_Pair(X24,X23,X25,X25),c_Transitive__Closure_Otrancl(X22,X25),tc_prod(X25,X25))
| ~ c_in(c_Pair(X24,X23,X25,X25),X22,tc_prod(X25,X25)) ),
inference(variable_rename,[status(thm)],[c_0_773]) ).
fof(c_0_1384,plain,
! [X22,X23,X24,X25] :
( c_in(c_Pair(X23,X24,X25,X25),X22,tc_prod(X25,X25))
| ~ c_in(c_Pair(X24,X23,X25,X25),X22,tc_prod(X25,X25))
| ~ c_Relation_Osym(X22,X25) ),
inference(variable_rename,[status(thm)],[c_0_774]) ).
fof(c_0_1385,plain,
! [X20,X21,X22,X23] :
( c_in(c_Pair(X20,X21,X23,X23),X22,tc_prod(X23,X23))
| ~ c_in(c_Pair(X21,X20,X23,X23),X22,tc_prod(X23,X23))
| ~ c_Relation_Osym(X22,X23) ),
inference(variable_rename,[status(thm)],[c_0_775]) ).
fof(c_0_1386,plain,
! [X38] :
( c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X38),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X38),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(variable_rename,[status(thm)],[c_0_776]) ).
fof(c_0_1387,plain,
! [X38] :
( c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X38),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X38),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(variable_rename,[status(thm)],[c_0_777]) ).
fof(c_0_1388,plain,
! [X50,X51,X52,X53] :
( c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X53,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X52 = X50
| ~ c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X53,X50),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(variable_rename,[status(thm)],[c_0_778]) ).
fof(c_0_1389,plain,
! [X50,X51,X52,X53] :
( c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X53,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X51 = X50
| ~ c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X53,X50),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(variable_rename,[status(thm)],[c_0_779]) ).
fof(c_0_1390,plain,
! [X50,X51,X52,X53] :
( c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X53,X50),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X53,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X52 = X50
| X51 = X50 ),
inference(variable_rename,[status(thm)],[c_0_780]) ).
fof(c_0_1391,plain,
! [X50,X51,X52,X53] :
( c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X53,X50),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X53,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X52 = X51
| X51 = X50 ),
inference(variable_rename,[status(thm)],[c_0_781]) ).
fof(c_0_1392,plain,
! [X50,X51,X52,X53] :
( c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X53,X50),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X53,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X51 = X50
| X52 = X50 ),
inference(variable_rename,[status(thm)],[c_0_782]) ).
fof(c_0_1393,plain,
! [X50,X51,X52,X53] :
( c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X53,X50),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X52,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X53,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X52 = X51
| X52 = X50 ),
inference(variable_rename,[status(thm)],[c_0_783]) ).
fof(c_0_1394,plain,
! [X13,X14,X15,X16,X17] : c_Relation_OImage(X13,c_Lattices_Oupper__semilattice__class_Osup(X15,X14,tc_fun(X16,tc_bool)),X16,X17) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X13,X15,X16,X17),c_Relation_OImage(X13,X14,X16,X17),tc_fun(X17,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_784]) ).
fof(c_0_1395,plain,
! [X18,X19,X20,X21] : c_Relation_Orel__comp(X18,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X19,X20),tc_bool)),X21,X19,X20) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X21,X20),tc_bool)),
inference(variable_rename,[status(thm)],[c_0_785]) ).
fof(c_0_1396,plain,
! [X18,X19,X20,X21] : c_Relation_Orel__comp(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X21,X19),tc_bool)),X18,X21,X19,X20) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X21,X20),tc_bool)),
inference(variable_rename,[status(thm)],[c_0_786]) ).
fof(c_0_1397,plain,
! [X20,X21,X22,X23,X24] :
( ~ c_in(X20,X23,X24)
| ~ c_in(c_Pair(X20,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X23,X22,X24),X24,X24),X22,tc_prod(X24,X24))
| ~ c_in(X21,X23,X24)
| ~ c_Wellfounded_Owf(X22,X24) ),
inference(variable_rename,[status(thm)],[c_0_787]) ).
fof(c_0_1398,plain,
! [X20,X21,X22,X23,X24] :
( ~ c_in(X20,X23,X24)
| ~ c_in(c_Pair(X20,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X23,X22,X24),X24,X24),X22,tc_prod(X24,X24))
| ~ c_in(X21,X23,X24)
| ~ c_Wellfounded_Owf(X22,X24) ),
inference(variable_rename,[status(thm)],[c_0_788]) ).
fof(c_0_1399,plain,
! [X9,X10,X11] :
( c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Relation_Oconverse(X11,X11),X10),c_Transitive__Closure_Ortrancl(X10,X11),tc_fun(tc_prod(X11,X11),tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X11,X11),tc_bool))
| ~ c_in(c_Pair(X9,X9,X11,X11),c_Transitive__Closure_Otrancl(X10,X11),tc_prod(X11,X11)) ),
inference(variable_rename,[status(thm)],[c_0_789]) ).
fof(c_0_1400,plain,
! [X22,X23,X24,X25,X26] :
( hBOOL(hAPP(X25,X24))
| hBOOL(hAPP(X25,X22))
| ~ c_in(c_Pair(X22,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X25,X23,X26),X26,X26),X23,tc_prod(X26,X26))
| ~ c_in(X24,c_Wellfounded_Oacc(X23,X26),X26) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_790])])]) ).
fof(c_0_1401,plain,
! [X22,X23,X24,X25,X26] :
( hBOOL(hAPP(X25,X24))
| hBOOL(hAPP(X25,X22))
| ~ c_in(c_Pair(X22,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X25,X23,X26),X26,X26),X23,tc_prod(X26,X26))
| ~ c_in(X24,c_Wellfounded_Oacc(X23,X26),X26) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_791])])]) ).
fof(c_0_1402,plain,
! [X9,X10,X11,X12,X13] :
( c_in(c_Pair(X9,X10,X13,X13),X11,tc_prod(X13,X13))
| c_in(c_Pair(X10,X9,X13,X13),X11,tc_prod(X13,X13))
| X10 = X9
| ~ c_in(X9,X12,X13)
| ~ c_in(X10,X12,X13)
| ~ c_Relation_Ototal__on(X12,X11,X13) ),
inference(variable_rename,[status(thm)],[c_0_792]) ).
fof(c_0_1403,plain,
! [X36,X37,X38,X39,X40,X41] :
( c_lessequals(c_Relation_OImage(X36,X38,X41,X40),c_Relation_OImage(X37,X39,X41,X40),tc_fun(X40,tc_bool))
| ~ c_lessequals(X38,X39,tc_fun(X41,tc_bool))
| ~ c_lessequals(X36,X37,tc_fun(tc_prod(X41,X40),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_793]) ).
fof(c_0_1404,plain,
! [X6,X7,X8] :
( c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X8,X8),X6),X6,X8,X8,X8) = X6
| ~ c_Equiv__Relations_Oequiv(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_794]) ).
fof(c_0_1405,plain,
! [X22,X23,X24,X25,X26] : c_Relation_ORange(c_Set_Oinsert(c_Pair(X24,X23,X25,X26),X22,tc_prod(X25,X26)),X25,X26) = c_Set_Oinsert(X23,c_Relation_ORange(X22,X25,X26),X26),
inference(variable_rename,[status(thm)],[c_0_795]) ).
fof(c_0_1406,plain,
! [X22,X23,X24,X25,X26] : c_Relation_ODomain(c_Set_Oinsert(c_Pair(X24,X23,X26,X25),X22,tc_prod(X26,X25)),X26,X25) = c_Set_Oinsert(X24,c_Relation_ODomain(X22,X26,X25),X26),
inference(variable_rename,[status(thm)],[c_0_796]) ).
fof(c_0_1407,plain,
! [X9,X10,X11,X12,X13,X14] :
( c_Product__Type_OSigma(X12,c_COMBK(X10,tc_fun(X14,tc_bool),X13),X13,X14) != c_Product__Type_OSigma(X11,c_COMBK(X10,tc_fun(X14,tc_bool),X13),X13,X14)
| ~ c_in(X9,X10,X14)
| X12 = X11 ),
inference(variable_rename,[status(thm)],[c_0_797]) ).
fof(c_0_1408,plain,
! [X22,X23,X24,X25,X26] :
( hBOOL(hAPP(X25,X24))
| hBOOL(hAPP(X25,X22))
| ~ c_in(c_Pair(X22,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X25,X23,X26),X26,X26),X23,tc_prod(X26,X26))
| ~ c_Wellfounded_Owf(X23,X26) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_798])])]) ).
fof(c_0_1409,plain,
! [X41,X42,X43,X44,X45] :
( hBOOL(hAPP(X44,X42))
| hBOOL(hAPP(X44,X41))
| ~ c_in(c_Pair(X41,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X44,X43,X45),X45,X45),X43,tc_prod(X45,X45))
| ~ c_Wellfounded_Owf(X43,X45) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_799])])]) ).
fof(c_0_1410,plain,
! [X20,X21,X22,X23,X24] :
( hBOOL(hAPP(X23,X21))
| hBOOL(hAPP(X23,X20))
| ~ c_in(c_Pair(X20,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X23,X22,X24),X24,X24),X22,tc_prod(X24,X24))
| ~ c_Wellfounded_Owf(X22,X24) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_800])])]) ).
fof(c_0_1411,plain,
! [X22,X23,X24,X25,X26] :
( hBOOL(hAPP(X25,X24))
| hBOOL(hAPP(X25,X22))
| ~ c_in(c_Pair(X22,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X25,X23,X26),X26,X26),X23,tc_prod(X26,X26))
| ~ c_Wellfounded_Owf(X23,X26) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_801])])]) ).
fof(c_0_1412,plain,
! [X30,X31,X32,X33,X34,X35] :
( hAPP(X33,X31) = hAPP(X33,X30)
| ~ c_in(c_Pair(X31,X30,X35,X35),X32,tc_prod(X35,X35))
| ~ c_Equiv__Relations_Ocongruent(X32,X33,X35,X34) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_802])])]) ).
fof(c_0_1413,plain,
! [X22,X23,X24,X25,X26,X27] :
( c_in(c_Pair(X23,X22,X27,X26),c_Product__Type_OSigma(X25,X24,X27,X26),tc_prod(X27,X26))
| ~ c_in(X22,hAPP(X24,X23),X26)
| ~ c_in(X23,X25,X27) ),
inference(variable_rename,[status(thm)],[c_0_803]) ).
fof(c_0_1414,plain,
! [X22,X23,X24,X25,X26,X27] :
( c_in(c_Pair(X23,X22,X27,X26),c_Product__Type_OSigma(X25,X24,X27,X26),tc_prod(X27,X26))
| ~ c_in(X22,hAPP(X24,X23),X26)
| ~ c_in(X23,X25,X27) ),
inference(variable_rename,[status(thm)],[c_0_804]) ).
fof(c_0_1415,plain,
! [X7,X8,X9,X10] : c_lessequals(c_Relation_ORange(c_Lattices_Olower__semilattice__class_Oinf(X8,X7,tc_fun(tc_prod(X9,X10),tc_bool)),X9,X10),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(X8,X9,X10),c_Relation_ORange(X7,X9,X10),tc_fun(X10,tc_bool)),tc_fun(X10,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_805]) ).
fof(c_0_1416,plain,
! [X7,X8,X9,X10] : c_lessequals(c_Relation_ODomain(c_Lattices_Olower__semilattice__class_Oinf(X8,X7,tc_fun(tc_prod(X10,X9),tc_bool)),X10,X9),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X8,X10,X9),c_Relation_ODomain(X7,X10,X9),tc_fun(X10,tc_bool)),tc_fun(X10,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_806]) ).
fof(c_0_1417,plain,
! [X13,X14] : c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X13,X14),c_Transitive__Closure_Ortrancl(X13,X14),X14,X14,X14) = c_Transitive__Closure_Ortrancl(X13,X14),
inference(variable_rename,[status(thm)],[c_0_807]) ).
fof(c_0_1418,plain,
! [X37] :
( c_Arrow__Order__Mirabelle_OIIA(X37)
| c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X37),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X37),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X37,v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X37)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X37),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X37),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X37,v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X37)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(variable_rename,[status(thm)],[c_0_808]) ).
fof(c_0_1419,plain,
! [X6,X7] : c_Transitive__Closure_Otrancl(X6,X7) = c_Relation_Orel__comp(X6,c_Transitive__Closure_Ortrancl(X6,X7),X7,X7,X7),
inference(variable_rename,[status(thm)],[c_0_809]) ).
fof(c_0_1420,plain,
! [X6,X7] : c_Transitive__Closure_Otrancl(X6,X7) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X6,X7),X6,X7,X7,X7),
inference(variable_rename,[status(thm)],[c_0_810]) ).
fof(c_0_1421,plain,
! [X13,X14,X15] : c_Relation_Orel__comp(X13,c_Relation_OId(X14),X15,X14,X14) = X13,
inference(variable_rename,[status(thm)],[c_0_811]) ).
fof(c_0_1422,plain,
! [X13,X14,X15] : c_Relation_Orel__comp(c_Relation_OId(X15),X13,X15,X15,X14) = X13,
inference(variable_rename,[status(thm)],[c_0_812]) ).
fof(c_0_1423,plain,
! [X48,X49,X50,X51] :
( hBOOL(hAPP(X51,X49))
| c_in(X48,c_Wellfounded_Oacc(X50,t_a),t_a)
| ~ c_in(c_Pair(X48,v_sko__Wellfounded__Xacc__Xinducts__1(X51,X50),t_a,t_a),X50,tc_prod(t_a,t_a))
| ~ c_in(X49,c_Wellfounded_Oacc(X50,t_a),t_a) ),
inference(variable_rename,[status(thm)],[c_0_813]) ).
fof(c_0_1424,plain,
! [X48,X49,X50,X51] :
( hBOOL(hAPP(X51,X49))
| c_in(X48,c_Wellfounded_Oacc(X50,t_a),t_a)
| ~ c_in(c_Pair(X48,v_sko__Wellfounded__Xacc__Xinduct__1(X51,X50),t_a,t_a),X50,tc_prod(t_a,t_a))
| ~ c_in(X49,c_Wellfounded_Oacc(X50,t_a),t_a) ),
inference(variable_rename,[status(thm)],[c_0_814]) ).
fof(c_0_1425,plain,
! [X22,X23,X24,X25] :
( c_in(X23,c_Wellfounded_Oacc(X22,X25),X25)
| ~ c_in(X24,c_Wellfounded_Oacc(X22,X25),X25)
| ~ c_in(c_Pair(X23,X24,X25,X25),c_Transitive__Closure_Ortrancl(X22,X25),tc_prod(X25,X25)) ),
inference(variable_rename,[status(thm)],[c_0_815]) ).
fof(c_0_1426,plain,
! [X22,X23,X24,X25] :
( c_in(X23,c_Wellfounded_Oacc(X22,X25),X25)
| ~ c_in(c_Pair(X23,X24,X25,X25),c_Transitive__Closure_Ortrancl(X22,X25),tc_prod(X25,X25))
| ~ c_in(X24,c_Wellfounded_Oacc(X22,X25),X25) ),
inference(variable_rename,[status(thm)],[c_0_816]) ).
fof(c_0_1427,plain,
! [X20,X21,X22,X23] :
( hBOOL(hAPP(X23,X21))
| hBOOL(hAPP(X23,X20))
| ~ c_in(c_Pair(X20,v_sko__Wellfounded__Xacc__Xinduct__1(X23,X22),t_a,t_a),X22,tc_prod(t_a,t_a))
| ~ c_in(X21,c_Wellfounded_Oacc(X22,t_a),t_a) ),
inference(variable_rename,[status(thm)],[c_0_817]) ).
fof(c_0_1428,plain,
! [X20,X21,X22,X23] :
( hBOOL(hAPP(X23,X21))
| hBOOL(hAPP(X23,X20))
| ~ c_in(c_Pair(X20,v_sko__Wellfounded__Xacc__Xinducts__1(X23,X22),t_a,t_a),X22,tc_prod(t_a,t_a))
| ~ c_in(X21,c_Wellfounded_Oacc(X22,t_a),t_a) ),
inference(variable_rename,[status(thm)],[c_0_818]) ).
fof(c_0_1429,plain,
! [X22,X23,X24,X25] :
( c_in(X23,c_Relation_OImage(X22,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X25,tc_bool)),X25),X25,X25),X25)
| ~ c_in(X23,X24,X25)
| ~ c_Equiv__Relations_Oequiv(X24,X22,X25) ),
inference(variable_rename,[status(thm)],[c_0_819]) ).
fof(c_0_1430,plain,
! [X22,X23,X24,X25] :
( c_in(X22,c_Wellfounded_Oacc(X23,X25),X25)
| ~ c_in(c_Pair(X22,X24,X25,X25),X23,tc_prod(X25,X25))
| ~ c_in(X24,c_Wellfounded_Oacc(X23,X25),X25) ),
inference(variable_rename,[status(thm)],[c_0_820]) ).
fof(c_0_1431,plain,
! [X22,X23,X24,X25] :
( c_in(X24,c_Wellfounded_Oacc(X22,X25),X25)
| ~ c_in(c_Pair(X24,X23,X25,X25),X22,tc_prod(X25,X25))
| ~ c_in(X23,c_Wellfounded_Oacc(X22,X25),X25) ),
inference(variable_rename,[status(thm)],[c_0_821]) ).
fof(c_0_1432,plain,
! [X6,X7] : c_lessequals(c_Transitive__Closure_Otrancl(X6,X7),c_Product__Type_OSigma(c_Relation_OField(X6,X7),c_COMBK(c_Relation_OField(X6,X7),tc_fun(X7,tc_bool),X7),X7,X7),tc_fun(tc_prod(X7,X7),tc_bool)),
inference(variable_rename,[status(thm)],[c_0_822]) ).
fof(c_0_1433,plain,
! [X20,X21,X22,X23] :
( X21 = X20
| ~ c_in(c_Pair(X21,X20,X23,X23),c_Transitive__Closure_Ortrancl(X22,X23),tc_prod(X23,X23))
| c_in(X21,c_Relation_ODomain(X22,X23,X23),X23) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_823])])]) ).
fof(c_0_1434,plain,
! [X30,X31,X32,X33,X34,X35] :
( ~ c_in(X30,X33,X35)
| c_in(hAPP(X31,X30),hAPP(X32,X30),X34)
| ~ c_in(X31,c_FuncSet_OPi(X33,X32,X35,X34),tc_fun(X35,X34)) ),
inference(variable_rename,[status(thm)],[c_0_824]) ).
fof(c_0_1435,plain,
! [X30,X31,X32,X33,X34,X35] :
( c_in(hAPP(X31,X30),hAPP(X32,X30),X34)
| ~ c_in(X30,X33,X35)
| ~ c_in(X31,c_FuncSet_OPi(X33,X32,X35,X34),tc_fun(X35,X34)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_825])])]) ).
fof(c_0_1436,plain,
! [X6,X7] :
( c_Nitpick_Orefl_H(X6,X7)
| ~ c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X6,X7),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X6,X7),X7,X7),X6,tc_prod(X7,X7)) ),
inference(variable_rename,[status(thm)],[c_0_826]) ).
fof(c_0_1437,plain,
! [X22,X23,X24,X25,X26] :
( c_in(X24,c_Relation_ODomain(X22,X26,X25),X26)
| ~ c_in(c_Pair(X24,X23,X26,X25),X22,tc_prod(X26,X25)) ),
inference(variable_rename,[status(thm)],[c_0_827]) ).
fof(c_0_1438,plain,
! [X22,X23,X24,X25,X26] :
( c_in(X24,c_Relation_ODomain(X23,X26,X25),X26)
| ~ c_in(c_Pair(X24,X22,X26,X25),X23,tc_prod(X26,X25)) ),
inference(variable_rename,[status(thm)],[c_0_828]) ).
fof(c_0_1439,plain,
! [X22,X23,X24,X25,X26] :
( c_in(X23,c_Relation_ORange(X22,X26,X25),X25)
| ~ c_in(c_Pair(X24,X23,X26,X25),X22,tc_prod(X26,X25)) ),
inference(variable_rename,[status(thm)],[c_0_829]) ).
fof(c_0_1440,plain,
! [X22,X23,X24,X25,X26] :
( c_in(X24,c_Relation_ORange(X23,X25,X26),X26)
| ~ c_in(c_Pair(X22,X24,X25,X26),X23,tc_prod(X25,X26)) ),
inference(variable_rename,[status(thm)],[c_0_830]) ).
fof(c_0_1441,plain,
! [X20,X21,X22,X23,X24] :
( c_in(X21,X23,X24)
| ~ c_in(c_Pair(X21,X20,X24,X24),X22,tc_prod(X24,X24))
| ~ c_Relation_Orefl__on(X23,X22,X24) ),
inference(variable_rename,[status(thm)],[c_0_831]) ).
fof(c_0_1442,plain,
! [X20,X21,X22,X23,X24] :
( c_in(X20,X23,X24)
| ~ c_in(c_Pair(X21,X20,X24,X24),X22,tc_prod(X24,X24))
| ~ c_Relation_Orefl__on(X23,X22,X24) ),
inference(variable_rename,[status(thm)],[c_0_832]) ).
fof(c_0_1443,plain,
! [X20,X21,X22,X23,X24] :
( c_in(X21,X23,X24)
| ~ c_in(c_Pair(X21,X20,X24,X24),X22,tc_prod(X24,X24))
| ~ c_Equiv__Relations_Oequiv(X23,X22,X24) ),
inference(variable_rename,[status(thm)],[c_0_833]) ).
fof(c_0_1444,plain,
! [X20,X21,X22,X23,X24] :
( c_in(X20,X23,X24)
| ~ c_in(c_Pair(X21,X20,X24,X24),X22,tc_prod(X24,X24))
| ~ c_Equiv__Relations_Oequiv(X23,X22,X24) ),
inference(variable_rename,[status(thm)],[c_0_834]) ).
fof(c_0_1445,plain,
! [X14,X15,X16] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X15,X16),c_Transitive__Closure_Ortrancl(X14,X16),tc_fun(tc_prod(X16,X16),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X15,X14,tc_fun(tc_prod(X16,X16),tc_bool)),X16),tc_fun(tc_prod(X16,X16),tc_bool)),
inference(variable_rename,[status(thm)],[c_0_835]) ).
fof(c_0_1446,plain,
! [X6,X7,X8] :
( c_lessequals(X6,c_Product__Type_OSigma(X7,c_COMBK(X7,tc_fun(X8,tc_bool),X8),X8,X8),tc_fun(tc_prod(X8,X8),tc_bool))
| ~ c_Equiv__Relations_Oequiv(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_836]) ).
fof(c_0_1447,plain,
! [X6,X7,X8] :
( c_lessequals(X6,c_Product__Type_OSigma(X7,c_COMBK(X7,tc_fun(X8,tc_bool),X8),X8,X8),tc_fun(tc_prod(X8,X8),tc_bool))
| ~ c_Relation_Orefl__on(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_837]) ).
fof(c_0_1448,plain,
! [X20,X21,X22,X23] :
( c_in(X21,X22,X23)
| ~ c_in(c_Pair(X21,X20,X23,X23),c_Relation_OId__on(X22,X23),tc_prod(X23,X23)) ),
inference(variable_rename,[status(thm)],[c_0_838]) ).
fof(c_0_1449,plain,
! [X37] :
( c_Arrow__Order__Mirabelle_Ounanimity(X37)
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3(X37),v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4(X37),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X37,v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2(X37)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(variable_rename,[status(thm)],[c_0_839]) ).
fof(c_0_1450,plain,
! [X9,X10,X11] :
( ~ c_in(c_Pair(X9,X9,X11,X11),c_Transitive__Closure_Otrancl(X10,X11),tc_prod(X11,X11))
| ~ c_Wellfounded_Oacyclic(X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_840]) ).
fof(c_0_1451,plain,
! [X5,X6] : c_lessequals(c_Relation_OId__on(X5,X6),c_Product__Type_OSigma(X5,c_COMBK(X5,tc_fun(X6,tc_bool),X6),X6,X6),tc_fun(tc_prod(X6,X6),tc_bool)),
inference(variable_rename,[status(thm)],[c_0_841]) ).
fof(c_0_1452,plain,
! [X13,X14,X15] :
( X14 = c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool))
| ~ c_lessequals(X14,c_Relation_OImage(X13,X14,X15,X15),tc_fun(X15,tc_bool))
| ~ c_Wellfounded_Owf(X13,X15) ),
inference(variable_rename,[status(thm)],[c_0_842]) ).
fof(c_0_1453,plain,
! [X20,X21,X22,X23] :
( X21 = X20
| ~ c_in(c_Pair(X21,X20,X23,X23),c_Relation_OId__on(X22,X23),tc_prod(X23,X23)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_843])])]) ).
fof(c_0_1454,plain,
! [X22,X23,X24] :
( ~ c_in(c_Pair(X23,X23,X24,X24),X22,tc_prod(X24,X24))
| ~ c_Wellfounded_Owf(X22,X24) ),
inference(variable_rename,[status(thm)],[c_0_844]) ).
fof(c_0_1455,plain,
! [X50,X51,X52] : ~ c_in(c_Pair(X50,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X52,X51),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(variable_rename,[status(thm)],[c_0_845]) ).
fof(c_0_1456,plain,
! [X50,X51] : ~ c_in(c_Pair(X50,X50,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X51,X50),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(variable_rename,[status(thm)],[c_0_846]) ).
fof(c_0_1457,plain,
! [X50,X51,X52] : ~ c_in(c_Pair(X51,X50,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X52,X51),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(variable_rename,[status(thm)],[c_0_847]) ).
fof(c_0_1458,plain,
! [X50,X51] : ~ c_in(c_Pair(X50,X50,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X51,X50),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(variable_rename,[status(thm)],[c_0_848]) ).
fof(c_0_1459,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Olattice(X23)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X22,X21,X23),c_Lattices_Olower__semilattice__class_Oinf(X22,X20,X23),X23),c_Lattices_Olower__semilattice__class_Oinf(X22,c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X23),X23),X23) ),
inference(variable_rename,[status(thm)],[c_0_849]) ).
fof(c_0_1460,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Olattice(X23)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X22,c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X23),X23),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X22,X21,X23),c_Lattices_Oupper__semilattice__class_Osup(X22,X20,X23),X23),X23) ),
inference(variable_rename,[status(thm)],[c_0_850]) ).
fof(c_0_1461,plain,
! [X22,X23,X24] :
( X23 = X22
| ~ c_in(c_Pair(X23,X22,X24,X24),c_Relation_OId(X24),tc_prod(X24,X24)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_851])])]) ).
fof(c_0_1462,plain,
! [X13,X14,X15] :
( c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X14,X13,X15),X13,X15,X15),X14,tc_prod(X15,X15))
| c_in(X13,c_Wellfounded_Oacc(X14,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_852]) ).
fof(c_0_1463,plain,
! [X9,X10,X11] :
( c_in(X9,c_Wellfounded_Oacc(X10,X11),X11)
| c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X10,X9,X11),X9,X11,X11),X10,tc_prod(X11,X11)) ),
inference(variable_rename,[status(thm)],[c_0_853]) ).
fof(c_0_1464,plain,
! [X30,X31,X32,X33] : hAPP(c_Relation_Oconverse(X33,X33),c_Relation_Oinv__image(X31,X30,X32,X33)) = c_Relation_Oinv__image(hAPP(c_Relation_Oconverse(X32,X32),X31),X30,X32,X33),
inference(variable_rename,[status(thm)],[c_0_854]) ).
fof(c_0_1465,plain,
! [X33,X34,X35,X36,X37] :
( c_Set_Oinsert(X36,c_Set_Oinsert(X35,c_Orderings_Obot__class_Obot(tc_fun(X37,tc_bool)),X37),X37) != c_Set_Oinsert(X34,c_Set_Oinsert(X33,c_Orderings_Obot__class_Obot(tc_fun(X37,tc_bool)),X37),X37)
| X35 = X34
| X35 = X33 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_855])])]) ).
fof(c_0_1466,plain,
! [X33,X34,X35,X36,X37] :
( c_Set_Oinsert(X36,c_Set_Oinsert(X35,c_Orderings_Obot__class_Obot(tc_fun(X37,tc_bool)),X37),X37) != c_Set_Oinsert(X34,c_Set_Oinsert(X33,c_Orderings_Obot__class_Obot(tc_fun(X37,tc_bool)),X37),X37)
| X36 = X33
| X35 = X33 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_856])])]) ).
fof(c_0_1467,plain,
! [X33,X34,X35,X36,X37] :
( c_Set_Oinsert(X36,c_Set_Oinsert(X35,c_Orderings_Obot__class_Obot(tc_fun(X37,tc_bool)),X37),X37) != c_Set_Oinsert(X34,c_Set_Oinsert(X33,c_Orderings_Obot__class_Obot(tc_fun(X37,tc_bool)),X37),X37)
| X35 = X34
| X36 = X34 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_857])])]) ).
fof(c_0_1468,plain,
! [X33,X34,X35,X36,X37] :
( c_Set_Oinsert(X36,c_Set_Oinsert(X35,c_Orderings_Obot__class_Obot(tc_fun(X37,tc_bool)),X37),X37) != c_Set_Oinsert(X34,c_Set_Oinsert(X33,c_Orderings_Obot__class_Obot(tc_fun(X37,tc_bool)),X37),X37)
| X36 = X33
| X36 = X34 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_858])])]) ).
fof(c_0_1469,plain,
! [X16,X17,X18] :
( c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X17,X18,X18),c_Relation_ORange(X16,X18,X18),tc_fun(X18,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X18,tc_bool))
| ~ c_Wellfounded_Owf(X16,X18)
| ~ c_Wellfounded_Owf(X17,X18)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X17,X16,tc_fun(tc_prod(X18,X18),tc_bool)),X18) ),
inference(variable_rename,[status(thm)],[c_0_859]) ).
fof(c_0_1470,plain,
! [X5,X6,X7,X8] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X8,tc_bool)),X5,tc_fun(X8,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Oupper__semilattice__class_Osup(X6,X5,tc_fun(X8,tc_bool)),tc_fun(X8,tc_bool))
| c_lessequals(X5,X7,tc_fun(X8,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_860]) ).
fof(c_0_1471,plain,
! [X14,X15,X16,X17] :
( c_in(X14,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X16,X15,tc_fun(tc_prod(X17,X17),tc_bool)),X17),tc_prod(X17,X17))
| ~ c_in(X14,c_Transitive__Closure_Ortrancl(X15,X17),tc_prod(X17,X17)) ),
inference(variable_rename,[status(thm)],[c_0_861]) ).
fof(c_0_1472,plain,
! [X14,X15,X16,X17] :
( c_in(X14,c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X16,X15,tc_fun(tc_prod(X17,X17),tc_bool)),X17),tc_prod(X17,X17))
| ~ c_in(X14,c_Transitive__Closure_Ortrancl(X16,X17),tc_prod(X17,X17)) ),
inference(variable_rename,[status(thm)],[c_0_862]) ).
fof(c_0_1473,plain,
! [X53,X54,X55,X56,X57,X58] :
( c_Pair(X56,X54,X58,X57) != c_Pair(X55,X53,X58,X57)
| X56 = X55 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_863])])]) ).
fof(c_0_1474,plain,
! [X53,X54,X55,X56,X57,X58] :
( c_Pair(X56,X54,X58,X57) != c_Pair(X55,X53,X58,X57)
| X54 = X53 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_864])])]) ).
fof(c_0_1475,plain,
! [X13,X14,X15] :
( c_in(X13,c_Relation_ODomain(X14,X15,X15),X15)
| c_in(c_Pair(X13,X13,X15,X15),c_Transitive__Closure_Ortrancl(X14,X15),tc_prod(X15,X15)) ),
inference(variable_rename,[status(thm)],[c_0_865]) ).
fof(c_0_1476,plain,
! [X22,X23,X24,X25] :
( c_in(c_Pair(X23,X23,X25,X25),X22,tc_prod(X25,X25))
| ~ c_in(X23,X24,X25)
| ~ c_Relation_Orefl__on(X24,X22,X25) ),
inference(variable_rename,[status(thm)],[c_0_866]) ).
fof(c_0_1477,plain,
! [X9,X10,X11,X12] :
( c_in(c_Pair(X9,X9,X12,X12),X10,tc_prod(X12,X12))
| ~ c_in(X9,X11,X12)
| ~ c_Relation_Orefl__on(X11,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_867]) ).
fof(c_0_1478,plain,
! [X9,X10,X11] :
( c_in(c_Pair(X9,X9,X11,X11),c_Relation_OId__on(X10,X11),tc_prod(X11,X11))
| ~ c_in(X9,X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_868]) ).
fof(c_0_1479,plain,
! [X14,X15,X16] : c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X15,X16),c_Transitive__Closure_Ortrancl(X14,X16),tc_fun(tc_prod(X16,X16),tc_bool)),X16) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X15,X14,tc_fun(tc_prod(X16,X16),tc_bool)),X16),
inference(variable_rename,[status(thm)],[c_0_869]) ).
fof(c_0_1480,plain,
! [X16,X17,X18,X19,X20] :
( c_Relation_Orefl__on(c_Lattices_Olower__semilattice__class_Oinf(X19,X18,tc_fun(X20,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X17,X16,tc_fun(tc_prod(X20,X20),tc_bool)),X20)
| ~ c_Relation_Orefl__on(X18,X16,X20)
| ~ c_Relation_Orefl__on(X19,X17,X20) ),
inference(variable_rename,[status(thm)],[c_0_870]) ).
fof(c_0_1481,plain,
! [X16,X17,X18,X19,X20] :
( c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(X19,X18,tc_fun(X20,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X17,X16,tc_fun(tc_prod(X20,X20),tc_bool)),X20)
| ~ c_Relation_Orefl__on(X18,X16,X20)
| ~ c_Relation_Orefl__on(X19,X17,X20) ),
inference(variable_rename,[status(thm)],[c_0_871]) ).
fof(c_0_1482,plain,
! [X31,X32,X33] :
( X31 = c_Pair(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X32,X31,X33),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X32,X31,X33),X33,X33)
| ~ c_in(X31,c_Relation_OId__on(X32,X33),tc_prod(X33,X33)) ),
inference(variable_rename,[status(thm)],[c_0_872]) ).
fof(c_0_1483,plain,
! [X38,X39] :
( c_Arrow__Order__Mirabelle_Ounanimity(X39)
| c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3(X39),v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4(X39),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2(X39),X38),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(variable_rename,[status(thm)],[c_0_873]) ).
fof(c_0_1484,plain,
! [X34,X35,X36,X37,X38] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X37,X36,tc_fun(X38,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X35,X34,tc_fun(X38,tc_bool)),tc_fun(X38,tc_bool))
| ~ c_lessequals(X36,X34,tc_fun(X38,tc_bool))
| ~ c_lessequals(X37,X35,tc_fun(X38,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_874]) ).
fof(c_0_1485,plain,
! [X34,X35,X36,X37,X38] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X37,X36,tc_fun(X38,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X35,X34,tc_fun(X38,tc_bool)),tc_fun(X38,tc_bool))
| ~ c_lessequals(X36,X34,tc_fun(X38,tc_bool))
| ~ c_lessequals(X37,X35,tc_fun(X38,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_875]) ).
fof(c_0_1486,plain,
! [X5,X6,X7,X8] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X5,tc_fun(X8,tc_bool)),X7,tc_fun(X8,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X8,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X5,X7,tc_fun(X8,tc_bool)),tc_fun(X8,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_876]) ).
fof(c_0_1487,plain,
! [X5,X6,X7,X8] : c_Lattices_Oupper__semilattice__class_Osup(X7,c_Lattices_Olower__semilattice__class_Oinf(X6,X5,tc_fun(X8,tc_bool)),tc_fun(X8,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X7,X6,tc_fun(X8,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X7,X5,tc_fun(X8,tc_bool)),tc_fun(X8,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_877]) ).
fof(c_0_1488,plain,
! [X5,X6,X7,X8] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X5,tc_fun(X8,tc_bool)),X7,tc_fun(X8,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X8,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X5,X7,tc_fun(X8,tc_bool)),tc_fun(X8,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_878]) ).
fof(c_0_1489,plain,
! [X5,X6,X7,X8] : c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Oupper__semilattice__class_Osup(X6,X5,tc_fun(X8,tc_bool)),tc_fun(X8,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X8,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X7,X5,tc_fun(X8,tc_bool)),tc_fun(X8,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_879]) ).
fof(c_0_1490,plain,
! [X7,X8,X9,X10] : c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X8,X7,tc_fun(tc_prod(X9,X10),tc_bool)),X9,X10) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X8,X9,X10),c_Relation_ORange(X7,X9,X10),tc_fun(X10,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_880]) ).
fof(c_0_1491,plain,
! [X7,X8,X9,X10] : c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X8,X7,tc_fun(tc_prod(X10,X9),tc_bool)),X10,X9) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X8,X10,X9),c_Relation_ODomain(X7,X10,X9),tc_fun(X10,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_881]) ).
fof(c_0_1492,plain,
! [X13,X14,X15] : c_in(c_Pair(X13,X13,X15,X15),c_Transitive__Closure_Ortrancl(X14,X15),tc_prod(X15,X15)),
inference(variable_rename,[status(thm)],[c_0_882]) ).
fof(c_0_1493,plain,
! [X22,X23,X24] : c_in(c_Pair(X23,X23,X24,X24),c_Transitive__Closure_Ortrancl(X22,X24),tc_prod(X24,X24)),
inference(variable_rename,[status(thm)],[c_0_883]) ).
fof(c_0_1494,plain,
! [X9,X10,X11] :
( c_in(c_Pair(X9,X9,X11,X11),X10,tc_prod(X11,X11))
| ~ c_Nitpick_Orefl_H(X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_884]) ).
fof(c_0_1495,plain,
! [X50,X51,X52] :
( X50 = X51
| X50 = X51
| c_in(c_Pair(X50,X51,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X52,X51),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_885])])]) ).
fof(c_0_1496,plain,
! [X50,X51,X52] :
( X51 = X50
| X50 = X51
| c_in(c_Pair(X51,X50,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X52,X51),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_886])])]) ).
fof(c_0_1497,plain,
! [X22,X23] :
( c_in(c_Pair(X23,X22,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X23,X22),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X23 = X22 ),
inference(variable_rename,[status(thm)],[c_0_887]) ).
fof(c_0_1498,plain,
! [X9,X10,X11] :
( X10 = c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),X11)
| X10 = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))
| ~ c_lessequals(X10,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),X11),tc_fun(X11,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_888]) ).
fof(c_0_1499,plain,
! [X9,X10,X11,X12] :
( hBOOL(hAPP(X10,X9))
| hBOOL(hAPP(X11,X9))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X11,X10,tc_fun(X12,tc_bool)),X9)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_889])])]) ).
fof(c_0_1500,plain,
! [X7,X8,X9] : c_Product__Type_OSigma(X7,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),tc_fun(X8,tc_bool),X9),X9,X8) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X9,X8),tc_bool)),
inference(variable_rename,[status(thm)],[c_0_890]) ).
fof(c_0_1501,plain,
! [X5,X6,X7,X8] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X8,tc_bool)),X5,tc_fun(X8,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Oupper__semilattice__class_Osup(X6,X5,tc_fun(X8,tc_bool)),tc_fun(X8,tc_bool))
| ~ c_lessequals(X5,X7,tc_fun(X8,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_891]) ).
fof(c_0_1502,plain,
! [X16,X17,X18,X19] : hAPP(c_Relation_Oconverse(X18,X19),c_Lattices_Olower__semilattice__class_Oinf(X17,X16,tc_fun(tc_prod(X18,X19),tc_bool))) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Relation_Oconverse(X18,X19),X17),hAPP(c_Relation_Oconverse(X18,X19),X16),tc_fun(tc_prod(X19,X18),tc_bool)),
inference(variable_rename,[status(thm)],[c_0_892]) ).
fof(c_0_1503,plain,
! [X16,X17,X18,X19] : hAPP(c_Relation_Oconverse(X18,X19),c_Lattices_Oupper__semilattice__class_Osup(X17,X16,tc_fun(tc_prod(X18,X19),tc_bool))) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Relation_Oconverse(X18,X19),X17),hAPP(c_Relation_Oconverse(X18,X19),X16),tc_fun(tc_prod(X19,X18),tc_bool)),
inference(variable_rename,[status(thm)],[c_0_893]) ).
fof(c_0_1504,plain,
! [X22,X23] : c_in(c_Pair(X22,X22,X23,X23),c_Relation_OId(X23),tc_prod(X23,X23)),
inference(variable_rename,[status(thm)],[c_0_894]) ).
fof(c_0_1505,plain,
! [X9,X10] : c_in(c_Pair(X9,X9,X10,X10),c_Relation_OId(X10),tc_prod(X10,X10)),
inference(variable_rename,[status(thm)],[c_0_895]) ).
fof(c_0_1506,plain,
! [X9,X10,X11,X12] :
( hBOOL(hAPP(X11,X9))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X11,X10,tc_fun(X12,tc_bool)),X9)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_896])])]) ).
fof(c_0_1507,plain,
! [X9,X10,X11,X12] :
( hBOOL(hAPP(X10,X9))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X11,X10,tc_fun(X12,tc_bool)),X9)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_897])])]) ).
fof(c_0_1508,plain,
! [X22,X23,X24,X25] :
( hBOOL(hAPP(X24,X23))
| ~ hBOOL(hAPP(X24,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X24,X22,X25)))
| ~ c_in(X23,c_Wellfounded_Oacc(X22,X25),X25) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_898])])]) ).
fof(c_0_1509,plain,
! [X22,X23,X24,X25] :
( hBOOL(hAPP(X24,X23))
| ~ hBOOL(hAPP(X24,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X24,X22,X25)))
| ~ c_in(X23,c_Wellfounded_Oacc(X22,X25),X25) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_899])])]) ).
fof(c_0_1510,plain,
! [X9,X10,X11] : c_Set_Oinsert(X9,c_Set_Oinsert(X10,c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),X11),X11) = c_Set_Oinsert(X10,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool)),X11),X11),
inference(variable_rename,[status(thm)],[c_0_900]) ).
fof(c_0_1511,plain,
! [X30,X31,X32,X33] :
( c_Relation_Osym(c_Relation_Oinv__image(X30,X31,X33,X32),X32)
| ~ c_Relation_Osym(X30,X33) ),
inference(variable_rename,[status(thm)],[c_0_901]) ).
fof(c_0_1512,plain,
! [X30,X31,X32,X33] :
( c_Wellfounded_Owf(c_Relation_Oinv__image(X30,X31,X33,X32),X32)
| ~ c_Wellfounded_Owf(X30,X33) ),
inference(variable_rename,[status(thm)],[c_0_902]) ).
fof(c_0_1513,plain,
! [X22,X23,X24,X25] : c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X22,X24,X25),c_Set_Oinsert(X22,X23,X25),tc_fun(X25,tc_bool)) = c_Set_Oinsert(X22,c_Lattices_Olower__semilattice__class_Oinf(X24,X23,tc_fun(X25,tc_bool)),X25),
inference(variable_rename,[status(thm)],[c_0_903]) ).
fof(c_0_1514,plain,
! [X16,X17,X18,X19] :
( c_lessequals(c_Relation_ODomain(X17,X19,X18),c_Relation_ODomain(X16,X19,X18),tc_fun(X19,tc_bool))
| ~ c_lessequals(X17,X16,tc_fun(tc_prod(X19,X18),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_904]) ).
fof(c_0_1515,plain,
! [X35,X36,X37,X38] :
( c_in(X37,c_Transitive__Closure_Otrancl(X35,X38),tc_prod(X38,X38))
| ~ c_lessequals(X36,X35,tc_fun(tc_prod(X38,X38),tc_bool))
| ~ c_in(X37,c_Transitive__Closure_Otrancl(X36,X38),tc_prod(X38,X38)) ),
inference(variable_rename,[status(thm)],[c_0_905]) ).
fof(c_0_1516,plain,
! [X22,X23,X24,X25] :
( c_Lattices_Olower__semilattice__class_Oinf(X24,c_Set_Oinsert(X22,X23,X25),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,X24,X25) ),
inference(variable_rename,[status(thm)],[c_0_906]) ).
fof(c_0_1517,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_907]) ).
fof(c_0_1518,plain,
! [X14,X15,X16] :
( c_Transitive__Closure_Ortrancl(X14,X16) = c_Transitive__Closure_Ortrancl(X15,X16)
| ~ c_lessequals(X14,c_Transitive__Closure_Ortrancl(X15,X16),tc_fun(tc_prod(X16,X16),tc_bool))
| ~ c_lessequals(X15,X14,tc_fun(tc_prod(X16,X16),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_908]) ).
fof(c_0_1519,plain,
! [X5,X6,X7,X8] :
( c_lessequals(X5,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X8,tc_bool)),tc_fun(X8,tc_bool))
| ~ c_lessequals(X5,X6,tc_fun(X8,tc_bool))
| ~ c_lessequals(X5,X7,tc_fun(X8,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_909]) ).
fof(c_0_1520,plain,
! [X5,X6,X7,X8] :
( c_lessequals(X5,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X8,tc_bool)),tc_fun(X8,tc_bool))
| ~ c_lessequals(X5,X6,tc_fun(X8,tc_bool))
| ~ c_lessequals(X5,X7,tc_fun(X8,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_910]) ).
fof(c_0_1521,plain,
! [X5,X6,X7,X8] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X7,X6,tc_fun(X8,tc_bool)),X5,tc_fun(X8,tc_bool))
| ~ c_lessequals(X6,X5,tc_fun(X8,tc_bool))
| ~ c_lessequals(X7,X5,tc_fun(X8,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_911]) ).
fof(c_0_1522,plain,
! [X5,X6,X7,X8] :
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X7,X6,tc_fun(X8,tc_bool)),X5,tc_fun(X8,tc_bool))
| ~ c_lessequals(X6,X5,tc_fun(X8,tc_bool))
| ~ c_lessequals(X7,X5,tc_fun(X8,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_912]) ).
fof(c_0_1523,plain,
! [X5,X6,X7,X8] : c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Olower__semilattice__class_Oinf(X6,X5,tc_fun(X8,tc_bool)),tc_fun(X8,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X5,tc_fun(X8,tc_bool)),tc_fun(X8,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_913]) ).
fof(c_0_1524,plain,
! [X5,X6,X7,X8] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X8,tc_bool)),X5,tc_fun(X8,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Olower__semilattice__class_Oinf(X6,X5,tc_fun(X8,tc_bool)),tc_fun(X8,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_914]) ).
fof(c_0_1525,plain,
! [X5,X6,X7,X8] : c_Lattices_Oupper__semilattice__class_Osup(X7,c_Lattices_Oupper__semilattice__class_Osup(X6,X5,tc_fun(X8,tc_bool)),tc_fun(X8,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X5,tc_fun(X8,tc_bool)),tc_fun(X8,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_915]) ).
fof(c_0_1526,plain,
! [X5,X6,X7,X8] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X7,X6,tc_fun(X8,tc_bool)),X5,tc_fun(X8,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X7,c_Lattices_Oupper__semilattice__class_Osup(X6,X5,tc_fun(X8,tc_bool)),tc_fun(X8,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_916]) ).
fof(c_0_1527,plain,
! [X6,X7] :
( c_Relation_Oantisym(X6,X7)
| ~ c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_OId(X7),tc_fun(tc_prod(X7,X7),tc_bool)),X7) ),
inference(variable_rename,[status(thm)],[c_0_917]) ).
fof(c_0_1528,plain,
! [X5,X6,X7,X8] :
( c_lessequals(X6,X5,tc_fun(X8,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X7,X6,tc_fun(X8,tc_bool)),X5,tc_fun(X8,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_918]) ).
fof(c_0_1529,plain,
! [X5,X6,X7,X8] :
( c_lessequals(X7,X5,tc_fun(X8,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X7,X6,tc_fun(X8,tc_bool)),X5,tc_fun(X8,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_919]) ).
fof(c_0_1530,plain,
! [X5,X6,X7,X8] :
( c_lessequals(X5,X7,tc_fun(X8,tc_bool))
| ~ c_lessequals(X5,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X8,tc_bool)),tc_fun(X8,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_920]) ).
fof(c_0_1531,plain,
! [X5,X6,X7,X8] :
( c_lessequals(X5,X6,tc_fun(X8,tc_bool))
| ~ c_lessequals(X5,c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X8,tc_bool)),tc_fun(X8,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_921]) ).
fof(c_0_1532,plain,
! [X35,X36] :
( X35 = c_Pair(c_ATP__Linkup_Osko__Relation__XIdE__1__1(X35,X36),c_ATP__Linkup_Osko__Relation__XIdE__1__1(X35,X36),X36,X36)
| ~ c_in(X35,c_Relation_OId(X36),tc_prod(X36,X36)) ),
inference(variable_rename,[status(thm)],[c_0_922]) ).
fof(c_0_1533,plain,
! [X22,X23,X24,X25] :
( hBOOL(hAPP(X24,X23))
| ~ hBOOL(hAPP(X24,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X24,X22,X25)))
| ~ c_Wellfounded_Owf(X22,X25) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_923])])]) ).
fof(c_0_1534,plain,
! [X25,X26,X27,X28] :
( hBOOL(hAPP(X27,X25))
| ~ hBOOL(hAPP(X27,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X27,X26,X28)))
| ~ c_Wellfounded_Owf(X26,X28) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_924])])]) ).
fof(c_0_1535,plain,
! [X22,X23,X24,X25] :
( hBOOL(hAPP(X24,X23))
| ~ hBOOL(hAPP(X24,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X24,X22,X25)))
| ~ c_Wellfounded_Owf(X22,X25) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_925])])]) ).
fof(c_0_1536,plain,
! [X13,X14,X15,X16] :
( hBOOL(hAPP(X15,X13))
| ~ hBOOL(hAPP(X15,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X15,X14,X16)))
| ~ c_Wellfounded_Owf(X14,X16) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_926])])]) ).
fof(c_0_1537,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Odistrib__lattice(X23)
| c_Lattices_Oupper__semilattice__class_Osup(X22,c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X23),X23) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X22,X21,X23),c_Lattices_Oupper__semilattice__class_Osup(X22,X20,X23),X23) ),
inference(variable_rename,[status(thm)],[c_0_927]) ).
fof(c_0_1538,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Odistrib__lattice(X23)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X23),X22,X23) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X21,X22,X23),c_Lattices_Oupper__semilattice__class_Osup(X20,X22,X23),X23) ),
inference(variable_rename,[status(thm)],[c_0_928]) ).
fof(c_0_1539,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Odistrib__lattice(X23)
| c_Lattices_Olower__semilattice__class_Oinf(X22,c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X23),X23) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X22,X21,X23),c_Lattices_Olower__semilattice__class_Oinf(X22,X20,X23),X23) ),
inference(variable_rename,[status(thm)],[c_0_929]) ).
fof(c_0_1540,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Odistrib__lattice(X23)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X23),X22,X23) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X21,X22,X23),c_Lattices_Olower__semilattice__class_Oinf(X20,X22,X23),X23) ),
inference(variable_rename,[status(thm)],[c_0_930]) ).
fof(c_0_1541,plain,
! [X31,X32,X33,X34] :
( c_in(X31,X32,X34)
| c_in(X31,X33,X34)
| ~ c_in(X31,c_Lattices_Oupper__semilattice__class_Osup(X33,X32,tc_fun(X34,tc_bool)),X34) ),
inference(variable_rename,[status(thm)],[c_0_931]) ).
fof(c_0_1542,plain,
! [X9,X10,X11,X12] :
( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X11,X10,tc_fun(X12,tc_bool)),X9))
| ~ hBOOL(hAPP(X10,X9))
| ~ hBOOL(hAPP(X11,X9)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_932])])]) ).
fof(c_0_1543,plain,
! [X6,X7] : c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X6,hAPP(c_Relation_Oconverse(X7,X7),X6),tc_fun(tc_prod(X7,X7),tc_bool)),X7),
inference(variable_rename,[status(thm)],[c_0_933]) ).
fof(c_0_1544,plain,
! [X6,X7] : c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X6,hAPP(c_Relation_Oconverse(X7,X7),X6),tc_fun(tc_prod(X7,X7),tc_bool)),X7),
inference(variable_rename,[status(thm)],[c_0_934]) ).
fof(c_0_1545,plain,
! [X16,X17,X18] :
( c_lessequals(c_Transitive__Closure_Ortrancl(X17,X18),c_Transitive__Closure_Ortrancl(X16,X18),tc_fun(tc_prod(X18,X18),tc_bool))
| ~ c_lessequals(X17,c_Transitive__Closure_Ortrancl(X16,X18),tc_fun(tc_prod(X18,X18),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_935]) ).
fof(c_0_1546,plain,
! [X9,X10,X11,X12] :
( c_lessequals(X11,X10,tc_fun(X12,tc_bool))
| ~ c_lessequals(X11,c_Set_Oinsert(X9,X10,X12),tc_fun(X12,tc_bool))
| c_in(X9,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_936]) ).
fof(c_0_1547,plain,
! [X9,X10,X11,X12] :
( c_lessequals(X11,X10,tc_fun(X12,tc_bool))
| c_in(X9,X11,X12)
| ~ c_lessequals(X11,c_Set_Oinsert(X9,X10,X12),tc_fun(X12,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_937]) ).
fof(c_0_1548,plain,
! [X22,X23,X24] :
( X22 = X23
| ~ c_in(X22,c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)),X24),X24) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_938])])]) ).
fof(c_0_1549,plain,
! [X20,X21,X22,X23] :
( hBOOL(hAPP(X22,X21))
| X20 = X21
| ~ hBOOL(hAPP(c_Set_Oinsert(X20,X22,X23),X21)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_939])])]) ).
fof(c_0_1550,plain,
! [X34,X35,X36,X37] :
( c_lessequals(c_Set_Oinsert(X34,X36,X37),c_Set_Oinsert(X34,X35,X37),tc_fun(X37,tc_bool))
| ~ c_lessequals(X36,X35,tc_fun(X37,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_940]) ).
fof(c_0_1551,plain,
! [X16,X17,X18] : c_Relation_OField(c_Lattices_Oupper__semilattice__class_Osup(X17,X16,tc_fun(tc_prod(X18,X18),tc_bool)),X18) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OField(X17,X18),c_Relation_OField(X16,X18),tc_fun(X18,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_941]) ).
fof(c_0_1552,plain,
! [X9,X10,X11,X12] :
( c_lessequals(c_Set_Oinsert(X9,X11,X12),X10,tc_fun(X12,tc_bool))
| ~ c_lessequals(X11,X10,tc_fun(X12,tc_bool))
| ~ c_in(X9,X10,X12) ),
inference(variable_rename,[status(thm)],[c_0_942]) ).
fof(c_0_1553,plain,
! [X22,X23,X24,X25] : c_Lattices_Oupper__semilattice__class_Osup(X24,c_Set_Oinsert(X22,X23,X25),tc_fun(X25,tc_bool)) = c_Set_Oinsert(X22,c_Lattices_Oupper__semilattice__class_Osup(X24,X23,tc_fun(X25,tc_bool)),X25),
inference(variable_rename,[status(thm)],[c_0_943]) ).
fof(c_0_1554,plain,
! [X22,X23,X24,X25] : c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X22,X24,X25),X23,tc_fun(X25,tc_bool)) = c_Set_Oinsert(X22,c_Lattices_Oupper__semilattice__class_Osup(X24,X23,tc_fun(X25,tc_bool)),X25),
inference(variable_rename,[status(thm)],[c_0_944]) ).
fof(c_0_1555,plain,
! [X16,X17,X18] :
( c_lessequals(c_Transitive__Closure_Ortrancl(X17,X18),c_Transitive__Closure_Ortrancl(X16,X18),tc_fun(tc_prod(X18,X18),tc_bool))
| ~ c_lessequals(X17,X16,tc_fun(tc_prod(X18,X18),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_945]) ).
fof(c_0_1556,plain,
! [X9,X10,X11,X12] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X11,X10,tc_fun(X12,tc_bool)),X9))
| ~ hBOOL(hAPP(X11,X9)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_946])])]) ).
fof(c_0_1557,plain,
! [X9,X10,X11,X12] :
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X11,X10,tc_fun(X12,tc_bool)),X9))
| ~ hBOOL(hAPP(X10,X9)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_947])])]) ).
fof(c_0_1558,plain,
! [X31,X32,X33,X34] :
( c_in(X31,X33,X34)
| ~ c_in(X31,c_Lattices_Olower__semilattice__class_Oinf(X33,X32,tc_fun(X34,tc_bool)),X34) ),
inference(variable_rename,[status(thm)],[c_0_948]) ).
fof(c_0_1559,plain,
! [X31,X32,X33,X34] :
( c_in(X31,X32,X34)
| ~ c_in(X31,c_Lattices_Olower__semilattice__class_Oinf(X33,X32,tc_fun(X34,tc_bool)),X34) ),
inference(variable_rename,[status(thm)],[c_0_949]) ).
fof(c_0_1560,plain,
! [X31,X32,X33,X34] :
( c_in(X31,c_Lattices_Olower__semilattice__class_Oinf(X33,X32,tc_fun(X34,tc_bool)),X34)
| ~ c_in(X31,X32,X34)
| ~ c_in(X31,X33,X34) ),
inference(variable_rename,[status(thm)],[c_0_950]) ).
fof(c_0_1561,plain,
! [X31,X32,X33,X34] :
( c_in(X31,c_Lattices_Olower__semilattice__class_Oinf(X33,X32,tc_fun(X34,tc_bool)),X34)
| ~ c_in(X31,X32,X34)
| ~ c_in(X31,X33,X34) ),
inference(variable_rename,[status(thm)],[c_0_951]) ).
fof(c_0_1562,plain,
! [X7,X8,X9] : c_Product__Type_OSigma(c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool)),X7,X9,X8) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X9,X8),tc_bool)),
inference(variable_rename,[status(thm)],[c_0_952]) ).
fof(c_0_1563,plain,
! [X13,X14,X15] :
( ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X14,X13,X15),c_Wellfounded_Oacc(X14,X15),X15)
| c_in(X13,c_Wellfounded_Oacc(X14,X15),X15) ),
inference(variable_rename,[status(thm)],[c_0_953]) ).
fof(c_0_1564,plain,
! [X9,X10,X11] :
( c_in(X9,c_Wellfounded_Oacc(X10,X11),X11)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X10,X9,X11),c_Wellfounded_Oacc(X10,X11),X11) ),
inference(variable_rename,[status(thm)],[c_0_954]) ).
fof(c_0_1565,plain,
! [X9,X10,X11,X12] :
( c_lessequals(X11,X10,tc_fun(X12,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X9,X11,X12),X10,tc_fun(X12,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_955]) ).
fof(c_0_1566,plain,
! [X38,X39,X40] :
( hAPP(X40,X38) = hAPP(X38,X39)
| ~ c_in(X38,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_Odictator(X40,X39) ),
inference(variable_rename,[status(thm)],[c_0_956]) ).
fof(c_0_1567,plain,
! [X9,X10,X11,X12] :
( c_lessequals(X11,c_Set_Oinsert(X9,X10,X12),tc_fun(X12,tc_bool))
| ~ c_lessequals(X11,X10,tc_fun(X12,tc_bool))
| c_in(X9,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_957]) ).
fof(c_0_1568,plain,
! [X9,X10,X11,X12] :
( c_lessequals(X11,c_Set_Oinsert(X9,X10,X12),tc_fun(X12,tc_bool))
| ~ c_lessequals(X11,X10,tc_fun(X12,tc_bool))
| c_in(X9,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_958]) ).
fof(c_0_1569,plain,
! [X5,X6,X7] : c_Relation_OImage(c_Relation_OId__on(X6,X7),X5,X7,X7) = c_Lattices_Olower__semilattice__class_Oinf(X6,X5,tc_fun(X7,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_959]) ).
fof(c_0_1570,plain,
! [X22,X23,X24,X25] :
( hBOOL(hAPP(X24,X23))
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X24,X22,X25),c_Wellfounded_Oacc(X22,X25),X25)
| ~ c_in(X23,c_Wellfounded_Oacc(X22,X25),X25) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_960])])]) ).
fof(c_0_1571,plain,
! [X22,X23,X24,X25] :
( hBOOL(hAPP(X24,X23))
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X24,X22,X25),c_Wellfounded_Oacc(X22,X25),X25)
| ~ c_in(X23,c_Wellfounded_Oacc(X22,X25),X25) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_961])])]) ).
fof(c_0_1572,plain,
! [X16,X17,X18,X19] :
( c_Relation_Osingle__valued(X17,X19,X18)
| ~ c_Relation_Osingle__valued(X16,X19,X18)
| ~ c_lessequals(X17,X16,tc_fun(tc_prod(X19,X18),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_962]) ).
fof(c_0_1573,plain,
! [X9,X10,X11,X12] :
( c_in(X9,X10,X12)
| ~ c_lessequals(c_Set_Oinsert(X9,X11,X12),X10,tc_fun(X12,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_963]) ).
fof(c_0_1574,plain,
! [X22,X23,X24] : c_Set_Oinsert(X22,X23,X24) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X22,c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)),X24),X23,tc_fun(X24,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_964]) ).
fof(c_0_1575,plain,
! [X22,X23,X24,X25] :
( ~ class_Lattices_Olower__semilattice(X25)
| c_lessequals(X22,c_Lattices_Olower__semilattice__class_Oinf(X24,X23,X25),X25)
| ~ c_lessequals(X22,X23,X25)
| ~ c_lessequals(X22,X24,X25) ),
inference(variable_rename,[status(thm)],[c_0_965]) ).
fof(c_0_1576,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Olower__semilattice(X23)
| c_lessequals(X22,c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X23),X23)
| ~ c_lessequals(X22,X20,X23)
| ~ c_lessequals(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_966]) ).
fof(c_0_1577,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Olower__semilattice(X23)
| c_lessequals(X22,c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X23),X23)
| ~ c_lessequals(X22,X20,X23)
| ~ c_lessequals(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_967]) ).
fof(c_0_1578,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Oupper__semilattice(X23)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X22,X21,X23),X20,X23)
| ~ c_lessequals(X21,X20,X23)
| ~ c_lessequals(X22,X20,X23) ),
inference(variable_rename,[status(thm)],[c_0_968]) ).
fof(c_0_1579,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Oupper__semilattice(X23)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X23),X22,X23)
| ~ c_lessequals(X20,X22,X23)
| ~ c_lessequals(X21,X22,X23) ),
inference(variable_rename,[status(thm)],[c_0_969]) ).
fof(c_0_1580,plain,
! [X22,X23,X24,X25] :
( ~ class_Lattices_Oupper__semilattice(X25)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X24,X23,X25),X22,X25)
| ~ c_lessequals(X23,X22,X25)
| ~ c_lessequals(X24,X22,X25) ),
inference(variable_rename,[status(thm)],[c_0_970]) ).
fof(c_0_1581,plain,
! [X9,X10,X11,X12] :
( ~ c_in(X9,X10,X12)
| ~ c_in(X9,X11,X12)
| c_Lattices_Olower__semilattice__class_Oinf(X11,X10,tc_fun(X12,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X12,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_971]) ).
fof(c_0_1582,plain,
! [X22,X23,X24] :
( c_Set_Oinsert(X23,c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)),X24) != c_Set_Oinsert(X22,c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)),X24)
| X23 = X22 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_972])])]) ).
fof(c_0_1583,plain,
! [X16,X17,X18] :
( c_lessequals(c_Relation_OField(X17,X18),c_Relation_OField(X16,X18),tc_fun(X18,tc_bool))
| ~ c_lessequals(X17,X16,tc_fun(tc_prod(X18,X18),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_973]) ).
fof(c_0_1584,plain,
! [X28,X29,X30] :
( c_lessequals(c_Wellfounded_Oacc(X28,X30),c_Wellfounded_Oacc(X29,X30),tc_fun(X30,tc_bool))
| ~ c_lessequals(X29,X28,tc_fun(tc_prod(X30,X30),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_974]) ).
fof(c_0_1585,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Olattice(X23)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X22,X21,X23),X20,X23) = c_Lattices_Oupper__semilattice__class_Osup(X22,c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X23),X23) ),
inference(variable_rename,[status(thm)],[c_0_975]) ).
fof(c_0_1586,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Olattice(X23)
| c_Lattices_Oupper__semilattice__class_Osup(X22,c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X23),X23) = c_Lattices_Oupper__semilattice__class_Osup(X21,c_Lattices_Oupper__semilattice__class_Osup(X22,X20,X23),X23) ),
inference(variable_rename,[status(thm)],[c_0_976]) ).
fof(c_0_1587,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Oupper__semilattice(X23)
| c_Lattices_Oupper__semilattice__class_Osup(X22,c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X23),X23) = c_Lattices_Oupper__semilattice__class_Osup(X21,c_Lattices_Oupper__semilattice__class_Osup(X22,X20,X23),X23) ),
inference(variable_rename,[status(thm)],[c_0_977]) ).
fof(c_0_1588,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Oupper__semilattice(X23)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X22,X21,X23),X20,X23) = c_Lattices_Oupper__semilattice__class_Osup(X22,c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X23),X23) ),
inference(variable_rename,[status(thm)],[c_0_978]) ).
fof(c_0_1589,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Olower__semilattice(X23)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X22,X21,X23),X20,X23) = c_Lattices_Olower__semilattice__class_Oinf(X22,c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X23),X23) ),
inference(variable_rename,[status(thm)],[c_0_979]) ).
fof(c_0_1590,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Olower__semilattice(X23)
| c_Lattices_Olower__semilattice__class_Oinf(X22,c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X23),X23) = c_Lattices_Olower__semilattice__class_Oinf(X21,c_Lattices_Olower__semilattice__class_Oinf(X22,X20,X23),X23) ),
inference(variable_rename,[status(thm)],[c_0_980]) ).
fof(c_0_1591,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Olattice(X23)
| c_Lattices_Olower__semilattice__class_Oinf(X22,c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X23),X23) = c_Lattices_Olower__semilattice__class_Oinf(X21,c_Lattices_Olower__semilattice__class_Oinf(X22,X20,X23),X23) ),
inference(variable_rename,[status(thm)],[c_0_981]) ).
fof(c_0_1592,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Olattice(X23)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X22,X21,X23),X20,X23) = c_Lattices_Olower__semilattice__class_Oinf(X22,c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X23),X23) ),
inference(variable_rename,[status(thm)],[c_0_982]) ).
fof(c_0_1593,plain,
! [X31,X32,X33] :
( c_in(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X32,X31,X33),X32,X33)
| ~ c_in(X31,c_Relation_OId__on(X32,X33),tc_prod(X33,X33)) ),
inference(variable_rename,[status(thm)],[c_0_983]) ).
fof(c_0_1594,plain,
! [X13,X14,X15] : c_Relation_OImage(X13,c_Orderings_Obot__class_Obot(tc_fun(X14,tc_bool)),X14,X15) = c_Orderings_Obot__class_Obot(tc_fun(X15,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_984]) ).
fof(c_0_1595,plain,
! [X20,X21,X22,X23] : c_Set_Oinsert(X21,c_Set_Oinsert(X20,X22,X23),X23) = c_Set_Oinsert(X20,c_Set_Oinsert(X21,X22,X23),X23),
inference(variable_rename,[status(thm)],[c_0_985]) ).
fof(c_0_1596,plain,
! [X5,X6,X7,X8] :
( c_lessequals(X7,X5,tc_fun(X8,tc_bool))
| ~ c_lessequals(X6,X5,tc_fun(X8,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X8,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_986]) ).
fof(c_0_1597,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_987]) ).
fof(c_0_1598,plain,
! [X22,X23,X24,X25] :
( c_Lattices_Olower__semilattice__class_Oinf(X24,c_Set_Oinsert(X22,X23,X25),tc_fun(X25,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X24,X23,tc_fun(X25,tc_bool))
| c_in(X22,X24,X25) ),
inference(variable_rename,[status(thm)],[c_0_988]) ).
fof(c_0_1599,plain,
! [X16,X17,X18] :
( c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X17,X16,tc_fun(tc_prod(X18,X18),tc_bool)),X18)
| ~ c_Relation_Osym(X16,X18)
| ~ c_Relation_Osym(X17,X18) ),
inference(variable_rename,[status(thm)],[c_0_989]) ).
fof(c_0_1600,plain,
! [X16,X17,X18] :
( c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X17,X16,tc_fun(tc_prod(X18,X18),tc_bool)),X18)
| ~ c_Relation_Osym(X16,X18)
| ~ c_Relation_Osym(X17,X18) ),
inference(variable_rename,[status(thm)],[c_0_990]) ).
fof(c_0_1601,plain,
! [X22,X23,X24,X25] :
( ~ class_Lattices_Oupper__semilattice(X25)
| c_lessequals(X24,X22,X25)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X24,X23,X25),X22,X25) ),
inference(variable_rename,[status(thm)],[c_0_991]) ).
fof(c_0_1602,plain,
! [X22,X23,X24,X25] :
( ~ class_Lattices_Oupper__semilattice(X25)
| c_lessequals(X23,X22,X25)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X24,X23,X25),X22,X25) ),
inference(variable_rename,[status(thm)],[c_0_992]) ).
fof(c_0_1603,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Oupper__semilattice(X23)
| c_lessequals(X22,X20,X23)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X22,X21,X23),X20,X23) ),
inference(variable_rename,[status(thm)],[c_0_993]) ).
fof(c_0_1604,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Oupper__semilattice(X23)
| c_lessequals(X21,X20,X23)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X22,X21,X23),X20,X23) ),
inference(variable_rename,[status(thm)],[c_0_994]) ).
fof(c_0_1605,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Olower__semilattice(X23)
| c_lessequals(X22,X20,X23)
| ~ c_lessequals(X22,c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X23),X23) ),
inference(variable_rename,[status(thm)],[c_0_995]) ).
fof(c_0_1606,plain,
! [X20,X21,X22,X23] :
( ~ class_Lattices_Olower__semilattice(X23)
| c_lessequals(X22,X21,X23)
| ~ c_lessequals(X22,c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X23),X23) ),
inference(variable_rename,[status(thm)],[c_0_996]) ).
fof(c_0_1607,plain,
! [X22,X23,X24,X25] :
( ~ class_Lattices_Olower__semilattice(X25)
| c_lessequals(X22,X23,X25)
| ~ c_lessequals(X22,c_Lattices_Olower__semilattice__class_Oinf(X24,X23,X25),X25) ),
inference(variable_rename,[status(thm)],[c_0_997]) ).
fof(c_0_1608,plain,
! [X22,X23,X24,X25] :
( ~ class_Lattices_Olower__semilattice(X25)
| c_lessequals(X22,X24,X25)
| ~ c_lessequals(X22,c_Lattices_Olower__semilattice__class_Oinf(X24,X23,X25),X25) ),
inference(variable_rename,[status(thm)],[c_0_998]) ).
fof(c_0_1609,plain,
! [X22,X23,X24,X25] :
( c_in(X23,X24,X25)
| X23 = X22
| ~ c_in(X23,c_Set_Oinsert(X22,X24,X25),X25) ),
inference(variable_rename,[status(thm)],[c_0_999]) ).
fof(c_0_1610,plain,
! [X5,X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X6,X5,tc_fun(X7,tc_bool)),tc_fun(X7,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,X5,tc_fun(X7,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1000]) ).
fof(c_0_1611,plain,
! [X5,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X5,tc_fun(X7,tc_bool)),tc_fun(X7,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X6,X5,tc_fun(X7,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1001]) ).
fof(c_0_1612,plain,
! [X21,X22,X23,X24] :
( c_lessequals(X23,c_Set_Oinsert(X21,X22,X24),tc_fun(X24,tc_bool))
| ~ c_lessequals(X23,X22,tc_fun(X24,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1002]) ).
fof(c_0_1613,plain,
! [X6,X7] :
( c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_OId(X7),tc_fun(tc_prod(X7,X7),tc_bool)),X7)
| ~ c_Relation_Oantisym(X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_1003]) ).
fof(c_0_1614,plain,
! [X6,X7] : c_Relation_OField(X6,X7) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X6,X7,X7),c_Relation_ORange(X6,X7,X7),tc_fun(X7,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1004]) ).
fof(c_0_1615,plain,
! [X6,X7] : c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X6,c_Relation_OId(X7),tc_fun(tc_prod(X7,X7),tc_bool)),X7) = c_Transitive__Closure_Ortrancl(X6,X7),
inference(variable_rename,[status(thm)],[c_0_1005]) ).
fof(c_0_1616,plain,
! [X13,X14] : c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X13,c_Relation_OId(X14),tc_fun(tc_prod(X14,X14),tc_bool)),X14) = c_Transitive__Closure_Ortrancl(X13,X14),
inference(variable_rename,[status(thm)],[c_0_1006]) ).
fof(c_0_1617,plain,
! [X31,X32,X33,X34] :
( c_in(X31,c_Lattices_Oupper__semilattice__class_Osup(X33,X32,tc_fun(X34,tc_bool)),X34)
| ~ c_in(X31,X32,X34) ),
inference(variable_rename,[status(thm)],[c_0_1007]) ).
fof(c_0_1618,plain,
! [X31,X32,X33,X34] :
( c_in(X31,c_Lattices_Oupper__semilattice__class_Osup(X33,X32,tc_fun(X34,tc_bool)),X34)
| ~ c_in(X31,X33,X34) ),
inference(variable_rename,[status(thm)],[c_0_1008]) ).
fof(c_0_1619,plain,
! [X17,X18,X19] :
( c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X17,X18,tc_fun(tc_prod(X19,X19),tc_bool)),X19)
| ~ c_Wellfounded_Owf(X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_1009]) ).
fof(c_0_1620,plain,
! [X17,X18,X19] :
( c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X18,X17,tc_fun(tc_prod(X19,X19),tc_bool)),X19)
| ~ c_Wellfounded_Owf(X18,X19) ),
inference(variable_rename,[status(thm)],[c_0_1010]) ).
fof(c_0_1621,plain,
! [X20,X21,X22,X23] :
( hBOOL(hAPP(c_Set_Oinsert(X20,X22,X23),X21))
| ~ hBOOL(hAPP(X22,X21)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1011])])]) ).
fof(c_0_1622,plain,
! [X6,X7] :
( c_Wellfounded_Owf(hAPP(c_Relation_Oconverse(X7,X7),c_Transitive__Closure_Otrancl(X6,X7)),X7)
| ~ c_Wellfounded_Owf(hAPP(c_Relation_Oconverse(X7,X7),X6),X7) ),
inference(variable_rename,[status(thm)],[c_0_1012]) ).
fof(c_0_1623,plain,
! [X5,X6] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X6,X6),tc_bool)),X5,tc_fun(tc_prod(X6,X6),tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1013]) ).
fof(c_0_1624,plain,
! [X9,X10,X11,X12] :
( c_Set_Oinsert(X9,X11,X12) != c_Set_Oinsert(X9,X10,X12)
| c_in(X9,X10,X12)
| c_in(X9,X11,X12)
| X11 = X10 ),
inference(variable_rename,[status(thm)],[c_0_1014]) ).
fof(c_0_1625,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)),
c_0_1015 ).
fof(c_0_1626,plain,
! [X11,X12,X13] :
( hBOOL(hAPP(X13,X11))
| ~ hBOOL(hAPP(X13,v_sko__Wellfounded__Xacc__Xinducts__1(X13,X12)))
| ~ c_in(X11,c_Wellfounded_Oacc(X12,t_a),t_a) ),
inference(variable_rename,[status(thm)],[c_0_1016]) ).
fof(c_0_1627,plain,
! [X11,X12,X13] :
( hBOOL(hAPP(X13,X11))
| ~ hBOOL(hAPP(X13,v_sko__Wellfounded__Xacc__Xinduct__1(X13,X12)))
| ~ c_in(X11,c_Wellfounded_Oacc(X12,t_a),t_a) ),
inference(variable_rename,[status(thm)],[c_0_1017]) ).
fof(c_0_1628,plain,
! [X10,X11,X12,X13] :
( c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X12,X11,X13),X12,X13)
| ~ c_in(X10,X12,X13)
| ~ c_Wellfounded_Owf(X11,X13) ),
inference(variable_rename,[status(thm)],[c_0_1018]) ).
fof(c_0_1629,plain,
! [X13,X14,X15,X16] :
( c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X15,X14,X16),X15,X16)
| ~ c_in(X13,X15,X16)
| ~ c_Wellfounded_Owf(X14,X16) ),
inference(variable_rename,[status(thm)],[c_0_1019]) ).
fof(c_0_1630,plain,
! [X9,X10] : c_in(X9,c_Set_Oinsert(X9,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X10),X10),
inference(variable_rename,[status(thm)],[c_0_1020]) ).
fof(c_0_1631,plain,
! [X6,X7,X8] :
( c_Relation_Ototal__on(X7,X6,X8)
| ~ c_Relation_Ototal__on(X7,hAPP(c_Relation_Oconverse(X8,X8),X6),X8) ),
inference(variable_rename,[status(thm)],[c_0_1021]) ).
fof(c_0_1632,plain,
! [X6,X7,X8] :
( c_Relation_Orefl__on(X7,X6,X8)
| ~ c_Relation_Orefl__on(X7,hAPP(c_Relation_Oconverse(X8,X8),X6),X8) ),
inference(variable_rename,[status(thm)],[c_0_1022]) ).
fof(c_0_1633,plain,
! [X9,X10,X11,X12] :
( c_in(X9,X10,X12)
| ~ c_in(X9,X11,X12)
| ~ c_lessequals(X11,X10,tc_fun(X12,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1023]) ).
fof(c_0_1634,plain,
! [X31,X32,X33,X34] :
( c_in(X31,X32,X34)
| ~ c_in(X31,X33,X34)
| ~ c_lessequals(X33,X32,tc_fun(X34,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1024]) ).
fof(c_0_1635,plain,
! [X9,X10,X11,X12] :
( c_in(X9,X10,X12)
| ~ c_lessequals(X11,X10,tc_fun(X12,tc_bool))
| ~ c_in(X9,X11,X12) ),
inference(variable_rename,[status(thm)],[c_0_1025]) ).
fof(c_0_1636,plain,
! [X32,X33,X34,X35] :
( c_in(X32,X33,X35)
| ~ c_in(X32,X34,X35)
| ~ c_lessequals(X34,X33,tc_fun(X35,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1026]) ).
fof(c_0_1637,plain,
! [X5] : c_Relation_Orefl__on(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_bool)),X5),
inference(variable_rename,[status(thm)],[c_0_1027]) ).
fof(c_0_1638,plain,
! [X22,X23,X24,X25] :
( ~ class_Lattices_Oupper__semilattice(X25)
| c_lessequals(X22,c_Lattices_Oupper__semilattice__class_Osup(X24,X23,X25),X25)
| ~ c_lessequals(X22,X24,X25) ),
inference(variable_rename,[status(thm)],[c_0_1028]) ).
fof(c_0_1639,plain,
! [X22,X23,X24,X25] :
( ~ class_Lattices_Oupper__semilattice(X25)
| c_lessequals(X22,c_Lattices_Oupper__semilattice__class_Osup(X24,X23,X25),X25)
| ~ c_lessequals(X22,X23,X25) ),
inference(variable_rename,[status(thm)],[c_0_1029]) ).
fof(c_0_1640,plain,
! [X22,X23,X24,X25] :
( ~ class_Lattices_Olower__semilattice(X25)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X24,X23,X25),X22,X25)
| ~ c_lessequals(X23,X22,X25) ),
inference(variable_rename,[status(thm)],[c_0_1030]) ).
fof(c_0_1641,plain,
! [X22,X23,X24,X25] :
( ~ class_Lattices_Olower__semilattice(X25)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X24,X23,X25),X22,X25)
| ~ c_lessequals(X24,X22,X25) ),
inference(variable_rename,[status(thm)],[c_0_1031]) ).
fof(c_0_1642,plain,
! [X5,X6] : c_Relation_OImage(c_Relation_OId(X6),X5,X6,X6) = X5,
inference(variable_rename,[status(thm)],[c_0_1032]) ).
fof(c_0_1643,plain,
! [X5] : c_Transitive__Closure_Otrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_bool)),X5) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1033]) ).
fof(c_0_1644,plain,
! [X22,X23,X24,X25] :
( c_in(X23,c_Set_Oinsert(X22,X24,X25),X25)
| ~ c_in(X23,X24,X25) ),
inference(variable_rename,[status(thm)],[c_0_1034]) ).
fof(c_0_1645,plain,
! [X22,X23,X24,X25] :
( c_in(X23,c_Set_Oinsert(X22,X24,X25),X25)
| ~ c_in(X23,X24,X25) ),
inference(variable_rename,[status(thm)],[c_0_1035]) ).
fof(c_0_1646,plain,
! [X5,X6,X7] :
( X6 = X5
| ~ c_lessequals(X5,X6,tc_fun(X7,tc_bool))
| ~ c_lessequals(X6,X5,tc_fun(X7,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1036])])]) ).
fof(c_0_1647,plain,
! [X5,X6,X7] :
( X6 = X5
| ~ c_lessequals(X5,X6,tc_fun(X7,tc_bool))
| ~ c_lessequals(X6,X5,tc_fun(X7,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1037])])]) ).
fof(c_0_1648,plain,
! [X9,X10,X11] : hBOOL(hAPP(c_Set_Oinsert(X9,X10,X11),X9)),
inference(variable_rename,[status(thm)],[c_0_1038]) ).
fof(c_0_1649,plain,
! [X38,X39] :
( c_Arrow__Order__Mirabelle_Odictator(X39,X38)
| c_in(v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(X39,X38),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
inference(variable_rename,[status(thm)],[c_0_1039]) ).
fof(c_0_1650,plain,
! [X16,X17,X18] :
( c_Wellfounded_Oacyclic(X17,X18)
| ~ c_lessequals(X17,X16,tc_fun(tc_prod(X18,X18),tc_bool))
| ~ c_Wellfounded_Oacyclic(X16,X18) ),
inference(variable_rename,[status(thm)],[c_0_1040]) ).
fof(c_0_1651,plain,
! [X16,X17,X18] :
( c_Relation_Oantisym(X17,X18)
| ~ c_Relation_Oantisym(X16,X18)
| ~ c_lessequals(X17,X16,tc_fun(tc_prod(X18,X18),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1041]) ).
fof(c_0_1652,plain,
! [X35,X36,X37] :
( c_Wellfounded_Owf(X36,X37)
| ~ c_lessequals(X36,X35,tc_fun(tc_prod(X37,X37),tc_bool))
| ~ c_Wellfounded_Owf(X35,X37) ),
inference(variable_rename,[status(thm)],[c_0_1042]) ).
fof(c_0_1653,plain,
! [X30,X31,X32,X33,X34] :
( ~ class_HOL_Oord(X33)
| c_lessequals(hAPP(X32,X30),hAPP(X31,X30),X33)
| ~ c_lessequals(X32,X31,tc_fun(X34,X33)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1043])])]) ).
fof(c_0_1654,plain,
! [X7,X8] : c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X8),tc_bool)),X7,X8) = c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1044]) ).
fof(c_0_1655,plain,
! [X7,X8] : c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X8,X7),tc_bool)),X8,X7) = c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1045]) ).
fof(c_0_1656,plain,
! [X20,X21,X22,X23] :
( ~ class_Orderings_Opreorder(X23)
| c_lessequals(X22,X20,X23)
| ~ c_lessequals(X21,X20,X23)
| ~ c_lessequals(X22,X21,X23) ),
inference(variable_rename,[status(thm)],[c_0_1046]) ).
fof(c_0_1657,plain,
! [X20,X21,X22,X23] :
( ~ class_Orderings_Oorder(X23)
| c_lessequals(X20,X22,X23)
| ~ c_lessequals(X20,X21,X23)
| ~ c_lessequals(X21,X22,X23) ),
inference(variable_rename,[status(thm)],[c_0_1047]) ).
fof(c_0_1658,plain,
! [X35,X36,X37] :
( c_in(X36,c_Transitive__Closure_Otrancl(X35,X37),tc_prod(X37,X37))
| ~ c_in(X36,X35,tc_prod(X37,X37)) ),
inference(variable_rename,[status(thm)],[c_0_1048]) ).
fof(c_0_1659,plain,
! [X35,X36,X37] :
( c_in(X36,c_Transitive__Closure_Ortrancl(X35,X37),tc_prod(X37,X37))
| ~ c_in(X36,X35,tc_prod(X37,X37)) ),
inference(variable_rename,[status(thm)],[c_0_1049]) ).
fof(c_0_1660,plain,
! [X5,X6] :
( X5 = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool))
| ~ c_lessequals(X5,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),tc_fun(X6,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1050]) ).
fof(c_0_1661,plain,
! [X5,X6,X7] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X5,tc_fun(X7,tc_bool)),X5,tc_fun(X7,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1051]) ).
fof(c_0_1662,plain,
! [X5,X6,X7] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X5,tc_fun(X7,tc_bool)),X6,tc_fun(X7,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1052]) ).
fof(c_0_1663,plain,
! [X5,X6,X7] : c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X5,tc_fun(X7,tc_bool)),tc_fun(X7,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1053]) ).
fof(c_0_1664,plain,
! [X5,X6,X7] : c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X6,X5,tc_fun(X7,tc_bool)),tc_fun(X7,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1054]) ).
fof(c_0_1665,plain,
! [X20,X21,X22] :
( ~ class_Lattices_Olower__semilattice(X22)
| c_Lattices_Olower__semilattice__class_Oinf(X21,c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X22),X22) = c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_1055]) ).
fof(c_0_1666,plain,
! [X20,X21,X22] :
( ~ class_Lattices_Olattice(X22)
| c_Lattices_Olower__semilattice__class_Oinf(X21,c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X22),X22) = c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_1056]) ).
fof(c_0_1667,plain,
! [X20,X21,X22] :
( ~ class_Lattices_Olattice(X22)
| c_Lattices_Oupper__semilattice__class_Osup(X21,c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X22),X22) = c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_1057]) ).
fof(c_0_1668,plain,
! [X20,X21,X22] :
( ~ class_Lattices_Oupper__semilattice(X22)
| c_Lattices_Oupper__semilattice__class_Osup(X21,c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X22),X22) = c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_1058]) ).
fof(c_0_1669,plain,
! [X6,X7,X8] :
( c_Relation_Ototal__on(X7,hAPP(c_Relation_Oconverse(X8,X8),X6),X8)
| ~ c_Relation_Ototal__on(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1059]) ).
fof(c_0_1670,plain,
! [X6,X7,X8] :
( c_Relation_Orefl__on(X7,hAPP(c_Relation_Oconverse(X8,X8),X6),X8)
| ~ c_Relation_Orefl__on(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1060]) ).
fof(c_0_1671,plain,
! [X9,X10,X11] : c_Set_Oinsert(X9,c_Set_Oinsert(X9,X10,X11),X11) = c_Set_Oinsert(X9,X10,X11),
inference(variable_rename,[status(thm)],[c_0_1061]) ).
fof(c_0_1672,plain,
! [X11,X12,X13] :
( ~ hBOOL(hAPP(X12,X11))
| ~ c_in(X11,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1062])])]) ).
fof(c_0_1673,plain,
! [X37] :
( c_Arrow__Order__Mirabelle_Ounanimity(X37)
| c_in(v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2(X37),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
inference(variable_rename,[status(thm)],[c_0_1063]) ).
fof(c_0_1674,plain,
! [X37] :
( c_Arrow__Order__Mirabelle_OIIA(X37)
| c_in(v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X37),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
inference(variable_rename,[status(thm)],[c_0_1064]) ).
fof(c_0_1675,plain,
! [X37] :
( c_Arrow__Order__Mirabelle_OIIA(X37)
| c_in(v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X37),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
inference(variable_rename,[status(thm)],[c_0_1065]) ).
fof(c_0_1676,plain,
! [X9,X10] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X9)),
inference(variable_rename,[status(thm)],[c_0_1066]) ).
fof(c_0_1677,plain,
! [X7,X8,X9] :
( c_Relation_ORange(X7,X8,X9) != c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))
| X7 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X8,X9),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1067]) ).
fof(c_0_1678,plain,
! [X7,X8,X9] :
( c_Relation_ODomain(X7,X9,X8) != c_Orderings_Obot__class_Obot(tc_fun(X9,tc_bool))
| X7 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X9,X8),tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1068]) ).
fof(c_0_1679,plain,
! [X5] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1069]) ).
fof(c_0_1680,plain,
! [X5,X6,X7] :
( c_Lattices_Oupper__semilattice__class_Osup(X6,X5,tc_fun(X7,tc_bool)) != X5
| c_lessequals(X6,X5,tc_fun(X7,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1070]) ).
fof(c_0_1681,plain,
! [X5,X6,X7] :
( c_Lattices_Olower__semilattice__class_Oinf(X6,X5,tc_fun(X7,tc_bool)) = X5
| ~ c_lessequals(X5,X6,tc_fun(X7,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1071]) ).
fof(c_0_1682,plain,
! [X5,X6,X7] :
( c_Lattices_Olower__semilattice__class_Oinf(X6,X5,tc_fun(X7,tc_bool)) = X6
| ~ c_lessequals(X6,X5,tc_fun(X7,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1072]) ).
fof(c_0_1683,plain,
! [X5,X6,X7] :
( c_Lattices_Oupper__semilattice__class_Osup(X6,X5,tc_fun(X7,tc_bool)) = X6
| ~ c_lessequals(X5,X6,tc_fun(X7,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1073]) ).
fof(c_0_1684,plain,
! [X5,X6,X7] :
( c_Lattices_Oupper__semilattice__class_Osup(X6,X5,tc_fun(X7,tc_bool)) = X5
| ~ c_lessequals(X6,X5,tc_fun(X7,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1074]) ).
fof(c_0_1685,plain,
! [X11,X12,X13,X14] :
( hBOOL(hAPP(X12,X11))
| ~ c_lessequals(X13,X12,tc_fun(X14,tc_bool))
| ~ hBOOL(hAPP(X13,X11)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1075])])]) ).
fof(c_0_1686,plain,
! [X11,X12,X13,X14] :
( hBOOL(hAPP(X12,X11))
| ~ hBOOL(hAPP(X13,X11))
| ~ c_lessequals(X13,X12,tc_fun(X14,tc_bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1076])])]) ).
fof(c_0_1687,axiom,
c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
c_0_1077 ).
fof(c_0_1688,axiom,
c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
c_0_1078 ).
fof(c_0_1689,plain,
! [X11,X12,X13] :
( hBOOL(hAPP(X12,X11))
| ~ c_in(X11,c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool)),X13) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1079])])]) ).
fof(c_0_1690,plain,
! [X5] : c_Relation_OField(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_bool)),X5) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1080]) ).
fof(c_0_1691,plain,
! [X5,X6,X7] :
( c_Lattices_Oupper__semilattice__class_Osup(X6,X5,tc_fun(X7,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool))
| X6 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1081]) ).
fof(c_0_1692,plain,
! [X5,X6,X7] :
( c_Lattices_Oupper__semilattice__class_Osup(X6,X5,tc_fun(X7,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool))
| X5 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)) ),
inference(variable_rename,[status(thm)],[c_0_1082]) ).
fof(c_0_1693,plain,
! [X7,X8,X9] : c_Relation_ORange(X7,X8,X9) = c_Relation_ODomain(hAPP(c_Relation_Oconverse(X8,X9),X7),X9,X8),
inference(variable_rename,[status(thm)],[c_0_1083]) ).
fof(c_0_1694,plain,
! [X7,X8,X9] : c_Relation_ODomain(hAPP(c_Relation_Oconverse(X8,X9),X7),X9,X8) = c_Relation_ORange(X7,X8,X9),
inference(variable_rename,[status(thm)],[c_0_1084]) ).
fof(c_0_1695,plain,
! [X7,X8,X9] : c_Relation_ORange(hAPP(c_Relation_Oconverse(X9,X8),X7),X8,X9) = c_Relation_ODomain(X7,X9,X8),
inference(variable_rename,[status(thm)],[c_0_1085]) ).
fof(c_0_1696,plain,
! [X22,X23,X24] : c_lessequals(X23,c_Set_Oinsert(X22,X23,X24),tc_fun(X24,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1086]) ).
fof(c_0_1697,plain,
! [X9,X10,X11] :
( c_Set_Oinsert(X10,X9,X11) != c_Orderings_Obot__class_Obot(tc_fun(X11,tc_bool))
| c_in(X10,X9,X11) ),
inference(variable_rename,[status(thm)],[c_0_1087]) ).
fof(c_0_1698,plain,
! [X6,X7] :
( c_Wellfounded_Owf(X6,X7)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X6,X7),c_Wellfounded_Oacc(X6,X7),X7) ),
inference(variable_rename,[status(thm)],[c_0_1088]) ).
fof(c_0_1699,plain,
! [X6,X7] :
( c_Wellfounded_Owf(X6,X7)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X6,X7),c_Wellfounded_Oacc(X6,X7),X7) ),
inference(variable_rename,[status(thm)],[c_0_1089]) ).
fof(c_0_1700,plain,
! [X20,X21,X22] :
( ~ class_Orderings_Oorder(X22)
| X21 = X20
| ~ c_lessequals(X21,X20,X22)
| ~ c_lessequals(X20,X21,X22) ),
inference(variable_rename,[status(thm)],[c_0_1090]) ).
fof(c_0_1701,plain,
! [X20,X21,X22] :
( ~ class_Orderings_Oorder(X22)
| X21 = X20
| ~ c_lessequals(X20,X21,X22)
| ~ c_lessequals(X21,X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_1091]) ).
fof(c_0_1702,plain,
! [X20,X21,X22] :
( ~ class_Orderings_Oorder(X22)
| X21 = X20
| ~ c_lessequals(X20,X21,X22)
| ~ c_lessequals(X21,X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_1092]) ).
fof(c_0_1703,plain,
! [X5] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1093]) ).
fof(c_0_1704,plain,
! [X6,X7] : c_Transitive__Closure_Ortrancl(X6,X7) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X6,X7),c_Relation_OId(X7),tc_fun(tc_prod(X7,X7),tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1094]) ).
fof(c_0_1705,plain,
! [X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X6,X7),c_Relation_OId(X7),tc_fun(tc_prod(X7,X7),tc_bool)) = c_Transitive__Closure_Ortrancl(X6,X7),
inference(variable_rename,[status(thm)],[c_0_1095]) ).
fof(c_0_1706,plain,
! [X13,X14] : c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X13,X14),c_Relation_OId(X14),tc_fun(tc_prod(X14,X14),tc_bool)) = c_Transitive__Closure_Ortrancl(X13,X14),
inference(variable_rename,[status(thm)],[c_0_1096]) ).
fof(c_0_1707,plain,
! [X5] : c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_bool)),X5) = c_Relation_OId(X5),
inference(variable_rename,[status(thm)],[c_0_1097]) ).
fof(c_0_1708,plain,
! [X5] : c_Relation_Oantisym(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_bool)),X5),
inference(variable_rename,[status(thm)],[c_0_1098]) ).
fof(c_0_1709,plain,
! [X5] : c_Wellfounded_Owf(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_bool)),X5),
inference(variable_rename,[status(thm)],[c_0_1099]) ).
fof(c_0_1710,plain,
! [X20,X21,X22] :
( ~ class_Lattices_Olattice(X22)
| c_Lattices_Olower__semilattice__class_Oinf(X21,c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X22),X22) = X21 ),
inference(variable_rename,[status(thm)],[c_0_1100]) ).
fof(c_0_1711,plain,
! [X20,X21,X22] :
( ~ class_Lattices_Olattice(X22)
| c_Lattices_Oupper__semilattice__class_Osup(X21,c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X22),X22) = X21 ),
inference(variable_rename,[status(thm)],[c_0_1101]) ).
fof(c_0_1712,plain,
! [X20,X21,X22] :
( ~ class_Lattices_Olower__semilattice(X22)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X22),X21,X22) ),
inference(variable_rename,[status(thm)],[c_0_1102]) ).
fof(c_0_1713,plain,
! [X20,X21,X22] :
( ~ class_Lattices_Olower__semilattice(X22)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X22),X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_1103]) ).
fof(c_0_1714,plain,
! [X20,X21,X22] :
( ~ class_Lattices_Olattice(X22)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X22),X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_1104]) ).
fof(c_0_1715,plain,
! [X20,X21,X22] :
( ~ class_Lattices_Olattice(X22)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X22),X21,X22) ),
inference(variable_rename,[status(thm)],[c_0_1105]) ).
fof(c_0_1716,plain,
! [X20,X21,X22] :
( ~ class_Lattices_Olattice(X22)
| c_lessequals(X21,c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X22),X22) ),
inference(variable_rename,[status(thm)],[c_0_1106]) ).
fof(c_0_1717,plain,
! [X20,X21,X22] :
( ~ class_Lattices_Olattice(X22)
| c_lessequals(X20,c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X22),X22) ),
inference(variable_rename,[status(thm)],[c_0_1107]) ).
fof(c_0_1718,plain,
! [X20,X21,X22] :
( ~ class_Lattices_Oupper__semilattice(X22)
| c_lessequals(X20,c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X22),X22) ),
inference(variable_rename,[status(thm)],[c_0_1108]) ).
fof(c_0_1719,plain,
! [X20,X21,X22] :
( ~ class_Lattices_Oupper__semilattice(X22)
| c_lessequals(X21,c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X22),X22) ),
inference(variable_rename,[status(thm)],[c_0_1109]) ).
fof(c_0_1720,plain,
! [X22,X23] : ~ c_in(X22,c_Orderings_Obot__class_Obot(tc_fun(X23,tc_bool)),X23),
inference(variable_rename,[status(thm)],[c_0_1110]) ).
fof(c_0_1721,plain,
! [X31,X32] : ~ c_in(X31,c_Orderings_Obot__class_Obot(tc_fun(X32,tc_bool)),X32),
inference(variable_rename,[status(thm)],[c_0_1111]) ).
fof(c_0_1722,plain,
! [X9,X10] : ~ c_in(X9,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X10),
inference(variable_rename,[status(thm)],[c_0_1112]) ).
fof(c_0_1723,axiom,
c_Relation_ORange(v_r,t_a,t_b) = c_Relation_ODomain(hAPP(c_Relation_Oconverse(t_a,t_b),v_r),t_b,t_a),
c_0_1113 ).
fof(c_0_1724,plain,
! [X9,X10,X11] : c_in(X9,c_Set_Oinsert(X9,X10,X11),X11),
inference(variable_rename,[status(thm)],[c_0_1114]) ).
fof(c_0_1725,plain,
! [X22,X23,X24] : c_in(X22,c_Set_Oinsert(X22,X23,X24),X24),
inference(variable_rename,[status(thm)],[c_0_1115]) ).
fof(c_0_1726,plain,
! [X9,X10,X11] : c_in(X9,c_Set_Oinsert(X9,X10,X11),X11),
inference(variable_rename,[status(thm)],[c_0_1116]) ).
fof(c_0_1727,plain,
! [X6,X7] :
( c_Relation_Oantisym(X6,X7)
| ~ c_Relation_Oantisym(hAPP(c_Relation_Oconverse(X7,X7),X6),X7) ),
inference(variable_rename,[status(thm)],[c_0_1117]) ).
fof(c_0_1728,plain,
! [X6,X7] :
( c_Relation_Osym(X6,X7)
| ~ c_Relation_Osym(hAPP(c_Relation_Oconverse(X7,X7),X6),X7) ),
inference(variable_rename,[status(thm)],[c_0_1118]) ).
fof(c_0_1729,plain,
! [X6,X7] :
( c_Wellfounded_Oacyclic(X6,X7)
| ~ c_Wellfounded_Oacyclic(hAPP(c_Relation_Oconverse(X7,X7),X6),X7) ),
inference(variable_rename,[status(thm)],[c_0_1119]) ).
fof(c_0_1730,plain,
! [X6,X7] : c_Transitive__Closure_Ortrancl(hAPP(c_Relation_Oconverse(X7,X7),X6),X7) = hAPP(c_Relation_Oconverse(X7,X7),c_Transitive__Closure_Ortrancl(X6,X7)),
inference(variable_rename,[status(thm)],[c_0_1120]) ).
fof(c_0_1731,plain,
! [X6,X7] : c_Transitive__Closure_Otrancl(hAPP(c_Relation_Oconverse(X7,X7),X6),X7) = hAPP(c_Relation_Oconverse(X7,X7),c_Transitive__Closure_Otrancl(X6,X7)),
inference(variable_rename,[status(thm)],[c_0_1121]) ).
fof(c_0_1732,plain,
! [X5,X6] : c_Lattices_Olower__semilattice__class_Oinf(X5,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),tc_fun(X6,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1122]) ).
fof(c_0_1733,plain,
! [X5,X6] : c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X5,tc_fun(X6,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1123]) ).
fof(c_0_1734,plain,
! [X5,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,X5,tc_fun(X7,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X5,X6,tc_fun(X7,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1124]) ).
fof(c_0_1735,plain,
! [X5,X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(X6,X5,tc_fun(X7,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X5,X6,tc_fun(X7,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1125]) ).
fof(c_0_1736,plain,
! [X20,X21,X22] :
( ~ class_Lattices_Olower__semilattice(X22)
| c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X22) != X21
| c_lessequals(X21,X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_1126]) ).
fof(c_0_1737,plain,
! [X20,X21,X22] :
( ~ class_Lattices_Oupper__semilattice(X22)
| c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X22) != X20
| c_lessequals(X21,X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_1127]) ).
fof(c_0_1738,plain,
! [X20,X21,X22] :
( ~ class_Lattices_Olower__semilattice(X22)
| c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X22) = X20
| ~ c_lessequals(X20,X21,X22) ),
inference(variable_rename,[status(thm)],[c_0_1128]) ).
fof(c_0_1739,plain,
! [X20,X21,X22] :
( ~ class_Lattices_Olower__semilattice(X22)
| c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X22) = X21
| ~ c_lessequals(X21,X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_1129]) ).
fof(c_0_1740,plain,
! [X20,X21,X22] :
( ~ class_Lattices_Oupper__semilattice(X22)
| c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X22) = X20
| ~ c_lessequals(X21,X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_1130]) ).
fof(c_0_1741,plain,
! [X20,X21,X22] :
( ~ class_Lattices_Oupper__semilattice(X22)
| c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X22) = X21
| ~ c_lessequals(X20,X21,X22) ),
inference(variable_rename,[status(thm)],[c_0_1131]) ).
fof(c_0_1742,plain,
! [X5] : c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1132]) ).
fof(c_0_1743,plain,
! [X22,X23,X24] :
( c_Set_Oinsert(X22,X23,X24) = X23
| ~ c_in(X22,X23,X24) ),
inference(variable_rename,[status(thm)],[c_0_1133]) ).
fof(c_0_1744,plain,
! [X6,X7,X8] :
( c_Relation_Orefl__on(X7,X6,X8)
| ~ c_Equiv__Relations_Oequiv(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1134]) ).
fof(c_0_1745,plain,
! [X38,X39] :
( hAPP(X39,v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(X39,X38)) != hAPP(v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(X39,X38),X38)
| c_Arrow__Order__Mirabelle_Odictator(X39,X38) ),
inference(variable_rename,[status(thm)],[c_0_1135]) ).
fof(c_0_1746,plain,
! [X6,X7] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X6,X7),X7,X7) = c_Relation_ORange(X6,X7,X7),
inference(variable_rename,[status(thm)],[c_0_1136]) ).
fof(c_0_1747,plain,
! [X6,X7] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X6,X7),X7,X7) = c_Relation_ODomain(X6,X7,X7),
inference(variable_rename,[status(thm)],[c_0_1137]) ).
fof(c_0_1748,plain,
! [X5,X6] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),tc_fun(X6,tc_bool)) = X5,
inference(variable_rename,[status(thm)],[c_0_1138]) ).
fof(c_0_1749,plain,
! [X5,X6] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X5,tc_fun(X6,tc_bool)) = X5,
inference(variable_rename,[status(thm)],[c_0_1139]) ).
fof(c_0_1750,plain,
! [X5,X6] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X5,tc_fun(X6,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1140]) ).
fof(c_0_1751,plain,
! [X22,X23,X24] : c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)) != c_Set_Oinsert(X22,X23,X24),
inference(variable_rename,[status(thm)],[c_0_1141]) ).
fof(c_0_1752,plain,
! [X22,X23,X24] : c_Set_Oinsert(X22,X23,X24) != c_Orderings_Obot__class_Obot(tc_fun(X24,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1142]) ).
fof(c_0_1753,plain,
! [X11,X12,X13,X14] : hAPP(c_COMBK(X12,X14,X13),X11) = X12,
inference(variable_rename,[status(thm)],[c_0_1143]) ).
fof(c_0_1754,plain,
! [X7,X8,X9] : hAPP(c_Relation_Oconverse(X8,X9),hAPP(c_Relation_Oconverse(X9,X8),X7)) = X7,
inference(variable_rename,[status(thm)],[c_0_1144]) ).
fof(c_0_1755,plain,
! [X20,X21,X22] :
( ~ class_Orderings_Olinorder(X22)
| c_lessequals(X20,X21,X22)
| c_lessequals(X21,X20,X22) ),
inference(variable_rename,[status(thm)],[c_0_1145]) ).
fof(c_0_1756,plain,
! [X14,X15,X16] :
( hBOOL(hAPP(X15,X14))
| ~ c_in(X14,X15,X16) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1146])])]) ).
fof(c_0_1757,plain,
! [X20,X21,X22] :
( ~ class_Lattices_Olattice(X22)
| c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X22) = c_Lattices_Oupper__semilattice__class_Osup(X20,X21,X22) ),
inference(variable_rename,[status(thm)],[c_0_1147]) ).
fof(c_0_1758,plain,
! [X20,X21,X22] :
( ~ class_Lattices_Oupper__semilattice(X22)
| c_Lattices_Oupper__semilattice__class_Osup(X21,X20,X22) = c_Lattices_Oupper__semilattice__class_Osup(X20,X21,X22) ),
inference(variable_rename,[status(thm)],[c_0_1148]) ).
fof(c_0_1759,plain,
! [X20,X21,X22] :
( ~ class_Lattices_Olattice(X22)
| c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X22) = c_Lattices_Olower__semilattice__class_Oinf(X20,X21,X22) ),
inference(variable_rename,[status(thm)],[c_0_1149]) ).
fof(c_0_1760,plain,
! [X20,X21,X22] :
( ~ class_Lattices_Olower__semilattice(X22)
| c_Lattices_Olower__semilattice__class_Oinf(X21,X20,X22) = c_Lattices_Olower__semilattice__class_Oinf(X20,X21,X22) ),
inference(variable_rename,[status(thm)],[c_0_1150]) ).
fof(c_0_1761,plain,
! [X6,X7] :
( c_Relation_Oantisym(hAPP(c_Relation_Oconverse(X7,X7),X6),X7)
| ~ c_Relation_Oantisym(X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_1151]) ).
fof(c_0_1762,plain,
! [X6,X7] :
( c_Relation_Osym(hAPP(c_Relation_Oconverse(X7,X7),X6),X7)
| ~ c_Relation_Osym(X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_1152]) ).
fof(c_0_1763,plain,
! [X6,X7] :
( c_Wellfounded_Oacyclic(hAPP(c_Relation_Oconverse(X7,X7),X6),X7)
| ~ c_Wellfounded_Oacyclic(X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_1153]) ).
fof(c_0_1764,plain,
! [X6,X7] : c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool)),X6,X7),
inference(variable_rename,[status(thm)],[c_0_1154]) ).
fof(c_0_1765,plain,
! [X6,X7] : c_Relation_OField(hAPP(c_Relation_Oconverse(X7,X7),X6),X7) = c_Relation_OField(X6,X7),
inference(variable_rename,[status(thm)],[c_0_1155]) ).
fof(c_0_1766,plain,
! [X5,X6,X7] :
( ~ class_Lattices_Obounded__lattice(X7)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X5,X7) != c_Orderings_Obot__class_Obot(X7)
| X5 = c_Orderings_Obot__class_Obot(X7) ),
inference(variable_rename,[status(thm)],[c_0_1156]) ).
fof(c_0_1767,plain,
! [X5,X6,X7] :
( ~ class_Lattices_Obounded__lattice(X7)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X5,X7) != c_Orderings_Obot__class_Obot(X7)
| X6 = c_Orderings_Obot__class_Obot(X7) ),
inference(variable_rename,[status(thm)],[c_0_1157]) ).
fof(c_0_1768,plain,
! [X9,X10,X11] :
( c_in(X9,c_Wellfounded_Oacc(X10,X11),X11)
| ~ c_Wellfounded_Owf(X10,X11) ),
inference(variable_rename,[status(thm)],[c_0_1158]) ).
fof(c_0_1769,plain,
! [X14,X15,X16] :
( c_in(X14,X15,X16)
| ~ hBOOL(hAPP(X15,X14)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1159])])]) ).
fof(c_0_1770,plain,
! [X6,X7,X8] :
( c_Relation_Osym(X6,X8)
| ~ c_Equiv__Relations_Oequiv(X7,X6,X8) ),
inference(variable_rename,[status(thm)],[c_0_1160]) ).
fof(c_0_1771,plain,
! [X63,X64,X65] :
( X64 = X63
| ~ c_fequal(X64,X63,X65) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1161])])]) ).
fof(c_0_1772,plain,
! [X5,X6] : c_Relation_ORange(c_Relation_OId__on(X5,X6),X6,X6) = X5,
inference(variable_rename,[status(thm)],[c_0_1162]) ).
fof(c_0_1773,plain,
! [X5,X6] : c_Relation_ODomain(c_Relation_OId__on(X5,X6),X6,X6) = X5,
inference(variable_rename,[status(thm)],[c_0_1163]) ).
fof(c_0_1774,plain,
! [X5,X6] : c_Relation_Orefl__on(X5,c_Relation_OId__on(X5,X6),X6),
inference(variable_rename,[status(thm)],[c_0_1164]) ).
fof(c_0_1775,plain,
! [X5,X6] : c_Relation_Osingle__valued(c_Relation_OId__on(X5,X6),X6,X6),
inference(variable_rename,[status(thm)],[c_0_1165]) ).
fof(c_0_1776,plain,
! [X5,X6] : hAPP(c_Relation_Oconverse(X6,X6),c_Relation_OId__on(X5,X6)) = c_Relation_OId__on(X5,X6),
inference(variable_rename,[status(thm)],[c_0_1166]) ).
fof(c_0_1777,plain,
! [X6,X7] :
( hAPP(c_Relation_Oconverse(X7,X7),X6) != X6
| c_Relation_Osym(X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_1167]) ).
fof(c_0_1778,plain,
! [X5,X6] : c_Lattices_Olower__semilattice__class_Oinf(X5,X5,tc_fun(X6,tc_bool)) = X5,
inference(variable_rename,[status(thm)],[c_0_1168]) ).
fof(c_0_1779,plain,
! [X5,X6] : c_Lattices_Oupper__semilattice__class_Osup(X5,X5,tc_fun(X6,tc_bool)) = X5,
inference(variable_rename,[status(thm)],[c_0_1169]) ).
fof(c_0_1780,plain,
! [X5,X6] : c_lessequals(X5,X5,tc_fun(X6,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1170]) ).
fof(c_0_1781,plain,
! [X9,X10] : c_lessequals(X9,X9,tc_fun(X10,tc_bool)),
inference(variable_rename,[status(thm)],[c_0_1171]) ).
fof(c_0_1782,plain,
! [X9,X10] :
( ~ class_Lattices_Obounded__lattice(X10)
| c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X10),X9,X10) = c_Orderings_Obot__class_Obot(X10) ),
inference(variable_rename,[status(thm)],[c_0_1172]) ).
fof(c_0_1783,plain,
! [X9,X10] :
( ~ class_Lattices_Obounded__lattice(X10)
| c_Lattices_Olower__semilattice__class_Oinf(X9,c_Orderings_Obot__class_Obot(X10),X10) = c_Orderings_Obot__class_Obot(X10) ),
inference(variable_rename,[status(thm)],[c_0_1173]) ).
fof(c_0_1784,plain,
! [X9,X10] :
( ~ class_Lattices_Obounded__lattice(X10)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X10),X9,X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_1174]) ).
fof(c_0_1785,plain,
! [X9,X10] :
( ~ class_Lattices_Obounded__lattice(X10)
| c_Lattices_Oupper__semilattice__class_Osup(X9,c_Orderings_Obot__class_Obot(X10),X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_1175]) ).
fof(c_0_1786,plain,
! [X9,X10] :
( ~ class_Orderings_Obot(X10)
| c_lessequals(c_Orderings_Obot__class_Obot(X10),X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_1176]) ).
fof(c_0_1787,plain,
! [X6,X7] :
( hAPP(c_Relation_Oconverse(X7,X7),X6) = X6
| ~ c_Relation_Osym(X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_1177]) ).
fof(c_0_1788,plain,
! [X6,X7] :
( c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X6,X7),X7)
| ~ c_Wellfounded_Owf(X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_1178]) ).
fof(c_0_1789,plain,
! [X6,X7] :
( c_Relation_Osym(c_Transitive__Closure_Ortrancl(X6,X7),X7)
| ~ c_Relation_Osym(X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_1179]) ).
fof(c_0_1790,plain,
! [X6,X7] :
( c_Relation_Osym(c_Transitive__Closure_Otrancl(X6,X7),X7)
| ~ c_Relation_Osym(X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_1180]) ).
fof(c_0_1791,plain,
! [X6,X7] :
( c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X6,X7),X7)
| ~ c_Wellfounded_Oacyclic(X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_1181]) ).
fof(c_0_1792,plain,
! [X9,X10] :
( ~ class_Lattices_Olower__semilattice(X10)
| c_Lattices_Olower__semilattice__class_Oinf(X9,X9,X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_1182]) ).
fof(c_0_1793,plain,
! [X9,X10] :
( ~ class_Lattices_Oupper__semilattice(X10)
| c_Lattices_Oupper__semilattice__class_Osup(X9,X9,X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_1183]) ).
fof(c_0_1794,plain,
! [X9,X10] :
( ~ class_Orderings_Opreorder(X10)
| c_lessequals(X9,X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_1184]) ).
fof(c_0_1795,plain,
! [X9,X10] :
( ~ class_Orderings_Oorder(X10)
| c_lessequals(X9,X9,X10) ),
inference(variable_rename,[status(thm)],[c_0_1185]) ).
fof(c_0_1796,plain,
! [X5] : c_Relation_Osingle__valued(c_Relation_OId(X5),X5,X5),
inference(variable_rename,[status(thm)],[c_0_1186]) ).
fof(c_0_1797,plain,
! [X9,X10] : c_fequal(X9,X9,X10),
inference(variable_rename,[status(thm)],[c_0_1187]) ).
fof(c_0_1798,plain,
! [X6,X7] : c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X6,X7),X7) = c_Transitive__Closure_Ortrancl(X6,X7),
inference(variable_rename,[status(thm)],[c_0_1188]) ).
fof(c_0_1799,plain,
! [X13,X14] : c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X13,X14),X14) = c_Transitive__Closure_Ortrancl(X13,X14),
inference(variable_rename,[status(thm)],[c_0_1189]) ).
fof(c_0_1800,plain,
! [X13,X14] : c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X13,X14),X14) = c_Transitive__Closure_Ortrancl(X13,X14),
inference(variable_rename,[status(thm)],[c_0_1190]) ).
fof(c_0_1801,plain,
! [X5] : hAPP(c_Relation_Oconverse(X5,X5),c_Relation_OId(X5)) = c_Relation_OId(X5),
inference(variable_rename,[status(thm)],[c_0_1191]) ).
fof(c_0_1802,plain,
! [X5,X6] : c_Relation_Osym(c_Relation_OId__on(X5,X6),X6),
inference(variable_rename,[status(thm)],[c_0_1192]) ).
fof(c_0_1803,plain,
! [X5,X6] : c_Relation_Oantisym(c_Relation_OId__on(X5,X6),X6),
inference(variable_rename,[status(thm)],[c_0_1193]) ).
fof(c_0_1804,plain,
! [X61,X62] :
( class_HOL_Oord(tc_fun(X61,X62))
| ~ class_HOL_Oord(X62) ),
inference(variable_rename,[status(thm)],[c_0_1194]) ).
fof(c_0_1805,plain,
! [X61,X62] :
( class_Orderings_Obot(tc_fun(X61,X62))
| ~ class_Orderings_Obot(X62) ),
inference(variable_rename,[status(thm)],[c_0_1195]) ).
fof(c_0_1806,plain,
! [X61,X62] :
( class_Orderings_Oorder(tc_fun(X61,X62))
| ~ class_Orderings_Oorder(X62) ),
inference(variable_rename,[status(thm)],[c_0_1196]) ).
fof(c_0_1807,plain,
! [X61,X62] :
( class_Lattices_Olattice(tc_fun(X61,X62))
| ~ class_Lattices_Olattice(X62) ),
inference(variable_rename,[status(thm)],[c_0_1197]) ).
fof(c_0_1808,plain,
! [X61,X62] :
( class_Orderings_Opreorder(tc_fun(X61,X62))
| ~ class_Orderings_Opreorder(X62) ),
inference(variable_rename,[status(thm)],[c_0_1198]) ).
fof(c_0_1809,plain,
! [X61,X62] :
( class_Lattices_Obounded__lattice(tc_fun(X61,X62))
| ~ class_Lattices_Obounded__lattice(X62) ),
inference(variable_rename,[status(thm)],[c_0_1199]) ).
fof(c_0_1810,plain,
! [X61,X62] :
( class_Lattices_Odistrib__lattice(tc_fun(X61,X62))
| ~ class_Lattices_Odistrib__lattice(X62) ),
inference(variable_rename,[status(thm)],[c_0_1200]) ).
fof(c_0_1811,plain,
! [X61,X62] :
( class_Lattices_Olower__semilattice(tc_fun(X61,X62))
| ~ class_Lattices_Olattice(X62) ),
inference(variable_rename,[status(thm)],[c_0_1201]) ).
fof(c_0_1812,plain,
! [X61,X62] :
( class_Lattices_Oupper__semilattice(tc_fun(X61,X62))
| ~ class_Lattices_Olattice(X62) ),
inference(variable_rename,[status(thm)],[c_0_1202]) ).
fof(c_0_1813,plain,
! [X6,X7] :
( c_Wellfounded_Oacyclic(X6,X7)
| ~ c_Wellfounded_Owf(X6,X7) ),
inference(variable_rename,[status(thm)],[c_0_1203]) ).
fof(c_0_1814,plain,
! [X5] : c_Relation_Oantisym(c_Relation_OId(X5),X5),
inference(variable_rename,[status(thm)],[c_0_1204]) ).
fof(c_0_1815,plain,
! [X5] : c_Relation_Osym(c_Relation_OId(X5),X5),
inference(variable_rename,[status(thm)],[c_0_1205]) ).
fof(c_0_1816,axiom,
class_HOL_Oord(tc_bool),
c_0_1206 ).
fof(c_0_1817,axiom,
class_Orderings_Obot(tc_bool),
c_0_1207 ).
fof(c_0_1818,axiom,
class_Orderings_Oorder(tc_bool),
c_0_1208 ).
fof(c_0_1819,axiom,
class_Lattices_Olattice(tc_bool),
c_0_1209 ).
fof(c_0_1820,axiom,
class_Orderings_Opreorder(tc_bool),
c_0_1210 ).
fof(c_0_1821,axiom,
class_Lattices_Obounded__lattice(tc_bool),
c_0_1211 ).
fof(c_0_1822,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
c_0_1212 ).
fof(c_0_1823,axiom,
class_Lattices_Olower__semilattice(tc_bool),
c_0_1213 ).
fof(c_0_1824,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
c_0_1214 ).
fof(c_0_1825,axiom,
c_Arrow__Order__Mirabelle_OIIA(v_F),
c_0_1215 ).
fof(c_0_1826,axiom,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
c_0_1216 ).
fof(c_0_1827,axiom,
v_a____ != v_c____,
c_0_1217 ).
fof(c_0_1828,axiom,
v_b____ != v_c____,
c_0_1218 ).
fof(c_0_1829,axiom,
v_a____ != v_b____,
c_0_1219 ).
cnf(c_0_1830,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_1220]) ).
cnf(c_0_1831,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_1221]) ).
cnf(c_0_1832,plain,
( X1 = X2
| X3 = X4
| X1 = X4
| X2 = X3
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X5,v_sko__local__X1__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X1__1(X5,X6,X1,X3,X2,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_1222]) ).
cnf(c_0_1833,plain,
( X1 = X2
| X3 = X4
| X1 = X4
| X2 = X3
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_1223]) ).
cnf(c_0_1834,plain,
( X1 = X2
| X3 = X4
| X1 = X4
| X2 = X3
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_1224]) ).
cnf(c_0_1835,plain,
( X1 = X2
| X3 = X4
| X1 = X4
| X2 = X3
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__local__X1__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X1__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_1225]) ).
cnf(c_0_1836,plain,
( X1 = X2
| X3 = X4
| X1 = X4
| X2 = X3
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_1226]) ).
cnf(c_0_1837,plain,
( X1 = X2
| X3 = X4
| X1 = X4
| X2 = X3
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_1227]) ).
cnf(c_0_1838,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_1228]) ).
cnf(c_0_1839,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_1229]) ).
cnf(c_0_1840,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_1230]) ).
cnf(c_0_1841,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_1231]) ).
cnf(c_0_1842,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_1232]) ).
cnf(c_0_1843,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_1233]) ).
cnf(c_0_1844,plain,
( hAPP(hAPP(X3,X7),X9) = hAPP(hAPP(X3,X8),X10)
| ~ c_Equiv__Relations_Ocongruent2(X1,X2,X3,X4,X5,X6)
| ~ c_in(c_Pair(X7,X8,X4,X4),X1,tc_prod(X4,X4))
| ~ c_in(c_Pair(X9,X10,X5,X5),X2,tc_prod(X5,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1234]) ).
cnf(c_0_1845,plain,
( c_Equiv__Relations_Ocongruent(X4,hAPP(X5,X8),X6,X7)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_Equiv__Relations_Ocongruent2(X2,X4,X5,X3,X6,X7)
| ~ c_in(X8,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1235]) ).
cnf(c_0_1846,plain,
c_Fun_Ocomp(X1,c_Fun_Ocomp(X2,X3,X4,X5,X6),X5,X7,X6) = c_Fun_Ocomp(c_Fun_Ocomp(X1,X2,X5,X7,X4),X3,X4,X7,X6),
inference(split_conjunct,[status(thm)],[c_0_1236]) ).
cnf(c_0_1847,plain,
c_Relation_Orel__comp(c_Relation_Orel__comp(X1,X2,X3,X4,X5),X6,X3,X5,X7) = c_Relation_Orel__comp(X1,c_Relation_Orel__comp(X2,X6,X4,X5,X7),X3,X4,X7),
inference(split_conjunct,[status(thm)],[c_0_1237]) ).
cnf(c_0_1848,plain,
( c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_1238]) ).
cnf(c_0_1849,plain,
( c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X1,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_1239]) ).
cnf(c_0_1850,plain,
( X1 = X2
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,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),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_1240]) ).
cnf(c_0_1851,plain,
( X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_1241]) ).
cnf(c_0_1852,plain,
( c_in(c_Pair(X5,X6,X3,X3),X2,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(X4,c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X2,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1242]) ).
cnf(c_0_1853,plain,
c_Relation_Orel__comp(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(tc_prod(X4,X5),tc_bool)),X6,X4,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,X2,X6,X4,X5),c_Relation_Orel__comp(X1,X3,X6,X4,X5),tc_fun(tc_prod(X6,X5),tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1243]) ).
cnf(c_0_1854,plain,
c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X5,X3,X4,X6) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,X5,X3,X4,X6),c_Relation_Orel__comp(X2,X5,X3,X4,X6),tc_fun(tc_prod(X3,X6),tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1244]) ).
cnf(c_0_1855,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_1245]) ).
cnf(c_0_1856,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_1246]) ).
cnf(c_0_1857,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_1247]) ).
cnf(c_0_1858,plain,
c_Product__Type_OSigma(c_Set_Oinsert(X1,X2,X3),c_COMBK(c_Set_Oinsert(X4,X5,X6),tc_fun(X6,tc_bool),X3),X3,X6) = c_Set_Oinsert(c_Pair(X1,X4,X3,X6),c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X2,c_COMBK(c_Set_Oinsert(X4,X5,X6),tc_fun(X6,tc_bool),X3),X3,X6),c_Product__Type_OSigma(c_Set_Oinsert(X1,X2,X3),c_COMBK(X5,tc_fun(X6,tc_bool),X3),X3,X6),tc_fun(tc_prod(X3,X6),tc_bool)),tc_prod(X3,X6)),
inference(split_conjunct,[status(thm)],[c_0_1248]) ).
cnf(c_0_1859,plain,
( c_Relation_Orel__comp(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(tc_prod(X4,X4),tc_bool)),X4,X4,X4) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool))
| c_Relation_Orel__comp(X1,X2,X4,X4,X4) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool))
| c_Relation_Orel__comp(X1,X3,X4,X4,X4) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1249]) ).
cnf(c_0_1860,plain,
( c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X4,X3,X3,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool))
| c_Relation_Orel__comp(X1,X4,X3,X3,X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool))
| c_Relation_Orel__comp(X2,X4,X3,X3,X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1250]) ).
cnf(c_0_1861,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_1251]) ).
cnf(c_0_1862,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_1252]) ).
cnf(c_0_1863,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_1253]) ).
cnf(c_0_1864,plain,
( c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X1,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_1254]) ).
cnf(c_0_1865,plain,
( c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X1,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_1255]) ).
cnf(c_0_1866,plain,
( X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_1256]) ).
cnf(c_0_1867,plain,
( X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,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),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_1257]) ).
cnf(c_0_1868,plain,
( hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(c_Fun_Ocomp(X7,X8,X9,X4,X10),X11)
| hAPP(X1,hAPP(X2,X6)) != hAPP(X7,hAPP(X8,X11)) ),
inference(split_conjunct,[status(thm)],[c_0_1258]) ).
cnf(c_0_1869,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_1259]) ).
cnf(c_0_1870,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_1260]) ).
cnf(c_0_1871,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_1261]) ).
cnf(c_0_1872,plain,
( hAPP(X1,hAPP(X2,X3)) = hAPP(X4,hAPP(X5,X3))
| c_Fun_Ocomp(X1,X2,X6,X7,X8) != c_Fun_Ocomp(X4,X5,X9,X7,X8) ),
inference(split_conjunct,[status(thm)],[c_0_1262]) ).
cnf(c_0_1873,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_1263]) ).
cnf(c_0_1874,plain,
hAPP(c_Relation_Oconverse(X1,X2),c_Relation_Orel__comp(X3,X4,X1,X5,X2)) = c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X5,X2),X4),hAPP(c_Relation_Oconverse(X1,X5),X3),X2,X5,X1),
inference(split_conjunct,[status(thm)],[c_0_1264]) ).
cnf(c_0_1875,plain,
( c_in(c_Pair(X5,X4,X3,X3),X2,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_lessequals(c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1265]) ).
cnf(c_0_1876,plain,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X5,X1,X4,X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X5,X1,X4,X3),X3,X3),X4,tc_prod(X3,X3))
| hBOOL(hAPP(X5,X2))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ hBOOL(hAPP(X5,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1266]) ).
cnf(c_0_1877,plain,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X5,X2,X4,X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X5,X2,X4,X3),X3,X3),X4,tc_prod(X3,X3))
| hBOOL(hAPP(X5,X1))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ hBOOL(hAPP(X5,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1267]) ).
cnf(c_0_1878,plain,
( c_in(c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1(X2,X3,X1,X4,X5),X2,X4)
| ~ c_in(X1,c_Product__Type_OSigma(X2,X3,X4,X5),tc_prod(X4,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_1268]) ).
cnf(c_0_1879,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_1269]) ).
cnf(c_0_1880,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_1270]) ).
cnf(c_0_1881,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_1271]) ).
cnf(c_0_1882,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_1272]) ).
cnf(c_0_1883,plain,
( c_in(c_Pair(X4,X5,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| c_in(c_Pair(X5,X4,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| ~ c_Relation_Osingle__valued(X1,X2,X2)
| ~ c_in(c_Pair(X3,X4,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X3,X5,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1273]) ).
cnf(c_0_1884,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__XtranclE__1__1(X1,X2,X4,X3),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_1274]) ).
cnf(c_0_1885,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_1275]) ).
cnf(c_0_1886,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_1276]) ).
cnf(c_0_1887,plain,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X1,X2,X4,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_1277]) ).
cnf(c_0_1888,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_1278]) ).
cnf(c_0_1889,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_1279]) ).
cnf(c_0_1890,plain,
c_lessequals(c_Relation_OImage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X1,X2,X4,X5),c_Relation_OImage(X1,X3,X4,X5),tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1280]) ).
cnf(c_0_1891,plain,
( c_lessequals(c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1281]) ).
cnf(c_0_1892,plain,
c_in(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
inference(split_conjunct,[status(thm)],[c_0_1282]) ).
cnf(c_0_1893,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_1283]) ).
cnf(c_0_1894,plain,
( c_lessequals(X2,c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X3,X3),X2),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_1284]) ).
cnf(c_0_1895,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_1285]) ).
cnf(c_0_1896,plain,
( ~ c_Wellfounded_Oacyclic(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_1286]) ).
cnf(c_0_1897,plain,
( c_Relation_Osingle__valued(c_Relation_Orel__comp(X1,X4,X2,X3,X5),X2,X5)
| ~ c_Relation_Osingle__valued(X1,X2,X3)
| ~ c_Relation_Osingle__valued(X4,X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_1287]) ).
cnf(c_0_1898,plain,
( hBOOL(hAPP(X5,X1))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ hBOOL(hAPP(X5,X2))
| ~ hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X5,X2,X4,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1288]) ).
cnf(c_0_1899,plain,
( hBOOL(hAPP(X5,X2))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ hBOOL(hAPP(X5,X1))
| ~ hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X5,X1,X4,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_1289]) ).
cnf(c_0_1900,plain,
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(split_conjunct,[status(thm)],[c_0_1290]) ).
cnf(c_0_1901,plain,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X5,X1,X4,X3),X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| hBOOL(hAPP(X5,X2))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ hBOOL(hAPP(X5,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1291]) ).
cnf(c_0_1902,plain,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X5,X2,X4,X3),X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| hBOOL(hAPP(X5,X1))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ hBOOL(hAPP(X5,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1292]) ).
cnf(c_0_1903,plain,
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(split_conjunct,[status(thm)],[c_0_1293]) ).
cnf(c_0_1904,plain,
( X1 = X2
| c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X1,X2,X4,X3),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)) ),
inference(split_conjunct,[status(thm)],[c_0_1294]) ).
cnf(c_0_1905,plain,
( X1 = X2
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__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_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1295]) ).
cnf(c_0_1906,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_1296]) ).
cnf(c_0_1907,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_1297]) ).
cnf(c_0_1908,plain,
( X1 = X2
| c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X4,X1,X2,X3),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)) ),
inference(split_conjunct,[status(thm)],[c_0_1298]) ).
cnf(c_0_1909,plain,
( X1 = X2
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X1,X2,X4,X3),X2,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)) ),
inference(split_conjunct,[status(thm)],[c_0_1299]) ).
cnf(c_0_1910,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_1300]) ).
cnf(c_0_1911,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_1301]) ).
cnf(c_0_1912,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_1302]) ).
cnf(c_0_1913,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_1303]) ).
cnf(c_0_1914,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_1304]) ).
cnf(c_0_1915,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_1305]) ).
cnf(c_0_1916,plain,
hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
inference(split_conjunct,[status(thm)],[c_0_1306]) ).
cnf(c_0_1917,plain,
hAPP(X1,hAPP(X2,X3)) = hAPP(c_Fun_Ocomp(X1,X2,X4,X5,X6),X3),
inference(split_conjunct,[status(thm)],[c_0_1307]) ).
cnf(c_0_1918,plain,
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(split_conjunct,[status(thm)],[c_0_1308]) ).
cnf(c_0_1919,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_1309]) ).
cnf(c_0_1920,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_1310]) ).
cnf(c_0_1921,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_1311]) ).
cnf(c_0_1922,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_1312]) ).
cnf(c_0_1923,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_1313]) ).
cnf(c_0_1924,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_1314]) ).
cnf(c_0_1925,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_1315]) ).
cnf(c_0_1926,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_1316]) ).
cnf(c_0_1927,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_1317]) ).
cnf(c_0_1928,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_1318]) ).
cnf(c_0_1929,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_1319]) ).
cnf(c_0_1930,plain,
c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X1,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),c_Product__Type_OSigma(X2,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),tc_fun(tc_prod(X3,X5),tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1320]) ).
cnf(c_0_1931,plain,
c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(X1,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),c_Product__Type_OSigma(X2,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),tc_fun(tc_prod(X3,X5),tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1321]) ).
cnf(c_0_1932,plain,
( c_in(c_Pair(X1,X2,t_a,t_a),X3,tc_prod(t_a,t_a))
| c_in(c_Pair(X1,v_sko__Transitive__Closure__Xtrancl__Xcases__1(X1,X2,X3),t_a,t_a),c_Transitive__Closure_Otrancl(X3,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X1,X2,t_a,t_a),c_Transitive__Closure_Otrancl(X3,t_a),tc_prod(t_a,t_a)) ),
inference(split_conjunct,[status(thm)],[c_0_1322]) ).
cnf(c_0_1933,plain,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X3)
| ~ c_in(X1,X5,X3)
| ~ c_in(X2,X5,X3)
| c_Relation_OImage(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1323]) ).
cnf(c_0_1934,plain,
( c_in(c_Pair(X1,X4,X3,X3),X5,tc_prod(X3,X3))
| ~ c_in(X1,X2,X3)
| ~ c_in(X4,X2,X3)
| ~ c_Equiv__Relations_Oequiv(X2,X5,X3)
| c_Relation_OImage(X5,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X5,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1324]) ).
cnf(c_0_1935,plain,
( c_in(c_Pair(X1,X2,t_a,t_a),X3,tc_prod(t_a,t_a))
| c_in(c_Pair(v_sko__Transitive__Closure__Xtrancl__Xcases__1(X1,X2,X3),X2,t_a,t_a),X3,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X1,X2,t_a,t_a),c_Transitive__Closure_Otrancl(X3,t_a),tc_prod(t_a,t_a)) ),
inference(split_conjunct,[status(thm)],[c_0_1325]) ).
cnf(c_0_1936,plain,
( c_in(c_Pair(X5,X4,X3,X3),X2,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(X4,X1,X3)
| c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1326]) ).
cnf(c_0_1937,plain,
( c_Equiv__Relations_Oequiv(c_Relation_ODomain(X1,X2,X2),X1,X2)
| c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X2,X2),X1),X1,X2,X2,X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_1327]) ).
cnf(c_0_1938,plain,
( c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1(X3,X4,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_1328]) ).
cnf(c_0_1939,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_1329]) ).
cnf(c_0_1940,plain,
( c_in(c_Pair(X3,X1,X4,X5),X2,tc_prod(X4,X5))
| ~ c_in(X1,c_Relation_OImage(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X5),X5) ),
inference(split_conjunct,[status(thm)],[c_0_1330]) ).
cnf(c_0_1941,plain,
( c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(X4,X1,X3)
| ~ c_in(X5,X1,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1331]) ).
cnf(c_0_1942,plain,
( hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X5,X1,X4,X3)))
| hBOOL(hAPP(X5,X2))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ hBOOL(hAPP(X5,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1332]) ).
cnf(c_0_1943,plain,
( hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X5,X2,X4,X3)))
| hBOOL(hAPP(X5,X1))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ hBOOL(hAPP(X5,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1333]) ).
cnf(c_0_1944,plain,
( c_Wellfounded_Owf(X1,X2)
| c_Relation_Orel__comp(X1,X1,X2,X2,X2) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1334]) ).
cnf(c_0_1945,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_1335]) ).
cnf(c_0_1946,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),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_1336]) ).
cnf(c_0_1947,plain,
( c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_1337]) ).
cnf(c_0_1948,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_1338]) ).
cnf(c_0_1949,plain,
( c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1339]) ).
cnf(c_0_1950,plain,
( c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1340]) ).
cnf(c_0_1951,plain,
( X5 = X6
| ~ c_Relation_Osingle__valued(X1,X2,X3)
| ~ c_in(c_Pair(X4,X5,X2,X3),X1,tc_prod(X2,X3))
| ~ c_in(c_Pair(X4,X6,X2,X3),X1,tc_prod(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1341]) ).
cnf(c_0_1952,plain,
( c_in(c_Pair(X1,X2,X3,X3),hAPP(c_Relation_Oconverse(X3,X3),c_Transitive__Closure_Otrancl(X4,X3)),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(hAPP(c_Relation_Oconverse(X3,X3),X4),X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1342]) ).
cnf(c_0_1953,plain,
( c_in(X2,c_Relation_OImage(X5,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X4),X4)
| ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1343]) ).
cnf(c_0_1954,plain,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(hAPP(c_Relation_Oconverse(X3,X3),X4),X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),hAPP(c_Relation_Oconverse(X3,X3),c_Transitive__Closure_Otrancl(X4,X3)),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1344]) ).
cnf(c_0_1955,plain,
( X1 = X2
| ~ c_Relation_Orefl__on(c_Relation_OField(X3,X4),X3,X4)
| ~ c_Relation_Oantisym(X3,X4)
| ~ c_in(X1,c_Relation_OField(X3,X4),X4)
| ~ c_in(X2,c_Relation_OField(X3,X4),X4)
| c_Relation_OImage(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4) != c_Relation_OImage(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1345]) ).
cnf(c_0_1956,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_1346]) ).
cnf(c_0_1957,plain,
( c_Wellfounded_Oacyclic(X4,X3)
| ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1347]) ).
cnf(c_0_1958,plain,
( X3 = X4
| ~ c_Relation_Oantisym(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_1348]) ).
cnf(c_0_1959,plain,
( X3 = X4
| ~ c_Relation_Oantisym(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_1349]) ).
cnf(c_0_1960,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_1350]) ).
cnf(c_0_1961,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_1351]) ).
cnf(c_0_1962,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_1352]) ).
cnf(c_0_1963,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_1353]) ).
cnf(c_0_1964,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_1354]) ).
cnf(c_0_1965,plain,
c_Relation_OField(c_Set_Oinsert(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)),X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),c_Relation_OField(X4,X3),tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1355]) ).
cnf(c_0_1966,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(hAPP(c_Relation_Oconverse(X3,X3),X4),X3),tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1356]) ).
cnf(c_0_1967,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_1357]) ).
cnf(c_0_1968,plain,
( c_in(c_Pair(X3,X4,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X4,X3,X2,X2),X1,tc_prod(X2,X2)),X2)
| ~ c_Wellfounded_Oacyclic(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1358]) ).
cnf(c_0_1969,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_1359]) ).
cnf(c_0_1970,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_1360]) ).
cnf(c_0_1971,plain,
( X2 = X1
| c_in(c_Pair(X1,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X1,X2,X3),t_a,t_a),c_Transitive__Closure_Ortrancl(X3,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X1,X2,t_a,t_a),c_Transitive__Closure_Ortrancl(X3,t_a),tc_prod(t_a,t_a)) ),
inference(split_conjunct,[status(thm)],[c_0_1361]) ).
cnf(c_0_1972,plain,
( c_in(c_Pair(X2,X1,X3,X3),c_Transitive__Closure_Ortrancl(hAPP(c_Relation_Oconverse(X3,X3),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_1362]) ).
cnf(c_0_1973,plain,
( X2 = X1
| c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X1,X2,X3),X2,t_a,t_a),X3,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X1,X2,t_a,t_a),c_Transitive__Closure_Ortrancl(X3,t_a),tc_prod(t_a,t_a)) ),
inference(split_conjunct,[status(thm)],[c_0_1363]) ).
cnf(c_0_1974,plain,
( c_Equiv__Relations_Oquotient(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,X3) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(X4,X1,X3)
| ~ c_in(X5,X1,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1364]) ).
cnf(c_0_1975,plain,
( c_Relation_OImage(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X1,tc_bool)),X1,X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X3,X4,X1,X2),c_Relation_OImage(X3,X5,X1,X2),tc_fun(X2,tc_bool))
| ~ c_Relation_Osingle__valued(hAPP(c_Relation_Oconverse(X1,X2),X3),X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_1365]) ).
cnf(c_0_1976,plain,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X3)
| ~ c_in(X1,X5,X3)
| ~ c_in(X2,X5,X3)
| c_Equiv__Relations_Oquotient(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X4,X3) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1366]) ).
cnf(c_0_1977,plain,
( c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X1),X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X1),X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_1367]) ).
cnf(c_0_1978,plain,
( c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X1),X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X1),X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_1368]) ).
cnf(c_0_1979,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_1369]) ).
cnf(c_0_1980,plain,
( c_in(c_Pair(X2,X1,X4,X3),X5,tc_prod(X4,X3))
| ~ c_in(c_Pair(X1,X2,X3,X4),hAPP(c_Relation_Oconverse(X4,X3),X5),tc_prod(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1370]) ).
cnf(c_0_1981,plain,
c_Relation_OImage(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X5,X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X1,X5,X3,X4),c_Relation_OImage(X2,X5,X3,X4),tc_fun(X4,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1371]) ).
cnf(c_0_1982,plain,
( c_in(c_Pair(X2,X1,X4,X3),hAPP(c_Relation_Oconverse(X3,X4),X5),tc_prod(X4,X3))
| ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1372]) ).
cnf(c_0_1983,plain,
( c_in(c_Pair(X2,X1,X4,X3),hAPP(c_Relation_Oconverse(X3,X4),X5),tc_prod(X4,X3))
| ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1373]) ).
cnf(c_0_1984,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_1374]) ).
cnf(c_0_1985,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_1375]) ).
cnf(c_0_1986,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_1376]) ).
cnf(c_0_1987,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_1377]) ).
cnf(c_0_1988,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_1378]) ).
cnf(c_0_1989,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_1379]) ).
cnf(c_0_1990,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_1380]) ).
cnf(c_0_1991,plain,
c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,X3,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X1,X4,X3,X5),c_Product__Type_OSigma(X2,X4,X3,X5),tc_fun(tc_prod(X3,X5),tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1381]) ).
cnf(c_0_1992,plain,
c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,X3,X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(X1,X4,X3,X5),c_Product__Type_OSigma(X2,X4,X3,X5),tc_fun(tc_prod(X3,X5),tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1382]) ).
cnf(c_0_1993,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_1383]) ).
cnf(c_0_1994,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_1384]) ).
cnf(c_0_1995,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_1385]) ).
cnf(c_0_1996,plain,
( c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_1386]) ).
cnf(c_0_1997,plain,
( c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_1387]) ).
cnf(c_0_1998,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_1388]) ).
cnf(c_0_1999,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_1389]) ).
cnf(c_0_2000,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_1390]) ).
cnf(c_0_2001,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_1391]) ).
cnf(c_0_2002,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_1392]) ).
cnf(c_0_2003,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_1393]) ).
cnf(c_0_2004,plain,
c_Relation_OImage(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X1,X2,X4,X5),c_Relation_OImage(X1,X3,X4,X5),tc_fun(X5,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1394]) ).
cnf(c_0_2005,plain,
c_Relation_Orel__comp(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)),X4,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X3),tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1395]) ).
cnf(c_0_2006,plain,
c_Relation_Orel__comp(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_bool)),X3,X1,X2,X4) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X4),tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1396]) ).
cnf(c_0_2007,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_1397]) ).
cnf(c_0_2008,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_1398]) ).
cnf(c_0_2009,plain,
( ~ c_in(c_Pair(X1,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
| c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Relation_Oconverse(X2,X2),X3),c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1399]) ).
cnf(c_0_2010,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_1400]) ).
cnf(c_0_2011,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_1401]) ).
cnf(c_0_2012,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_1402]) ).
cnf(c_0_2013,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_1403]) ).
cnf(c_0_2014,plain,
( c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X3,X3),X2),X2,X3,X3,X3) = X2
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1404]) ).
cnf(c_0_2015,plain,
c_Relation_ORange(c_Set_Oinsert(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)),X3,X4) = c_Set_Oinsert(X2,c_Relation_ORange(X5,X3,X4),X4),
inference(split_conjunct,[status(thm)],[c_0_1405]) ).
cnf(c_0_2016,plain,
c_Relation_ODomain(c_Set_Oinsert(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)),X3,X4) = c_Set_Oinsert(X1,c_Relation_ODomain(X5,X3,X4),X3),
inference(split_conjunct,[status(thm)],[c_0_1406]) ).
cnf(c_0_2017,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_1407]) ).
cnf(c_0_2018,plain,
( hBOOL(hAPP(X4,X3))
| hBOOL(hAPP(X4,X5))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1408]) ).
cnf(c_0_2019,plain,
( hBOOL(hAPP(X4,X3))
| hBOOL(hAPP(X4,X5))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_Pair(X3,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1409]) ).
cnf(c_0_2020,plain,
( hBOOL(hAPP(X4,X3))
| hBOOL(hAPP(X4,X5))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1410]) ).
cnf(c_0_2021,plain,
( hBOOL(hAPP(X4,X3))
| hBOOL(hAPP(X4,X5))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1411]) ).
cnf(c_0_2022,plain,
( hAPP(X2,X5) = hAPP(X2,X6)
| ~ c_Equiv__Relations_Ocongruent(X1,X2,X3,X4)
| ~ c_in(c_Pair(X5,X6,X3,X3),X1,tc_prod(X3,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_1412]) ).
cnf(c_0_2023,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_1413]) ).
cnf(c_0_2024,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_1414]) ).
cnf(c_0_2025,plain,
c_lessequals(c_Relation_ORange(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(X1,X3,X4),c_Relation_ORange(X2,X3,X4),tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1415]) ).
cnf(c_0_2026,plain,
c_lessequals(c_Relation_ODomain(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X1,X3,X4),c_Relation_ODomain(X2,X3,X4),tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1416]) ).
cnf(c_0_2027,plain,
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(split_conjunct,[status(thm)],[c_0_1417]) ).
cnf(c_0_2028,plain,
( c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1418]) ).
cnf(c_0_2029,plain,
c_Transitive__Closure_Otrancl(X1,X2) = c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),
inference(split_conjunct,[status(thm)],[c_0_1419]) ).
cnf(c_0_2030,plain,
c_Transitive__Closure_Otrancl(X1,X2) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),X1,X2,X2,X2),
inference(split_conjunct,[status(thm)],[c_0_1420]) ).
cnf(c_0_2031,plain,
c_Relation_Orel__comp(X1,c_Relation_OId(X2),X3,X2,X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_1421]) ).
cnf(c_0_2032,plain,
c_Relation_Orel__comp(c_Relation_OId(X1),X2,X1,X1,X3) = X2,
inference(split_conjunct,[status(thm)],[c_0_1422]) ).
cnf(c_0_2033,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_1423]) ).
cnf(c_0_2034,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_1424]) ).
cnf(c_0_2035,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_1425]) ).
cnf(c_0_2036,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_1426]) ).
cnf(c_0_2037,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_1427]) ).
cnf(c_0_2038,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_1428]) ).
cnf(c_0_2039,plain,
( c_in(X4,c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(X4,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1429]) ).
cnf(c_0_2040,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_1430]) ).
cnf(c_0_2041,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_1431]) ).
cnf(c_0_2042,plain,
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(split_conjunct,[status(thm)],[c_0_1432]) ).
cnf(c_0_2043,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_1433]) ).
cnf(c_0_2044,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_1434]) ).
cnf(c_0_2045,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_1435]) ).
cnf(c_0_2046,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_1436]) ).
cnf(c_0_2047,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_1437]) ).
cnf(c_0_2048,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_1438]) ).
cnf(c_0_2049,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_1439]) ).
cnf(c_0_2050,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_1440]) ).
cnf(c_0_2051,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_1441]) ).
cnf(c_0_2052,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_1442]) ).
cnf(c_0_2053,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_1443]) ).
cnf(c_0_2054,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_1444]) ).
cnf(c_0_2055,plain,
c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1445]) ).
cnf(c_0_2056,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_1446]) ).
cnf(c_0_2057,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_1447]) ).
cnf(c_0_2058,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_1448]) ).
cnf(c_0_2059,plain,
( c_Arrow__Order__Mirabelle_Ounanimity(X1)
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3(X1),v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2(X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_1449]) ).
cnf(c_0_2060,plain,
( ~ c_Wellfounded_Oacyclic(X1,X2)
| ~ c_in(c_Pair(X3,X3,X2,X2),c_Transitive__Closure_Otrancl(X1,X2),tc_prod(X2,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1450]) ).
cnf(c_0_2061,plain,
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(split_conjunct,[status(thm)],[c_0_1451]) ).
cnf(c_0_2062,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_lessequals(X3,c_Relation_OImage(X1,X3,X2,X2),tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1452]) ).
cnf(c_0_2063,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_1453]) ).
cnf(c_0_2064,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_1454]) ).
cnf(c_0_2065,plain,
~ 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(split_conjunct,[status(thm)],[c_0_1455]) ).
cnf(c_0_2066,plain,
~ 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(split_conjunct,[status(thm)],[c_0_1456]) ).
cnf(c_0_2067,plain,
~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X3,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(split_conjunct,[status(thm)],[c_0_1457]) ).
cnf(c_0_2068,plain,
~ 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(split_conjunct,[status(thm)],[c_0_1458]) ).
cnf(c_0_2069,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_1459]) ).
cnf(c_0_2070,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_1460]) ).
cnf(c_0_2071,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_1461]) ).
cnf(c_0_2072,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_1462]) ).
cnf(c_0_2073,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_1463]) ).
cnf(c_0_2074,plain,
hAPP(c_Relation_Oconverse(X1,X1),c_Relation_Oinv__image(X2,X3,X4,X1)) = c_Relation_Oinv__image(hAPP(c_Relation_Oconverse(X4,X4),X2),X3,X4,X1),
inference(split_conjunct,[status(thm)],[c_0_1464]) ).
cnf(c_0_2075,plain,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
inference(split_conjunct,[status(thm)],[c_0_1465]) ).
cnf(c_0_2076,plain,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1466]) ).
cnf(c_0_2077,plain,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_1467]) ).
cnf(c_0_2078,plain,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
inference(split_conjunct,[status(thm)],[c_0_1468]) ).
cnf(c_0_2079,plain,
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Wellfounded_Owf(X1,X3)
| ~ c_Wellfounded_Owf(X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X1,X3,X3),c_Relation_ORange(X2,X3,X3),tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1469]) ).
cnf(c_0_2080,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_1470]) ).
cnf(c_0_2081,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_1471]) ).
cnf(c_0_2082,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_1472]) ).
cnf(c_0_2083,plain,
( X1 = X2
| c_Pair(X1,X3,X4,X5) != c_Pair(X2,X6,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_1473]) ).
cnf(c_0_2084,plain,
( X1 = X2
| c_Pair(X3,X1,X4,X5) != c_Pair(X6,X2,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_1474]) ).
cnf(c_0_2085,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_1475]) ).
cnf(c_0_2086,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_1476]) ).
cnf(c_0_2087,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_1477]) ).
cnf(c_0_2088,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_1478]) ).
cnf(c_0_2089,plain,
c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2),
inference(split_conjunct,[status(thm)],[c_0_1479]) ).
cnf(c_0_2090,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_1480]) ).
cnf(c_0_2091,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_1481]) ).
cnf(c_0_2092,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_1482]) ).
cnf(c_0_2093,plain,
( c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3(X1),v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2(X1),X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_Arrow__Order__Mirabelle_Ounanimity(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1483]) ).
cnf(c_0_2094,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_1484]) ).
cnf(c_0_2095,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_1485]) ).
cnf(c_0_2096,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1486]) ).
cnf(c_0_2097,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X4,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1487]) ).
cnf(c_0_2098,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1488]) ).
cnf(c_0_2099,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X4,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1489]) ).
cnf(c_0_2100,plain,
c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X1,X3,X4),c_Relation_ORange(X2,X3,X4),tc_fun(X4,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1490]) ).
cnf(c_0_2101,plain,
c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X1,X3,X4),c_Relation_ODomain(X2,X3,X4),tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1491]) ).
cnf(c_0_2102,plain,
c_in(c_Pair(X1,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)),
inference(split_conjunct,[status(thm)],[c_0_1492]) ).
cnf(c_0_2103,plain,
c_in(c_Pair(X1,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)),
inference(split_conjunct,[status(thm)],[c_0_1493]) ).
cnf(c_0_2104,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_1494]) ).
cnf(c_0_2105,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_1495]) ).
cnf(c_0_2106,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_1496]) ).
cnf(c_0_2107,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_1497]) ).
cnf(c_0_2108,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X1 = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| ~ c_lessequals(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1498]) ).
cnf(c_0_2109,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_1499]) ).
cnf(c_0_2110,plain,
c_Product__Type_OSigma(X1,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool),X3),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X2),tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1500]) ).
cnf(c_0_2111,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_1501]) ).
cnf(c_0_2112,plain,
hAPP(c_Relation_Oconverse(X1,X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(tc_prod(X1,X2),tc_bool))) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Relation_Oconverse(X1,X2),X3),hAPP(c_Relation_Oconverse(X1,X2),X4),tc_fun(tc_prod(X2,X1),tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1502]) ).
cnf(c_0_2113,plain,
hAPP(c_Relation_Oconverse(X1,X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(tc_prod(X1,X2),tc_bool))) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Relation_Oconverse(X1,X2),X3),hAPP(c_Relation_Oconverse(X1,X2),X4),tc_fun(tc_prod(X2,X1),tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1503]) ).
cnf(c_0_2114,plain,
c_in(c_Pair(X1,X1,X2,X2),c_Relation_OId(X2),tc_prod(X2,X2)),
inference(split_conjunct,[status(thm)],[c_0_1504]) ).
cnf(c_0_2115,plain,
c_in(c_Pair(X1,X1,X2,X2),c_Relation_OId(X2),tc_prod(X2,X2)),
inference(split_conjunct,[status(thm)],[c_0_1505]) ).
cnf(c_0_2116,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_1506]) ).
cnf(c_0_2117,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_1507]) ).
cnf(c_0_2118,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_1508]) ).
cnf(c_0_2119,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_1509]) ).
cnf(c_0_2120,plain,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),
inference(split_conjunct,[status(thm)],[c_0_1510]) ).
cnf(c_0_2121,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_1511]) ).
cnf(c_0_2122,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_1512]) ).
cnf(c_0_2123,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X2,X3),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),
inference(split_conjunct,[status(thm)],[c_0_1513]) ).
cnf(c_0_2124,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_1514]) ).
cnf(c_0_2125,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_1515]) ).
cnf(c_0_2126,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_1516]) ).
cnf(c_0_2127,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_1517]) ).
cnf(c_0_2128,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_1518]) ).
cnf(c_0_2129,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_1519]) ).
cnf(c_0_2130,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_1520]) ).
cnf(c_0_2131,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_1521]) ).
cnf(c_0_2132,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_1522]) ).
cnf(c_0_2133,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1523]) ).
cnf(c_0_2134,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1524]) ).
cnf(c_0_2135,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1525]) ).
cnf(c_0_2136,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1526]) ).
cnf(c_0_2137,plain,
( c_Relation_Oantisym(X1,X2)
| ~ c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1527]) ).
cnf(c_0_2138,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_1528]) ).
cnf(c_0_2139,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_1529]) ).
cnf(c_0_2140,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_1530]) ).
cnf(c_0_2141,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_1531]) ).
cnf(c_0_2142,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_1532]) ).
cnf(c_0_2143,plain,
( hBOOL(hAPP(X3,X4))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X3,X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1533]) ).
cnf(c_0_2144,plain,
( hBOOL(hAPP(X3,X4))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X3,X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1534]) ).
cnf(c_0_2145,plain,
( hBOOL(hAPP(X3,X4))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X3,X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1535]) ).
cnf(c_0_2146,plain,
( hBOOL(hAPP(X3,X4))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(X3,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X3,X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_1536]) ).
cnf(c_0_2147,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_1537]) ).
cnf(c_0_2148,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_1538]) ).
cnf(c_0_2149,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_1539]) ).
cnf(c_0_2150,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_1540]) ).
cnf(c_0_2151,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_1541]) ).
cnf(c_0_2152,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_1542]) ).
cnf(c_0_2153,plain,
c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X1,hAPP(c_Relation_Oconverse(X2,X2),X1),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
inference(split_conjunct,[status(thm)],[c_0_1543]) ).
cnf(c_0_2154,plain,
c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X1,hAPP(c_Relation_Oconverse(X2,X2),X1),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
inference(split_conjunct,[status(thm)],[c_0_1544]) ).
cnf(c_0_2155,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_1545]) ).
cnf(c_0_2156,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_1546]) ).
cnf(c_0_2157,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_1547]) ).
cnf(c_0_2158,plain,
( X1 = X2
| ~ c_in(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1548]) ).
cnf(c_0_2159,plain,
( X1 = X4
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_1549]) ).
cnf(c_0_2160,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_1550]) ).
cnf(c_0_2161,plain,
c_Relation_OField(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OField(X1,X3),c_Relation_OField(X2,X3),tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1551]) ).
cnf(c_0_2162,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_1552]) ).
cnf(c_0_2163,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),X4),
inference(split_conjunct,[status(thm)],[c_0_1553]) ).
cnf(c_0_2164,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),X3),
inference(split_conjunct,[status(thm)],[c_0_1554]) ).
cnf(c_0_2165,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_1555]) ).
cnf(c_0_2166,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_1556]) ).
cnf(c_0_2167,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_1557]) ).
cnf(c_0_2168,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_1558]) ).
cnf(c_0_2169,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_1559]) ).
cnf(c_0_2170,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_1560]) ).
cnf(c_0_2171,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_1561]) ).
cnf(c_0_2172,plain,
c_Product__Type_OSigma(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X3),tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1562]) ).
cnf(c_0_2173,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_1563]) ).
cnf(c_0_2174,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_1564]) ).
cnf(c_0_2175,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_1565]) ).
cnf(c_0_2176,plain,
( hAPP(X1,X3) = hAPP(X3,X2)
| ~ c_Arrow__Order__Mirabelle_Odictator(X1,X2)
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
inference(split_conjunct,[status(thm)],[c_0_1566]) ).
cnf(c_0_2177,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_1567]) ).
cnf(c_0_2178,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_1568]) ).
cnf(c_0_2179,plain,
c_Relation_OImage(c_Relation_OId__on(X1,X2),X3,X2,X2) = c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1569]) ).
cnf(c_0_2180,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_1570]) ).
cnf(c_0_2181,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_1571]) ).
cnf(c_0_2182,plain,
( c_Relation_Osingle__valued(X1,X3,X4)
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool))
| ~ c_Relation_Osingle__valued(X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_1572]) ).
cnf(c_0_2183,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_1573]) ).
cnf(c_0_2184,plain,
c_Set_Oinsert(X1,X2,X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1574]) ).
cnf(c_0_2185,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_1575]) ).
cnf(c_0_2186,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_1576]) ).
cnf(c_0_2187,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_1577]) ).
cnf(c_0_2188,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_1578]) ).
cnf(c_0_2189,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_1579]) ).
cnf(c_0_2190,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_1580]) ).
cnf(c_0_2191,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3)
| ~ c_in(X4,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1581]) ).
cnf(c_0_2192,plain,
( X1 = X2
| c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) != c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_1582]) ).
cnf(c_0_2193,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_1583]) ).
cnf(c_0_2194,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_1584]) ).
cnf(c_0_2195,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_1585]) ).
cnf(c_0_2196,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_1586]) ).
cnf(c_0_2197,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_1587]) ).
cnf(c_0_2198,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_1588]) ).
cnf(c_0_2199,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_1589]) ).
cnf(c_0_2200,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_1590]) ).
cnf(c_0_2201,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_1591]) ).
cnf(c_0_2202,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_1592]) ).
cnf(c_0_2203,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_1593]) ).
cnf(c_0_2204,plain,
c_Relation_OImage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1594]) ).
cnf(c_0_2205,plain,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,X3,X4),X4) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,X3,X4),X4),
inference(split_conjunct,[status(thm)],[c_0_1595]) ).
cnf(c_0_2206,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_1596]) ).
cnf(c_0_2207,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_1597]) ).
cnf(c_0_2208,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_1598]) ).
cnf(c_0_2209,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_1599]) ).
cnf(c_0_2210,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_1600]) ).
cnf(c_0_2211,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_1601]) ).
cnf(c_0_2212,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_1602]) ).
cnf(c_0_2213,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_1603]) ).
cnf(c_0_2214,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_1604]) ).
cnf(c_0_2215,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_1605]) ).
cnf(c_0_2216,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_1606]) ).
cnf(c_0_2217,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_1607]) ).
cnf(c_0_2218,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_1608]) ).
cnf(c_0_2219,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_1609]) ).
cnf(c_0_2220,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1610]) ).
cnf(c_0_2221,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1611]) ).
cnf(c_0_2222,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_1612]) ).
cnf(c_0_2223,plain,
( c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Oantisym(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1613]) ).
cnf(c_0_2224,plain,
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(split_conjunct,[status(thm)],[c_0_1614]) ).
cnf(c_0_2225,plain,
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(split_conjunct,[status(thm)],[c_0_1615]) ).
cnf(c_0_2226,plain,
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(split_conjunct,[status(thm)],[c_0_1616]) ).
cnf(c_0_2227,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_1617]) ).
cnf(c_0_2228,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_1618]) ).
cnf(c_0_2229,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_1619]) ).
cnf(c_0_2230,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_1620]) ).
cnf(c_0_2231,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1621]) ).
cnf(c_0_2232,plain,
( c_Wellfounded_Owf(hAPP(c_Relation_Oconverse(X1,X1),c_Transitive__Closure_Otrancl(X2,X1)),X1)
| ~ c_Wellfounded_Owf(hAPP(c_Relation_Oconverse(X1,X1),X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_1622]) ).
cnf(c_0_2233,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X2,tc_fun(tc_prod(X1,X1),tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1623]) ).
cnf(c_0_2234,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_1624]) ).
cnf(c_0_2235,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)),
inference(split_conjunct,[status(thm)],[c_0_1625]) ).
cnf(c_0_2236,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_1626]) ).
cnf(c_0_2237,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_1627]) ).
cnf(c_0_2238,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_1628]) ).
cnf(c_0_2239,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_1629]) ).
cnf(c_0_2240,plain,
c_in(X1,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),
inference(split_conjunct,[status(thm)],[c_0_1630]) ).
cnf(c_0_2241,plain,
( c_Relation_Ototal__on(X1,X3,X2)
| ~ c_Relation_Ototal__on(X1,hAPP(c_Relation_Oconverse(X2,X2),X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1631]) ).
cnf(c_0_2242,plain,
( c_Relation_Orefl__on(X1,X3,X2)
| ~ c_Relation_Orefl__on(X1,hAPP(c_Relation_Oconverse(X2,X2),X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1632]) ).
cnf(c_0_2243,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_1633]) ).
cnf(c_0_2244,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_1634]) ).
cnf(c_0_2245,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_1635]) ).
cnf(c_0_2246,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_1636]) ).
cnf(c_0_2247,plain,
c_Relation_Orefl__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
inference(split_conjunct,[status(thm)],[c_0_1637]) ).
cnf(c_0_2248,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_1638]) ).
cnf(c_0_2249,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_1639]) ).
cnf(c_0_2250,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_1640]) ).
cnf(c_0_2251,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_1641]) ).
cnf(c_0_2252,plain,
c_Relation_OImage(c_Relation_OId(X1),X2,X1,X1) = X2,
inference(split_conjunct,[status(thm)],[c_0_1642]) ).
cnf(c_0_2253,plain,
c_Transitive__Closure_Otrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1643]) ).
cnf(c_0_2254,plain,
( c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1644]) ).
cnf(c_0_2255,plain,
( c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1645]) ).
cnf(c_0_2256,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_1646]) ).
cnf(c_0_2257,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_1647]) ).
cnf(c_0_2258,plain,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
inference(split_conjunct,[status(thm)],[c_0_1648]) ).
cnf(c_0_2259,plain,
( c_in(v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(X1,X2),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_Arrow__Order__Mirabelle_Odictator(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1649]) ).
cnf(c_0_2260,plain,
( c_Wellfounded_Oacyclic(X3,X2)
| ~ c_Wellfounded_Oacyclic(X1,X2)
| ~ c_lessequals(X3,X1,tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1650]) ).
cnf(c_0_2261,plain,
( c_Relation_Oantisym(X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Relation_Oantisym(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1651]) ).
cnf(c_0_2262,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_1652]) ).
cnf(c_0_2263,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_1653]) ).
cnf(c_0_2264,plain,
c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_bool)),X1,X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1654]) ).
cnf(c_0_2265,plain,
c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_bool)),X1,X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1655]) ).
cnf(c_0_2266,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_1656]) ).
cnf(c_0_2267,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_1657]) ).
cnf(c_0_2268,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_1658]) ).
cnf(c_0_2269,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_1659]) ).
cnf(c_0_2270,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1660]) ).
cnf(c_0_2271,plain,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1661]) ).
cnf(c_0_2272,plain,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1662]) ).
cnf(c_0_2273,plain,
c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1663]) ).
cnf(c_0_2274,plain,
c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1664]) ).
cnf(c_0_2275,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_1665]) ).
cnf(c_0_2276,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_1666]) ).
cnf(c_0_2277,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_1667]) ).
cnf(c_0_2278,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_1668]) ).
cnf(c_0_2279,plain,
( c_Relation_Ototal__on(X1,hAPP(c_Relation_Oconverse(X3,X3),X2),X3)
| ~ c_Relation_Ototal__on(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1669]) ).
cnf(c_0_2280,plain,
( c_Relation_Orefl__on(X1,hAPP(c_Relation_Oconverse(X3,X3),X2),X3)
| ~ c_Relation_Orefl__on(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1670]) ).
cnf(c_0_2281,plain,
c_Set_Oinsert(X1,c_Set_Oinsert(X1,X2,X3),X3) = c_Set_Oinsert(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_1671]) ).
cnf(c_0_2282,plain,
( ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_1672]) ).
cnf(c_0_2283,plain,
( c_in(v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2(X1),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_Arrow__Order__Mirabelle_Ounanimity(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1673]) ).
cnf(c_0_2284,plain,
( c_in(v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X1),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1674]) ).
cnf(c_0_2285,plain,
( c_in(v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X1),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1675]) ).
cnf(c_0_2286,plain,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
inference(split_conjunct,[status(thm)],[c_0_1676]) ).
cnf(c_0_2287,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool))
| c_Relation_ORange(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1677]) ).
cnf(c_0_2288,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool))
| c_Relation_ODomain(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1678]) ).
cnf(c_0_2289,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1679]) ).
cnf(c_0_2290,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_1680]) ).
cnf(c_0_2291,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_1681]) ).
cnf(c_0_2292,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_1682]) ).
cnf(c_0_2293,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_1683]) ).
cnf(c_0_2294,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_1684]) ).
cnf(c_0_2295,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_1685]) ).
cnf(c_0_2296,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_1686]) ).
cnf(c_0_2297,plain,
c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
inference(split_conjunct,[status(thm)],[c_0_1687]) ).
cnf(c_0_2298,plain,
c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
inference(split_conjunct,[status(thm)],[c_0_1688]) ).
cnf(c_0_2299,plain,
( hBOOL(hAPP(X3,X1))
| ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1689]) ).
cnf(c_0_2300,plain,
c_Relation_OField(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1690]) ).
cnf(c_0_2301,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1691]) ).
cnf(c_0_2302,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1692]) ).
cnf(c_0_2303,plain,
c_Relation_ORange(X1,X2,X3) = c_Relation_ODomain(hAPP(c_Relation_Oconverse(X2,X3),X1),X3,X2),
inference(split_conjunct,[status(thm)],[c_0_1693]) ).
cnf(c_0_2304,plain,
c_Relation_ODomain(hAPP(c_Relation_Oconverse(X1,X2),X3),X2,X1) = c_Relation_ORange(X3,X1,X2),
inference(split_conjunct,[status(thm)],[c_0_1694]) ).
cnf(c_0_2305,plain,
c_Relation_ORange(hAPP(c_Relation_Oconverse(X1,X2),X3),X2,X1) = c_Relation_ODomain(X3,X1,X2),
inference(split_conjunct,[status(thm)],[c_0_1695]) ).
cnf(c_0_2306,plain,
c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1696]) ).
cnf(c_0_2307,plain,
( c_in(X1,X2,X3)
| c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(split_conjunct,[status(thm)],[c_0_1697]) ).
cnf(c_0_2308,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_1698]) ).
cnf(c_0_2309,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_1699]) ).
cnf(c_0_2310,plain,
( X2 = X1
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1700]) ).
cnf(c_0_2311,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1701]) ).
cnf(c_0_2312,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1702]) ).
cnf(c_0_2313,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1703]) ).
cnf(c_0_2314,plain,
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(split_conjunct,[status(thm)],[c_0_1704]) ).
cnf(c_0_2315,plain,
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(split_conjunct,[status(thm)],[c_0_1705]) ).
cnf(c_0_2316,plain,
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(split_conjunct,[status(thm)],[c_0_1706]) ).
cnf(c_0_2317,plain,
c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1) = c_Relation_OId(X1),
inference(split_conjunct,[status(thm)],[c_0_1707]) ).
cnf(c_0_2318,plain,
c_Relation_Oantisym(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
inference(split_conjunct,[status(thm)],[c_0_1708]) ).
cnf(c_0_2319,plain,
c_Wellfounded_Owf(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
inference(split_conjunct,[status(thm)],[c_0_1709]) ).
cnf(c_0_2320,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_1710]) ).
cnf(c_0_2321,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_1711]) ).
cnf(c_0_2322,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_1712]) ).
cnf(c_0_2323,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_1713]) ).
cnf(c_0_2324,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_1714]) ).
cnf(c_0_2325,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_1715]) ).
cnf(c_0_2326,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_1716]) ).
cnf(c_0_2327,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_1717]) ).
cnf(c_0_2328,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_1718]) ).
cnf(c_0_2329,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_1719]) ).
cnf(c_0_2330,plain,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
inference(split_conjunct,[status(thm)],[c_0_1720]) ).
cnf(c_0_2331,plain,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
inference(split_conjunct,[status(thm)],[c_0_1721]) ).
cnf(c_0_2332,plain,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
inference(split_conjunct,[status(thm)],[c_0_1722]) ).
cnf(c_0_2333,plain,
c_Relation_ORange(v_r,t_a,t_b) = c_Relation_ODomain(hAPP(c_Relation_Oconverse(t_a,t_b),v_r),t_b,t_a),
inference(split_conjunct,[status(thm)],[c_0_1723]) ).
cnf(c_0_2334,plain,
c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
inference(split_conjunct,[status(thm)],[c_0_1724]) ).
cnf(c_0_2335,plain,
c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
inference(split_conjunct,[status(thm)],[c_0_1725]) ).
cnf(c_0_2336,plain,
c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
inference(split_conjunct,[status(thm)],[c_0_1726]) ).
cnf(c_0_2337,plain,
( c_Relation_Oantisym(X2,X1)
| ~ c_Relation_Oantisym(hAPP(c_Relation_Oconverse(X1,X1),X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_1727]) ).
cnf(c_0_2338,plain,
( c_Relation_Osym(X2,X1)
| ~ c_Relation_Osym(hAPP(c_Relation_Oconverse(X1,X1),X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_1728]) ).
cnf(c_0_2339,plain,
( c_Wellfounded_Oacyclic(X2,X1)
| ~ c_Wellfounded_Oacyclic(hAPP(c_Relation_Oconverse(X1,X1),X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_1729]) ).
cnf(c_0_2340,plain,
c_Transitive__Closure_Ortrancl(hAPP(c_Relation_Oconverse(X1,X1),X2),X1) = hAPP(c_Relation_Oconverse(X1,X1),c_Transitive__Closure_Ortrancl(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_1730]) ).
cnf(c_0_2341,plain,
c_Transitive__Closure_Otrancl(hAPP(c_Relation_Oconverse(X1,X1),X2),X1) = hAPP(c_Relation_Oconverse(X1,X1),c_Transitive__Closure_Otrancl(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_1731]) ).
cnf(c_0_2342,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1732]) ).
cnf(c_0_2343,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1733]) ).
cnf(c_0_2344,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1734]) ).
cnf(c_0_2345,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1735]) ).
cnf(c_0_2346,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_1736]) ).
cnf(c_0_2347,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_1737]) ).
cnf(c_0_2348,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_1738]) ).
cnf(c_0_2349,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_1739]) ).
cnf(c_0_2350,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_1740]) ).
cnf(c_0_2351,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_1741]) ).
cnf(c_0_2352,plain,
c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1742]) ).
cnf(c_0_2353,plain,
( c_Set_Oinsert(X1,X2,X3) = X2
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1743]) ).
cnf(c_0_2354,plain,
( c_Relation_Orefl__on(X1,X2,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1744]) ).
cnf(c_0_2355,plain,
( c_Arrow__Order__Mirabelle_Odictator(X1,X2)
| hAPP(X1,v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(X1,X2)) != hAPP(v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_1745]) ).
cnf(c_0_2356,plain,
c_Relation_ORange(c_Transitive__Closure_Otrancl(X1,X2),X2,X2) = c_Relation_ORange(X1,X2,X2),
inference(split_conjunct,[status(thm)],[c_0_1746]) ).
cnf(c_0_2357,plain,
c_Relation_ODomain(c_Transitive__Closure_Otrancl(X1,X2),X2,X2) = c_Relation_ODomain(X1,X2,X2),
inference(split_conjunct,[status(thm)],[c_0_1747]) ).
cnf(c_0_2358,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
inference(split_conjunct,[status(thm)],[c_0_1748]) ).
cnf(c_0_2359,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = X2,
inference(split_conjunct,[status(thm)],[c_0_1749]) ).
cnf(c_0_2360,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1750]) ).
cnf(c_0_2361,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oinsert(X2,X3,X1),
inference(split_conjunct,[status(thm)],[c_0_1751]) ).
cnf(c_0_2362,plain,
c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1752]) ).
cnf(c_0_2363,plain,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
inference(split_conjunct,[status(thm)],[c_0_1753]) ).
cnf(c_0_2364,plain,
hAPP(c_Relation_Oconverse(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3)) = X3,
inference(split_conjunct,[status(thm)],[c_0_1754]) ).
cnf(c_0_2365,plain,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[c_0_1755]) ).
cnf(c_0_2366,plain,
( hBOOL(hAPP(X2,X1))
| ~ c_in(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1756]) ).
cnf(c_0_2367,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_1757]) ).
cnf(c_0_2368,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_1758]) ).
cnf(c_0_2369,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_1759]) ).
cnf(c_0_2370,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_1760]) ).
cnf(c_0_2371,plain,
( c_Relation_Oantisym(hAPP(c_Relation_Oconverse(X2,X2),X1),X2)
| ~ c_Relation_Oantisym(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1761]) ).
cnf(c_0_2372,plain,
( c_Relation_Osym(hAPP(c_Relation_Oconverse(X2,X2),X1),X2)
| ~ c_Relation_Osym(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1762]) ).
cnf(c_0_2373,plain,
( c_Wellfounded_Oacyclic(hAPP(c_Relation_Oconverse(X2,X2),X1),X2)
| ~ c_Wellfounded_Oacyclic(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1763]) ).
cnf(c_0_2374,plain,
c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1),
inference(split_conjunct,[status(thm)],[c_0_1764]) ).
cnf(c_0_2375,plain,
c_Relation_OField(hAPP(c_Relation_Oconverse(X1,X1),X2),X1) = c_Relation_OField(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_1765]) ).
cnf(c_0_2376,plain,
( X1 = c_Orderings_Obot__class_Obot(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1766]) ).
cnf(c_0_2377,plain,
( X1 = c_Orderings_Obot__class_Obot(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1767]) ).
cnf(c_0_2378,plain,
( c_in(X3,c_Wellfounded_Oacc(X1,X2),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1768]) ).
cnf(c_0_2379,plain,
( c_in(X2,X1,X3)
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_1769]) ).
cnf(c_0_2380,plain,
( c_Relation_Osym(X2,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1770]) ).
cnf(c_0_2381,plain,
( X1 = X2
| ~ c_fequal(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_1771]) ).
cnf(c_0_2382,plain,
c_Relation_ORange(c_Relation_OId__on(X1,X2),X2,X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_1772]) ).
cnf(c_0_2383,plain,
c_Relation_ODomain(c_Relation_OId__on(X1,X2),X2,X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_1773]) ).
cnf(c_0_2384,plain,
c_Relation_Orefl__on(X1,c_Relation_OId__on(X1,X2),X2),
inference(split_conjunct,[status(thm)],[c_0_1774]) ).
cnf(c_0_2385,plain,
c_Relation_Osingle__valued(c_Relation_OId__on(X1,X2),X2,X2),
inference(split_conjunct,[status(thm)],[c_0_1775]) ).
cnf(c_0_2386,plain,
hAPP(c_Relation_Oconverse(X1,X1),c_Relation_OId__on(X2,X1)) = c_Relation_OId__on(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_1776]) ).
cnf(c_0_2387,plain,
( c_Relation_Osym(X1,X2)
| hAPP(c_Relation_Oconverse(X2,X2),X1) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_1777]) ).
cnf(c_0_2388,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_fun(X2,tc_bool)) = X1,
inference(split_conjunct,[status(thm)],[c_0_1778]) ).
cnf(c_0_2389,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,X1,tc_fun(X2,tc_bool)) = X1,
inference(split_conjunct,[status(thm)],[c_0_1779]) ).
cnf(c_0_2390,plain,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1780]) ).
cnf(c_0_2391,plain,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
inference(split_conjunct,[status(thm)],[c_0_1781]) ).
cnf(c_0_2392,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X1),X2,X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1782]) ).
cnf(c_0_2393,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(X2),X2) = c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1783]) ).
cnf(c_0_2394,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X1),X2,X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1784]) ).
cnf(c_0_2395,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(X2),X2) = X1
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1785]) ).
cnf(c_0_2396,plain,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1786]) ).
cnf(c_0_2397,plain,
( hAPP(c_Relation_Oconverse(X2,X2),X1) = X1
| ~ c_Relation_Osym(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1787]) ).
cnf(c_0_2398,plain,
( c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X1,X2),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1788]) ).
cnf(c_0_2399,plain,
( c_Relation_Osym(c_Transitive__Closure_Ortrancl(X1,X2),X2)
| ~ c_Relation_Osym(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1789]) ).
cnf(c_0_2400,plain,
( c_Relation_Osym(c_Transitive__Closure_Otrancl(X1,X2),X2)
| ~ c_Relation_Osym(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1790]) ).
cnf(c_0_2401,plain,
( c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X1,X2),X2)
| ~ c_Wellfounded_Oacyclic(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1791]) ).
cnf(c_0_2402,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X1,X2) = X1
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1792]) ).
cnf(c_0_2403,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X2) = X1
| ~ class_Lattices_Oupper__semilattice(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1793]) ).
cnf(c_0_2404,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1794]) ).
cnf(c_0_2405,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[c_0_1795]) ).
cnf(c_0_2406,plain,
c_Relation_Osingle__valued(c_Relation_OId(X1),X1,X1),
inference(split_conjunct,[status(thm)],[c_0_1796]) ).
cnf(c_0_2407,plain,
c_fequal(X1,X1,X2),
inference(split_conjunct,[status(thm)],[c_0_1797]) ).
cnf(c_0_2408,plain,
c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_1798]) ).
cnf(c_0_2409,plain,
c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X1,X2),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_1799]) ).
cnf(c_0_2410,plain,
c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_1800]) ).
cnf(c_0_2411,plain,
hAPP(c_Relation_Oconverse(X1,X1),c_Relation_OId(X1)) = c_Relation_OId(X1),
inference(split_conjunct,[status(thm)],[c_0_1801]) ).
cnf(c_0_2412,plain,
c_Relation_Osym(c_Relation_OId__on(X1,X2),X2),
inference(split_conjunct,[status(thm)],[c_0_1802]) ).
cnf(c_0_2413,plain,
c_Relation_Oantisym(c_Relation_OId__on(X1,X2),X2),
inference(split_conjunct,[status(thm)],[c_0_1803]) ).
cnf(c_0_2414,plain,
( class_HOL_Oord(tc_fun(X2,X1))
| ~ class_HOL_Oord(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1804]) ).
cnf(c_0_2415,plain,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1805]) ).
cnf(c_0_2416,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1806]) ).
cnf(c_0_2417,plain,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1807]) ).
cnf(c_0_2418,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1808]) ).
cnf(c_0_2419,plain,
( class_Lattices_Obounded__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1809]) ).
cnf(c_0_2420,plain,
( class_Lattices_Odistrib__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1810]) ).
cnf(c_0_2421,plain,
( class_Lattices_Olower__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1811]) ).
cnf(c_0_2422,plain,
( class_Lattices_Oupper__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(split_conjunct,[status(thm)],[c_0_1812]) ).
cnf(c_0_2423,plain,
( c_Wellfounded_Oacyclic(X1,X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_1813]) ).
cnf(c_0_2424,plain,
c_Relation_Oantisym(c_Relation_OId(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_1814]) ).
cnf(c_0_2425,plain,
c_Relation_Osym(c_Relation_OId(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_1815]) ).
cnf(c_0_2426,plain,
class_HOL_Oord(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1816]) ).
cnf(c_0_2427,plain,
class_Orderings_Obot(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1817]) ).
cnf(c_0_2428,plain,
class_Orderings_Oorder(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1818]) ).
cnf(c_0_2429,plain,
class_Lattices_Olattice(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1819]) ).
cnf(c_0_2430,plain,
class_Orderings_Opreorder(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1820]) ).
cnf(c_0_2431,plain,
class_Lattices_Obounded__lattice(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1821]) ).
cnf(c_0_2432,plain,
class_Lattices_Odistrib__lattice(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1822]) ).
cnf(c_0_2433,plain,
class_Lattices_Olower__semilattice(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1823]) ).
cnf(c_0_2434,plain,
class_Lattices_Oupper__semilattice(tc_bool),
inference(split_conjunct,[status(thm)],[c_0_1824]) ).
cnf(c_0_2435,plain,
c_Arrow__Order__Mirabelle_OIIA(v_F),
inference(split_conjunct,[status(thm)],[c_0_1825]) ).
cnf(c_0_2436,plain,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
inference(split_conjunct,[status(thm)],[c_0_1826]) ).
cnf(c_0_2437,plain,
v_a____ != v_c____,
inference(split_conjunct,[status(thm)],[c_0_1827]) ).
cnf(c_0_2438,plain,
v_b____ != v_c____,
inference(split_conjunct,[status(thm)],[c_0_1828]) ).
cnf(c_0_2439,plain,
v_a____ != v_b____,
inference(split_conjunct,[status(thm)],[c_0_1829]) ).
cnf(c_0_2440,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_1830,
[final] ).
cnf(c_0_2441,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_1831,
[final] ).
cnf(c_0_2442,plain,
( X1 = X2
| X3 = X4
| X1 = X4
| X2 = X3
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X5,v_sko__local__X1__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X1__1(X5,X6,X1,X3,X2,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1832,
[final] ).
cnf(c_0_2443,plain,
( X1 = X2
| X3 = X4
| X1 = X4
| X2 = X3
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1833,
[final] ).
cnf(c_0_2444,plain,
( X1 = X2
| X3 = X4
| X1 = X4
| X2 = X3
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1834,
[final] ).
cnf(c_0_2445,plain,
( X1 = X2
| X3 = X4
| X1 = X4
| X2 = X3
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__local__X1__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X1__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1835,
[final] ).
cnf(c_0_2446,plain,
( X1 = X2
| X3 = X4
| X1 = X4
| X2 = X3
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1836,
[final] ).
cnf(c_0_2447,plain,
( X1 = X2
| X3 = X4
| X1 = X4
| X2 = X3
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1837,
[final] ).
cnf(c_0_2448,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_1838,
[final] ).
cnf(c_0_2449,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_1839,
[final] ).
cnf(c_0_2450,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_1840,
[final] ).
cnf(c_0_2451,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_1841,
[final] ).
cnf(c_0_2452,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_1842,
[final] ).
cnf(c_0_2453,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_1843,
[final] ).
cnf(c_0_2454,plain,
( hAPP(hAPP(X3,X7),X9) = hAPP(hAPP(X3,X8),X10)
| ~ c_Equiv__Relations_Ocongruent2(X1,X2,X3,X4,X5,X6)
| ~ c_in(c_Pair(X7,X8,X4,X4),X1,tc_prod(X4,X4))
| ~ c_in(c_Pair(X9,X10,X5,X5),X2,tc_prod(X5,X5)) ),
c_0_1844,
[final] ).
cnf(c_0_2455,plain,
( c_Equiv__Relations_Ocongruent(X4,hAPP(X5,X8),X6,X7)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_Equiv__Relations_Ocongruent2(X2,X4,X5,X3,X6,X7)
| ~ c_in(X8,X1,X3) ),
c_0_1845,
[final] ).
cnf(c_0_2456,plain,
c_Fun_Ocomp(X1,c_Fun_Ocomp(X2,X3,X4,X5,X6),X5,X7,X6) = c_Fun_Ocomp(c_Fun_Ocomp(X1,X2,X5,X7,X4),X3,X4,X7,X6),
c_0_1846,
[final] ).
cnf(c_0_2457,plain,
c_Relation_Orel__comp(c_Relation_Orel__comp(X1,X2,X3,X4,X5),X6,X3,X5,X7) = c_Relation_Orel__comp(X1,c_Relation_Orel__comp(X2,X6,X4,X5,X7),X3,X4,X7),
c_0_1847,
[final] ).
cnf(c_0_2458,plain,
( c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1848,
[final] ).
cnf(c_0_2459,plain,
( c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X1,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1849,
[final] ).
cnf(c_0_2460,plain,
( X1 = X2
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,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),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1850,
[final] ).
cnf(c_0_2461,plain,
( X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1851,
[final] ).
cnf(c_0_2462,plain,
( c_in(c_Pair(X5,X6,X3,X3),X2,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(X4,c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X2,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool)),X3) ),
c_0_1852,
[final] ).
cnf(c_0_2463,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,X2,X6,X4,X5),c_Relation_Orel__comp(X1,X3,X6,X4,X5),tc_fun(tc_prod(X6,X5),tc_bool)) = c_Relation_Orel__comp(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(tc_prod(X4,X5),tc_bool)),X6,X4,X5),
c_0_1853,
[final] ).
cnf(c_0_2464,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,X5,X3,X4,X6),c_Relation_Orel__comp(X2,X5,X3,X4,X6),tc_fun(tc_prod(X3,X6),tc_bool)) = c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X5,X3,X4,X6),
c_0_1854,
[final] ).
cnf(c_0_2465,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_1855,
[final] ).
cnf(c_0_2466,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_1856,
[final] ).
cnf(c_0_2467,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_1857,
[final] ).
cnf(c_0_2468,plain,
c_Set_Oinsert(c_Pair(X1,X4,X3,X6),c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X2,c_COMBK(c_Set_Oinsert(X4,X5,X6),tc_fun(X6,tc_bool),X3),X3,X6),c_Product__Type_OSigma(c_Set_Oinsert(X1,X2,X3),c_COMBK(X5,tc_fun(X6,tc_bool),X3),X3,X6),tc_fun(tc_prod(X3,X6),tc_bool)),tc_prod(X3,X6)) = c_Product__Type_OSigma(c_Set_Oinsert(X1,X2,X3),c_COMBK(c_Set_Oinsert(X4,X5,X6),tc_fun(X6,tc_bool),X3),X3,X6),
c_0_1858,
[final] ).
cnf(c_0_2469,plain,
( c_Relation_Orel__comp(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(tc_prod(X4,X4),tc_bool)),X4,X4,X4) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool))
| c_Relation_Orel__comp(X1,X2,X4,X4,X4) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool))
| c_Relation_Orel__comp(X1,X3,X4,X4,X4) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool)) ),
c_0_1859,
[final] ).
cnf(c_0_2470,plain,
( c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X4,X3,X3,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool))
| c_Relation_Orel__comp(X1,X4,X3,X3,X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool))
| c_Relation_Orel__comp(X2,X4,X3,X3,X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool)) ),
c_0_1860,
[final] ).
cnf(c_0_2471,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_1861,
[final] ).
cnf(c_0_2472,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_1862,
[final] ).
cnf(c_0_2473,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_1863,
[final] ).
cnf(c_0_2474,plain,
( c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X1,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1864,
[final] ).
cnf(c_0_2475,plain,
( c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X1,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1865,
[final] ).
cnf(c_0_2476,plain,
( X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1866,
[final] ).
cnf(c_0_2477,plain,
( X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,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),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1867,
[final] ).
cnf(c_0_2478,plain,
( hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(c_Fun_Ocomp(X7,X8,X9,X4,X10),X11)
| hAPP(X1,hAPP(X2,X6)) != hAPP(X7,hAPP(X8,X11)) ),
c_0_1868,
[final] ).
cnf(c_0_2479,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_1869,
[final] ).
cnf(c_0_2480,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_1870,
[final] ).
cnf(c_0_2481,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_1871,
[final] ).
cnf(c_0_2482,plain,
( hAPP(X1,hAPP(X2,X3)) = hAPP(X4,hAPP(X5,X3))
| c_Fun_Ocomp(X1,X2,X6,X7,X8) != c_Fun_Ocomp(X4,X5,X9,X7,X8) ),
c_0_1872,
[final] ).
cnf(c_0_2483,plain,
( c_Wellfounded_Owf(X1,X2)
| ~ c_Wellfounded_Owf(c_Relation_Orel__comp(X1,X1,X2,X2,X2),X2) ),
c_0_1873,
[final] ).
cnf(c_0_2484,plain,
c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X5,X2),X4),hAPP(c_Relation_Oconverse(X1,X5),X3),X2,X5,X1) = hAPP(c_Relation_Oconverse(X1,X2),c_Relation_Orel__comp(X3,X4,X1,X5,X2)),
c_0_1874,
[final] ).
cnf(c_0_2485,plain,
( c_in(c_Pair(X5,X4,X3,X3),X2,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_lessequals(c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
c_0_1875,
[final] ).
cnf(c_0_2486,plain,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X5,X1,X4,X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X5,X1,X4,X3),X3,X3),X4,tc_prod(X3,X3))
| hBOOL(hAPP(X5,X2))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ hBOOL(hAPP(X5,X1)) ),
c_0_1876,
[final] ).
cnf(c_0_2487,plain,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X5,X2,X4,X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X5,X2,X4,X3),X3,X3),X4,tc_prod(X3,X3))
| hBOOL(hAPP(X5,X1))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ hBOOL(hAPP(X5,X2)) ),
c_0_1877,
[final] ).
cnf(c_0_2488,plain,
( c_in(c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1(X2,X3,X1,X4,X5),X2,X4)
| ~ c_in(X1,c_Product__Type_OSigma(X2,X3,X4,X5),tc_prod(X4,X5)) ),
c_0_1878,
[final] ).
cnf(c_0_2489,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_1879,
[final] ).
cnf(c_0_2490,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_1880,
[final] ).
cnf(c_0_2491,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_1881,
[final] ).
cnf(c_0_2492,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_1882,
[final] ).
cnf(c_0_2493,plain,
( c_in(c_Pair(X4,X5,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| c_in(c_Pair(X5,X4,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| ~ c_Relation_Osingle__valued(X1,X2,X2)
| ~ c_in(c_Pair(X3,X4,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X3,X5,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2)) ),
c_0_1883,
[final] ).
cnf(c_0_2494,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__XtranclE__1__1(X1,X2,X4,X3),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_1884,
[final] ).
cnf(c_0_2495,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_1885,
[final] ).
cnf(c_0_2496,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_1886,
[final] ).
cnf(c_0_2497,plain,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X1,X2,X4,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_1887,
[final] ).
cnf(c_0_2498,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_1888,
[final] ).
cnf(c_0_2499,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_1889,
[final] ).
cnf(c_0_2500,plain,
c_lessequals(c_Relation_OImage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X1,X2,X4,X5),c_Relation_OImage(X1,X3,X4,X5),tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
c_0_1890,
[final] ).
cnf(c_0_2501,plain,
( c_lessequals(c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
c_0_1891,
[final] ).
cnf(c_0_2502,plain,
c_in(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
c_0_1892,
[final] ).
cnf(c_0_2503,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_1893,
[final] ).
cnf(c_0_2504,plain,
( c_lessequals(X2,c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X3,X3),X2),X2,X3,X3,X3),tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Relation_Orefl__on(X1,X2,X3) ),
c_0_1894,
[final] ).
cnf(c_0_2505,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_1895,
[final] ).
cnf(c_0_2506,plain,
( ~ c_Wellfounded_Oacyclic(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_1896,
[final] ).
cnf(c_0_2507,plain,
( c_Relation_Osingle__valued(c_Relation_Orel__comp(X1,X4,X2,X3,X5),X2,X5)
| ~ c_Relation_Osingle__valued(X1,X2,X3)
| ~ c_Relation_Osingle__valued(X4,X3,X5) ),
c_0_1897,
[final] ).
cnf(c_0_2508,plain,
( hBOOL(hAPP(X5,X1))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ hBOOL(hAPP(X5,X2))
| ~ hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X5,X2,X4,X3))) ),
c_0_1898,
[final] ).
cnf(c_0_2509,plain,
( hBOOL(hAPP(X5,X2))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ hBOOL(hAPP(X5,X1))
| ~ hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X5,X1,X4,X3))) ),
c_0_1899,
[final] ).
cnf(c_0_2510,plain,
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)) = c_Transitive__Closure_Ortrancl(X1,X2),
c_0_1900,
[final] ).
cnf(c_0_2511,plain,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X5,X1,X4,X3),X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| hBOOL(hAPP(X5,X2))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ hBOOL(hAPP(X5,X1)) ),
c_0_1901,
[final] ).
cnf(c_0_2512,plain,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X5,X2,X4,X3),X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| hBOOL(hAPP(X5,X1))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ hBOOL(hAPP(X5,X2)) ),
c_0_1902,
[final] ).
cnf(c_0_2513,plain,
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)) = c_Transitive__Closure_Otrancl(X1,X2),
c_0_1903,
[final] ).
cnf(c_0_2514,plain,
( X1 = X2
| c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X1,X2,X4,X3),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_0_1904,
[final] ).
cnf(c_0_2515,plain,
( X1 = X2
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__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_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
c_0_1905,
[final] ).
cnf(c_0_2516,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_1906,
[final] ).
cnf(c_0_2517,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_1907,
[final] ).
cnf(c_0_2518,plain,
( X1 = X2
| c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X4,X1,X2,X3),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_0_1908,
[final] ).
cnf(c_0_2519,plain,
( X1 = X2
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X1,X2,X4,X3),X2,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_0_1909,
[final] ).
cnf(c_0_2520,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_1910,
[final] ).
cnf(c_0_2521,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_1911,
[final] ).
cnf(c_0_2522,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_1912,
[final] ).
cnf(c_0_2523,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_1913,
[final] ).
cnf(c_0_2524,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_1914,
[final] ).
cnf(c_0_2525,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_1915,
[final] ).
cnf(c_0_2526,plain,
hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
c_0_1916,
[final] ).
cnf(c_0_2527,plain,
hAPP(c_Fun_Ocomp(X1,X2,X4,X5,X6),X3) = hAPP(X1,hAPP(X2,X3)),
c_0_1917,
[final] ).
cnf(c_0_2528,plain,
c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),X1,X2,X2,X2) = c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),
c_0_1918,
[final] ).
cnf(c_0_2529,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_1919,
[final] ).
cnf(c_0_2530,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_1920,
[final] ).
cnf(c_0_2531,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_1921,
[final] ).
cnf(c_0_2532,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_1922,
[final] ).
cnf(c_0_2533,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_1923,
[final] ).
cnf(c_0_2534,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_1924,
[final] ).
cnf(c_0_2535,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_1925,
[final] ).
cnf(c_0_2536,plain,
( c_Wellfounded_Owf(c_Relation_Orel__comp(X1,X1,X2,X2,X2),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
c_0_1926,
[final] ).
cnf(c_0_2537,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_1927,
[final] ).
cnf(c_0_2538,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_1928,
[final] ).
cnf(c_0_2539,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_1929,
[final] ).
cnf(c_0_2540,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X1,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),c_Product__Type_OSigma(X2,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),tc_fun(tc_prod(X3,X5),tc_bool)) = c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),
c_0_1930,
[final] ).
cnf(c_0_2541,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(X1,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),c_Product__Type_OSigma(X2,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),tc_fun(tc_prod(X3,X5),tc_bool)) = c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),
c_0_1931,
[final] ).
cnf(c_0_2542,plain,
( c_in(c_Pair(X1,X2,t_a,t_a),X3,tc_prod(t_a,t_a))
| c_in(c_Pair(X1,v_sko__Transitive__Closure__Xtrancl__Xcases__1(X1,X2,X3),t_a,t_a),c_Transitive__Closure_Otrancl(X3,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X1,X2,t_a,t_a),c_Transitive__Closure_Otrancl(X3,t_a),tc_prod(t_a,t_a)) ),
c_0_1932,
[final] ).
cnf(c_0_2543,plain,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X3)
| ~ c_in(X1,X5,X3)
| ~ c_in(X2,X5,X3)
| c_Relation_OImage(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) ),
c_0_1933,
[final] ).
cnf(c_0_2544,plain,
( c_in(c_Pair(X1,X4,X3,X3),X5,tc_prod(X3,X3))
| ~ c_in(X1,X2,X3)
| ~ c_in(X4,X2,X3)
| ~ c_Equiv__Relations_Oequiv(X2,X5,X3)
| c_Relation_OImage(X5,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X5,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) ),
c_0_1934,
[final] ).
cnf(c_0_2545,plain,
( c_in(c_Pair(X1,X2,t_a,t_a),X3,tc_prod(t_a,t_a))
| c_in(c_Pair(v_sko__Transitive__Closure__Xtrancl__Xcases__1(X1,X2,X3),X2,t_a,t_a),X3,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X1,X2,t_a,t_a),c_Transitive__Closure_Otrancl(X3,t_a),tc_prod(t_a,t_a)) ),
c_0_1935,
[final] ).
cnf(c_0_2546,plain,
( c_in(c_Pair(X5,X4,X3,X3),X2,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(X4,X1,X3)
| c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) ),
c_0_1936,
[final] ).
cnf(c_0_2547,plain,
( c_Equiv__Relations_Oequiv(c_Relation_ODomain(X1,X2,X2),X1,X2)
| c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X2,X2),X1),X1,X2,X2,X2) != X1 ),
c_0_1937,
[final] ).
cnf(c_0_2548,plain,
( c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1(X3,X4,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1938,
[final] ).
cnf(c_0_2549,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_1939,
[final] ).
cnf(c_0_2550,plain,
( c_in(c_Pair(X3,X1,X4,X5),X2,tc_prod(X4,X5))
| ~ c_in(X1,c_Relation_OImage(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X5),X5) ),
c_0_1940,
[final] ).
cnf(c_0_2551,plain,
( c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(X4,X1,X3)
| ~ c_in(X5,X1,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
c_0_1941,
[final] ).
cnf(c_0_2552,plain,
( hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X5,X1,X4,X3)))
| hBOOL(hAPP(X5,X2))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ hBOOL(hAPP(X5,X1)) ),
c_0_1942,
[final] ).
cnf(c_0_2553,plain,
( hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X5,X2,X4,X3)))
| hBOOL(hAPP(X5,X1))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ hBOOL(hAPP(X5,X2)) ),
c_0_1943,
[final] ).
cnf(c_0_2554,plain,
( c_Wellfounded_Owf(X1,X2)
| c_Relation_Orel__comp(X1,X1,X2,X2,X2) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) ),
c_0_1944,
[final] ).
cnf(c_0_2555,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_1945,
[final] ).
cnf(c_0_2556,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
c_0_1946,
[final] ).
cnf(c_0_2557,plain,
( c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1947,
[final] ).
cnf(c_0_2558,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_1948,
[final] ).
cnf(c_0_2559,plain,
( c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
c_0_1949,
[final] ).
cnf(c_0_2560,plain,
( c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
c_0_1950,
[final] ).
cnf(c_0_2561,plain,
( X5 = X6
| ~ c_Relation_Osingle__valued(X1,X2,X3)
| ~ c_in(c_Pair(X4,X5,X2,X3),X1,tc_prod(X2,X3))
| ~ c_in(c_Pair(X4,X6,X2,X3),X1,tc_prod(X2,X3)) ),
c_0_1951,
[final] ).
cnf(c_0_2562,plain,
( c_in(c_Pair(X1,X2,X3,X3),hAPP(c_Relation_Oconverse(X3,X3),c_Transitive__Closure_Otrancl(X4,X3)),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(hAPP(c_Relation_Oconverse(X3,X3),X4),X3),tc_prod(X3,X3)) ),
c_0_1952,
[final] ).
cnf(c_0_2563,plain,
( c_in(X2,c_Relation_OImage(X5,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X4),X4)
| ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)) ),
c_0_1953,
[final] ).
cnf(c_0_2564,plain,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(hAPP(c_Relation_Oconverse(X3,X3),X4),X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),hAPP(c_Relation_Oconverse(X3,X3),c_Transitive__Closure_Otrancl(X4,X3)),tc_prod(X3,X3)) ),
c_0_1954,
[final] ).
cnf(c_0_2565,plain,
( X1 = X2
| ~ c_Relation_Orefl__on(c_Relation_OField(X3,X4),X3,X4)
| ~ c_Relation_Oantisym(X3,X4)
| ~ c_in(X1,c_Relation_OField(X3,X4),X4)
| ~ c_in(X2,c_Relation_OField(X3,X4),X4)
| c_Relation_OImage(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4) != c_Relation_OImage(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4) ),
c_0_1955,
[final] ).
cnf(c_0_2566,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_1956,
[final] ).
cnf(c_0_2567,plain,
( c_Wellfounded_Oacyclic(X4,X3)
| ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)),X3) ),
c_0_1957,
[final] ).
cnf(c_0_2568,plain,
( X3 = X4
| ~ c_Relation_Oantisym(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_1958,
[final] ).
cnf(c_0_2569,plain,
( X3 = X4
| ~ c_Relation_Oantisym(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_1959,
[final] ).
cnf(c_0_2570,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_1960,
[final] ).
cnf(c_0_2571,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_1961,
[final] ).
cnf(c_0_2572,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_1962,
[final] ).
cnf(c_0_2573,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_1963,
[final] ).
cnf(c_0_2574,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_1964,
[final] ).
cnf(c_0_2575,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),c_Relation_OField(X4,X3),tc_fun(X3,tc_bool)) = c_Relation_OField(c_Set_Oinsert(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)),X3),
c_0_1965,
[final] ).
cnf(c_0_2576,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(hAPP(c_Relation_Oconverse(X3,X3),X4),X3),tc_prod(X3,X3)) ),
c_0_1966,
[final] ).
cnf(c_0_2577,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_1967,
[final] ).
cnf(c_0_2578,plain,
( c_in(c_Pair(X3,X4,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X4,X3,X2,X2),X1,tc_prod(X2,X2)),X2)
| ~ c_Wellfounded_Oacyclic(X1,X2) ),
c_0_1968,
[final] ).
cnf(c_0_2579,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_1969,
[final] ).
cnf(c_0_2580,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_1970,
[final] ).
cnf(c_0_2581,plain,
( X2 = X1
| c_in(c_Pair(X1,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X1,X2,X3),t_a,t_a),c_Transitive__Closure_Ortrancl(X3,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X1,X2,t_a,t_a),c_Transitive__Closure_Ortrancl(X3,t_a),tc_prod(t_a,t_a)) ),
c_0_1971,
[final] ).
cnf(c_0_2582,plain,
( c_in(c_Pair(X2,X1,X3,X3),c_Transitive__Closure_Ortrancl(hAPP(c_Relation_Oconverse(X3,X3),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_1972,
[final] ).
cnf(c_0_2583,plain,
( X2 = X1
| c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X1,X2,X3),X2,t_a,t_a),X3,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X1,X2,t_a,t_a),c_Transitive__Closure_Ortrancl(X3,t_a),tc_prod(t_a,t_a)) ),
c_0_1973,
[final] ).
cnf(c_0_2584,plain,
( c_Equiv__Relations_Oquotient(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,X3) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(X4,X1,X3)
| ~ c_in(X5,X1,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
c_0_1974,
[final] ).
cnf(c_0_2585,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X3,X4,X1,X2),c_Relation_OImage(X3,X5,X1,X2),tc_fun(X2,tc_bool)) = c_Relation_OImage(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X1,tc_bool)),X1,X2)
| ~ c_Relation_Osingle__valued(hAPP(c_Relation_Oconverse(X1,X2),X3),X2,X1) ),
c_0_1975,
[final] ).
cnf(c_0_2586,plain,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X3)
| ~ c_in(X1,X5,X3)
| ~ c_in(X2,X5,X3)
| c_Equiv__Relations_Oquotient(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X4,X3) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X4,X3) ),
c_0_1976,
[final] ).
cnf(c_0_2587,plain,
( c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X1),X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X1),X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1977,
[final] ).
cnf(c_0_2588,plain,
( c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X1),X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X1),X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1978,
[final] ).
cnf(c_0_2589,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_1979,
[final] ).
cnf(c_0_2590,plain,
( c_in(c_Pair(X2,X1,X4,X3),X5,tc_prod(X4,X3))
| ~ c_in(c_Pair(X1,X2,X3,X4),hAPP(c_Relation_Oconverse(X4,X3),X5),tc_prod(X3,X4)) ),
c_0_1980,
[final] ).
cnf(c_0_2591,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X1,X5,X3,X4),c_Relation_OImage(X2,X5,X3,X4),tc_fun(X4,tc_bool)) = c_Relation_OImage(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X5,X3,X4),
c_0_1981,
[final] ).
cnf(c_0_2592,plain,
( c_in(c_Pair(X2,X1,X4,X3),hAPP(c_Relation_Oconverse(X3,X4),X5),tc_prod(X4,X3))
| ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)) ),
c_0_1982,
[final] ).
cnf(c_0_2593,plain,
( c_in(c_Pair(X2,X1,X4,X3),hAPP(c_Relation_Oconverse(X3,X4),X5),tc_prod(X4,X3))
| ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)) ),
c_0_1983,
[final] ).
cnf(c_0_2594,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_1984,
[final] ).
cnf(c_0_2595,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_1985,
[final] ).
cnf(c_0_2596,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_1986,
[final] ).
cnf(c_0_2597,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_1987,
[final] ).
cnf(c_0_2598,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_1988,
[final] ).
cnf(c_0_2599,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_1989,
[final] ).
cnf(c_0_2600,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_1990,
[final] ).
cnf(c_0_2601,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X1,X4,X3,X5),c_Product__Type_OSigma(X2,X4,X3,X5),tc_fun(tc_prod(X3,X5),tc_bool)) = c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,X3,X5),
c_0_1991,
[final] ).
cnf(c_0_2602,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(X1,X4,X3,X5),c_Product__Type_OSigma(X2,X4,X3,X5),tc_fun(tc_prod(X3,X5),tc_bool)) = c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,X3,X5),
c_0_1992,
[final] ).
cnf(c_0_2603,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_1993,
[final] ).
cnf(c_0_2604,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_1994,
[final] ).
cnf(c_0_2605,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_1995,
[final] ).
cnf(c_0_2606,plain,
( c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1996,
[final] ).
cnf(c_0_2607,plain,
( c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_1997,
[final] ).
cnf(c_0_2608,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_1998,
[final] ).
cnf(c_0_2609,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_1999,
[final] ).
cnf(c_0_2610,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_2000,
[final] ).
cnf(c_0_2611,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_2001,
[final] ).
cnf(c_0_2612,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_2002,
[final] ).
cnf(c_0_2613,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_2003,
[final] ).
cnf(c_0_2614,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X1,X2,X4,X5),c_Relation_OImage(X1,X3,X4,X5),tc_fun(X5,tc_bool)) = c_Relation_OImage(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5),
c_0_2004,
[final] ).
cnf(c_0_2615,plain,
c_Relation_Orel__comp(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)),X4,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X3),tc_bool)),
c_0_2005,
[final] ).
cnf(c_0_2616,plain,
c_Relation_Orel__comp(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_bool)),X3,X1,X2,X4) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X4),tc_bool)),
c_0_2006,
[final] ).
cnf(c_0_2617,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_2007,
[final] ).
cnf(c_0_2618,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_2008,
[final] ).
cnf(c_0_2619,plain,
( ~ c_in(c_Pair(X1,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
| c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Relation_Oconverse(X2,X2),X3),c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) ),
c_0_2009,
[final] ).
cnf(c_0_2620,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_2010,
[final] ).
cnf(c_0_2621,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_2011,
[final] ).
cnf(c_0_2622,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_2012,
[final] ).
cnf(c_0_2623,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_2013,
[final] ).
cnf(c_0_2624,plain,
( c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X3,X3),X2),X2,X3,X3,X3) = X2
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
c_0_2014,
[final] ).
cnf(c_0_2625,plain,
c_Relation_ORange(c_Set_Oinsert(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)),X3,X4) = c_Set_Oinsert(X2,c_Relation_ORange(X5,X3,X4),X4),
c_0_2015,
[final] ).
cnf(c_0_2626,plain,
c_Relation_ODomain(c_Set_Oinsert(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)),X3,X4) = c_Set_Oinsert(X1,c_Relation_ODomain(X5,X3,X4),X3),
c_0_2016,
[final] ).
cnf(c_0_2627,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_2017,
[final] ).
cnf(c_0_2628,plain,
( hBOOL(hAPP(X4,X3))
| hBOOL(hAPP(X4,X5))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2)) ),
c_0_2018,
[final] ).
cnf(c_0_2629,plain,
( hBOOL(hAPP(X4,X3))
| hBOOL(hAPP(X4,X5))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_Pair(X3,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2)) ),
c_0_2019,
[final] ).
cnf(c_0_2630,plain,
( hBOOL(hAPP(X4,X3))
| hBOOL(hAPP(X4,X5))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2)) ),
c_0_2020,
[final] ).
cnf(c_0_2631,plain,
( hBOOL(hAPP(X4,X3))
| hBOOL(hAPP(X4,X5))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2)) ),
c_0_2021,
[final] ).
cnf(c_0_2632,plain,
( hAPP(X2,X5) = hAPP(X2,X6)
| ~ c_Equiv__Relations_Ocongruent(X1,X2,X3,X4)
| ~ c_in(c_Pair(X5,X6,X3,X3),X1,tc_prod(X3,X3)) ),
c_0_2022,
[final] ).
cnf(c_0_2633,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_2023,
[final] ).
cnf(c_0_2634,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_2024,
[final] ).
cnf(c_0_2635,plain,
c_lessequals(c_Relation_ORange(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(X1,X3,X4),c_Relation_ORange(X2,X3,X4),tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
c_0_2025,
[final] ).
cnf(c_0_2636,plain,
c_lessequals(c_Relation_ODomain(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X1,X3,X4),c_Relation_ODomain(X2,X3,X4),tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
c_0_2026,
[final] ).
cnf(c_0_2637,plain,
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),
c_0_2027,
[final] ).
cnf(c_0_2638,plain,
( c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
c_0_2028,
[final] ).
cnf(c_0_2639,plain,
c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2) = c_Transitive__Closure_Otrancl(X1,X2),
c_0_2029,
[final] ).
cnf(c_0_2640,plain,
c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),X1,X2,X2,X2) = c_Transitive__Closure_Otrancl(X1,X2),
c_0_2030,
[final] ).
cnf(c_0_2641,plain,
c_Relation_Orel__comp(X1,c_Relation_OId(X2),X3,X2,X2) = X1,
c_0_2031,
[final] ).
cnf(c_0_2642,plain,
c_Relation_Orel__comp(c_Relation_OId(X1),X2,X1,X1,X3) = X2,
c_0_2032,
[final] ).
cnf(c_0_2643,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_2033,
[final] ).
cnf(c_0_2644,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_2034,
[final] ).
cnf(c_0_2645,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_2035,
[final] ).
cnf(c_0_2646,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_2036,
[final] ).
cnf(c_0_2647,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_2037,
[final] ).
cnf(c_0_2648,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_2038,
[final] ).
cnf(c_0_2649,plain,
( c_in(X4,c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(X4,X1,X3) ),
c_0_2039,
[final] ).
cnf(c_0_2650,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_2040,
[final] ).
cnf(c_0_2651,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_2041,
[final] ).
cnf(c_0_2652,plain,
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)),
c_0_2042,
[final] ).
cnf(c_0_2653,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_2043,
[final] ).
cnf(c_0_2654,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_2044,
[final] ).
cnf(c_0_2655,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_2045,
[final] ).
cnf(c_0_2656,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_2046,
[final] ).
cnf(c_0_2657,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_2047,
[final] ).
cnf(c_0_2658,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_2048,
[final] ).
cnf(c_0_2659,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_2049,
[final] ).
cnf(c_0_2660,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_2050,
[final] ).
cnf(c_0_2661,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_2051,
[final] ).
cnf(c_0_2662,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_2052,
[final] ).
cnf(c_0_2663,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_2053,
[final] ).
cnf(c_0_2664,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_2054,
[final] ).
cnf(c_0_2665,plain,
c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),
c_0_2055,
[final] ).
cnf(c_0_2666,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_2056,
[final] ).
cnf(c_0_2667,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_2057,
[final] ).
cnf(c_0_2668,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_2058,
[final] ).
cnf(c_0_2669,plain,
( c_Arrow__Order__Mirabelle_Ounanimity(X1)
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3(X1),v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2(X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_2059,
[final] ).
cnf(c_0_2670,plain,
( ~ c_Wellfounded_Oacyclic(X1,X2)
| ~ c_in(c_Pair(X3,X3,X2,X2),c_Transitive__Closure_Otrancl(X1,X2),tc_prod(X2,X2)) ),
c_0_2060,
[final] ).
cnf(c_0_2671,plain,
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)),
c_0_2061,
[final] ).
cnf(c_0_2672,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_lessequals(X3,c_Relation_OImage(X1,X3,X2,X2),tc_fun(X2,tc_bool)) ),
c_0_2062,
[final] ).
cnf(c_0_2673,plain,
( X1 = X2
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId__on(X4,X3),tc_prod(X3,X3)) ),
c_0_2063,
[final] ).
cnf(c_0_2674,plain,
( ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_Pair(X3,X3,X2,X2),X1,tc_prod(X2,X2)) ),
c_0_2064,
[final] ).
cnf(c_0_2675,plain,
~ 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)),
c_0_2065,
[final] ).
cnf(c_0_2676,plain,
~ 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)),
c_0_2066,
[final] ).
cnf(c_0_2677,plain,
~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X3,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
c_0_2067,
[final] ).
cnf(c_0_2678,plain,
~ 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)),
c_0_2068,
[final] ).
cnf(c_0_2679,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_2069,
[final] ).
cnf(c_0_2680,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_2070,
[final] ).
cnf(c_0_2681,plain,
( X1 = X2
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Relation_OId(X3),tc_prod(X3,X3)) ),
c_0_2071,
[final] ).
cnf(c_0_2682,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_2072,
[final] ).
cnf(c_0_2683,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_2073,
[final] ).
cnf(c_0_2684,plain,
hAPP(c_Relation_Oconverse(X1,X1),c_Relation_Oinv__image(X2,X3,X4,X1)) = c_Relation_Oinv__image(hAPP(c_Relation_Oconverse(X4,X4),X2),X3,X4,X1),
c_0_2074,
[final] ).
cnf(c_0_2685,plain,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
c_0_2075,
[final] ).
cnf(c_0_2686,plain,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
c_0_2076,
[final] ).
cnf(c_0_2687,plain,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
c_0_2077,
[final] ).
cnf(c_0_2688,plain,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
c_0_2078,
[final] ).
cnf(c_0_2689,plain,
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Wellfounded_Owf(X1,X3)
| ~ c_Wellfounded_Owf(X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X1,X3,X3),c_Relation_ORange(X2,X3,X3),tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_2079,
[final] ).
cnf(c_0_2690,plain,
( c_lessequals(X1,X2,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_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_0_2080,
[final] ).
cnf(c_0_2691,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_2081,
[final] ).
cnf(c_0_2692,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_2082,
[final] ).
cnf(c_0_2693,plain,
( X1 = X2
| c_Pair(X1,X3,X4,X5) != c_Pair(X2,X6,X4,X5) ),
c_0_2083,
[final] ).
cnf(c_0_2694,plain,
( X1 = X2
| c_Pair(X3,X1,X4,X5) != c_Pair(X6,X2,X4,X5) ),
c_0_2084,
[final] ).
cnf(c_0_2695,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_2085,
[final] ).
cnf(c_0_2696,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_2086,
[final] ).
cnf(c_0_2697,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_2087,
[final] ).
cnf(c_0_2698,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_2088,
[final] ).
cnf(c_0_2699,plain,
c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2),
c_0_2089,
[final] ).
cnf(c_0_2700,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_2090,
[final] ).
cnf(c_0_2701,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_2091,
[final] ).
cnf(c_0_2702,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_2092,
[final] ).
cnf(c_0_2703,plain,
( c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3(X1),v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2(X1),X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_Arrow__Order__Mirabelle_Ounanimity(X1) ),
c_0_2093,
[final] ).
cnf(c_0_2704,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_2094,
[final] ).
cnf(c_0_2705,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_2095,
[final] ).
cnf(c_0_2706,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)),
c_0_2096,
[final] ).
cnf(c_0_2707,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X4,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
c_0_2097,
[final] ).
cnf(c_0_2708,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)),
c_0_2098,
[final] ).
cnf(c_0_2709,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,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(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
c_0_2099,
[final] ).
cnf(c_0_2710,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X1,X3,X4),c_Relation_ORange(X2,X3,X4),tc_fun(X4,tc_bool)) = c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4),
c_0_2100,
[final] ).
cnf(c_0_2711,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X1,X3,X4),c_Relation_ODomain(X2,X3,X4),tc_fun(X3,tc_bool)) = c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4),
c_0_2101,
[final] ).
cnf(c_0_2712,plain,
c_in(c_Pair(X1,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)),
c_0_2102,
[final] ).
cnf(c_0_2713,plain,
c_in(c_Pair(X1,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)),
c_0_2103,
[final] ).
cnf(c_0_2714,plain,
( c_in(c_Pair(X3,X3,X2,X2),X1,tc_prod(X2,X2))
| ~ c_Nitpick_Orefl_H(X1,X2) ),
c_0_2104,
[final] ).
cnf(c_0_2715,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_2105,
[final] ).
cnf(c_0_2716,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_2106,
[final] ).
cnf(c_0_2717,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_2107,
[final] ).
cnf(c_0_2718,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X1 = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| ~ c_lessequals(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) ),
c_0_2108,
[final] ).
cnf(c_0_2719,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_2109,
[final] ).
cnf(c_0_2720,plain,
c_Product__Type_OSigma(X1,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool),X3),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X2),tc_bool)),
c_0_2110,
[final] ).
cnf(c_0_2721,plain,
( 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_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_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
c_0_2111,
[final] ).
cnf(c_0_2722,plain,
c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Relation_Oconverse(X1,X2),X3),hAPP(c_Relation_Oconverse(X1,X2),X4),tc_fun(tc_prod(X2,X1),tc_bool)) = hAPP(c_Relation_Oconverse(X1,X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(tc_prod(X1,X2),tc_bool))),
c_0_2112,
[final] ).
cnf(c_0_2723,plain,
c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Relation_Oconverse(X1,X2),X3),hAPP(c_Relation_Oconverse(X1,X2),X4),tc_fun(tc_prod(X2,X1),tc_bool)) = hAPP(c_Relation_Oconverse(X1,X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(tc_prod(X1,X2),tc_bool))),
c_0_2113,
[final] ).
cnf(c_0_2724,plain,
c_in(c_Pair(X1,X1,X2,X2),c_Relation_OId(X2),tc_prod(X2,X2)),
c_0_2114,
[final] ).
cnf(c_0_2725,plain,
c_in(c_Pair(X1,X1,X2,X2),c_Relation_OId(X2),tc_prod(X2,X2)),
c_0_2115,
[final] ).
cnf(c_0_2726,plain,
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
c_0_2116,
[final] ).
cnf(c_0_2727,plain,
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4)) ),
c_0_2117,
[final] ).
cnf(c_0_2728,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_2118,
[final] ).
cnf(c_0_2729,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_2119,
[final] ).
cnf(c_0_2730,plain,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),
c_0_2120,
[final] ).
cnf(c_0_2731,plain,
( c_Relation_Osym(c_Relation_Oinv__image(X1,X3,X2,X4),X4)
| ~ c_Relation_Osym(X1,X2) ),
c_0_2121,
[final] ).
cnf(c_0_2732,plain,
( c_Wellfounded_Owf(c_Relation_Oinv__image(X1,X3,X2,X4),X4)
| ~ c_Wellfounded_Owf(X1,X2) ),
c_0_2122,
[final] ).
cnf(c_0_2733,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X2,X3),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_0_2123,
[final] ).
cnf(c_0_2734,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_2124,
[final] ).
cnf(c_0_2735,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_2125,
[final] ).
cnf(c_0_2736,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) ),
c_0_2126,
[final] ).
cnf(c_0_2737,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) ),
c_0_2127,
[final] ).
cnf(c_0_2738,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_2128,
[final] ).
cnf(c_0_2739,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_2129,
[final] ).
cnf(c_0_2740,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_2130,
[final] ).
cnf(c_0_2741,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_2131,
[final] ).
cnf(c_0_2742,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_2132,
[final] ).
cnf(c_0_2743,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
c_0_2133,
[final] ).
cnf(c_0_2744,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
c_0_2134,
[final] ).
cnf(c_0_2745,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
c_0_2135,
[final] ).
cnf(c_0_2746,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
c_0_2136,
[final] ).
cnf(c_0_2747,plain,
( c_Relation_Oantisym(X1,X2)
| ~ c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
c_0_2137,
[final] ).
cnf(c_0_2748,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_2138,
[final] ).
cnf(c_0_2749,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_2139,
[final] ).
cnf(c_0_2750,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_2140,
[final] ).
cnf(c_0_2751,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_2141,
[final] ).
cnf(c_0_2752,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_2142,
[final] ).
cnf(c_0_2753,plain,
( hBOOL(hAPP(X3,X4))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X3,X1,X2))) ),
c_0_2143,
[final] ).
cnf(c_0_2754,plain,
( hBOOL(hAPP(X3,X4))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X3,X1,X2))) ),
c_0_2144,
[final] ).
cnf(c_0_2755,plain,
( hBOOL(hAPP(X3,X4))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X3,X1,X2))) ),
c_0_2145,
[final] ).
cnf(c_0_2756,plain,
( hBOOL(hAPP(X3,X4))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(X3,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X3,X1,X2))) ),
c_0_2146,
[final] ).
cnf(c_0_2757,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_2147,
[final] ).
cnf(c_0_2758,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_2148,
[final] ).
cnf(c_0_2759,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_2149,
[final] ).
cnf(c_0_2760,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_2150,
[final] ).
cnf(c_0_2761,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_2151,
[final] ).
cnf(c_0_2762,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_2152,
[final] ).
cnf(c_0_2763,plain,
c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X1,hAPP(c_Relation_Oconverse(X2,X2),X1),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
c_0_2153,
[final] ).
cnf(c_0_2764,plain,
c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X1,hAPP(c_Relation_Oconverse(X2,X2),X1),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
c_0_2154,
[final] ).
cnf(c_0_2765,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_2155,
[final] ).
cnf(c_0_2766,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_2156,
[final] ).
cnf(c_0_2767,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_2157,
[final] ).
cnf(c_0_2768,plain,
( X1 = X2
| ~ c_in(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
c_0_2158,
[final] ).
cnf(c_0_2769,plain,
( X1 = X4
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
c_0_2159,
[final] ).
cnf(c_0_2770,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_2160,
[final] ).
cnf(c_0_2771,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OField(X1,X3),c_Relation_OField(X2,X3),tc_fun(X3,tc_bool)) = c_Relation_OField(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3),
c_0_2161,
[final] ).
cnf(c_0_2772,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_2162,
[final] ).
cnf(c_0_2773,plain,
c_Set_Oinsert(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),X4) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)),
c_0_2163,
[final] ).
cnf(c_0_2774,plain,
c_Set_Oinsert(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)),
c_0_2164,
[final] ).
cnf(c_0_2775,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_2165,
[final] ).
cnf(c_0_2776,plain,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_2166,
[final] ).
cnf(c_0_2777,plain,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X4,tc_bool)),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_2167,
[final] ).
cnf(c_0_2778,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_2168,
[final] ).
cnf(c_0_2779,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_2169,
[final] ).
cnf(c_0_2780,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_2170,
[final] ).
cnf(c_0_2781,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_2171,
[final] ).
cnf(c_0_2782,plain,
c_Product__Type_OSigma(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X3),tc_bool)),
c_0_2172,
[final] ).
cnf(c_0_2783,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_2173,
[final] ).
cnf(c_0_2784,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_2174,
[final] ).
cnf(c_0_2785,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_2175,
[final] ).
cnf(c_0_2786,plain,
( hAPP(X1,X3) = hAPP(X3,X2)
| ~ c_Arrow__Order__Mirabelle_Odictator(X1,X2)
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
c_0_2176,
[final] ).
cnf(c_0_2787,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_2177,
[final] ).
cnf(c_0_2788,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_2178,
[final] ).
cnf(c_0_2789,plain,
c_Relation_OImage(c_Relation_OId__on(X1,X2),X3,X2,X2) = c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),
c_0_2179,
[final] ).
cnf(c_0_2790,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_2180,
[final] ).
cnf(c_0_2791,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_2181,
[final] ).
cnf(c_0_2792,plain,
( c_Relation_Osingle__valued(X1,X3,X4)
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool))
| ~ c_Relation_Osingle__valued(X2,X3,X4) ),
c_0_2182,
[final] ).
cnf(c_0_2793,plain,
( c_in(X1,X4,X3)
| ~ c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)) ),
c_0_2183,
[final] ).
cnf(c_0_2794,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,X2,X3),
c_0_2184,
[final] ).
cnf(c_0_2795,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_2185,
[final] ).
cnf(c_0_2796,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_2186,
[final] ).
cnf(c_0_2797,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_2187,
[final] ).
cnf(c_0_2798,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_2188,
[final] ).
cnf(c_0_2799,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_2189,
[final] ).
cnf(c_0_2800,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_2190,
[final] ).
cnf(c_0_2801,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3)
| ~ c_in(X4,X2,X3) ),
c_0_2191,
[final] ).
cnf(c_0_2802,plain,
( X1 = X2
| c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) != c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
c_0_2192,
[final] ).
cnf(c_0_2803,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_2193,
[final] ).
cnf(c_0_2804,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_2194,
[final] ).
cnf(c_0_2805,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_2195,
[final] ).
cnf(c_0_2806,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_2196,
[final] ).
cnf(c_0_2807,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_2197,
[final] ).
cnf(c_0_2808,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_2198,
[final] ).
cnf(c_0_2809,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_2199,
[final] ).
cnf(c_0_2810,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_2200,
[final] ).
cnf(c_0_2811,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_2201,
[final] ).
cnf(c_0_2812,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_2202,
[final] ).
cnf(c_0_2813,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_2203,
[final] ).
cnf(c_0_2814,plain,
c_Relation_OImage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
c_0_2204,
[final] ).
cnf(c_0_2815,plain,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,X3,X4),X4) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,X3,X4),X4),
c_0_2205,
[final] ).
cnf(c_0_2816,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_2206,
[final] ).
cnf(c_0_2817,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_2207,
[final] ).
cnf(c_0_2818,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_2208,
[final] ).
cnf(c_0_2819,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_2209,
[final] ).
cnf(c_0_2820,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_2210,
[final] ).
cnf(c_0_2821,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_2211,
[final] ).
cnf(c_0_2822,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_2212,
[final] ).
cnf(c_0_2823,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_2213,
[final] ).
cnf(c_0_2824,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_2214,
[final] ).
cnf(c_0_2825,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_2215,
[final] ).
cnf(c_0_2826,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_2216,
[final] ).
cnf(c_0_2827,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_2217,
[final] ).
cnf(c_0_2828,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_2218,
[final] ).
cnf(c_0_2829,plain,
( X1 = X2
| c_in(X1,X3,X4)
| ~ c_in(X1,c_Set_Oinsert(X2,X3,X4),X4) ),
c_0_2219,
[final] ).
cnf(c_0_2830,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),
c_0_2220,
[final] ).
cnf(c_0_2831,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
c_0_2221,
[final] ).
cnf(c_0_2832,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_2222,
[final] ).
cnf(c_0_2833,plain,
( c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Oantisym(X1,X2) ),
c_0_2223,
[final] ).
cnf(c_0_2834,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X1,X2,X2),c_Relation_ORange(X1,X2,X2),tc_fun(X2,tc_bool)) = c_Relation_OField(X1,X2),
c_0_2224,
[final] ).
cnf(c_0_2835,plain,
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),
c_0_2225,
[final] ).
cnf(c_0_2836,plain,
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),
c_0_2226,
[final] ).
cnf(c_0_2837,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_2227,
[final] ).
cnf(c_0_2838,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_2228,
[final] ).
cnf(c_0_2839,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_2229,
[final] ).
cnf(c_0_2840,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_2230,
[final] ).
cnf(c_0_2841,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_2231,
[final] ).
cnf(c_0_2842,plain,
( c_Wellfounded_Owf(hAPP(c_Relation_Oconverse(X1,X1),c_Transitive__Closure_Otrancl(X2,X1)),X1)
| ~ c_Wellfounded_Owf(hAPP(c_Relation_Oconverse(X1,X1),X2),X1) ),
c_0_2232,
[final] ).
cnf(c_0_2843,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X2,tc_fun(tc_prod(X1,X1),tc_bool)),
c_0_2233,
[final] ).
cnf(c_0_2844,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_2234,
[final] ).
cnf(c_0_2845,plain,
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)) = c_Relation_OField(v_r,t_a),
c_0_2235,
[final] ).
cnf(c_0_2846,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_2236,
[final] ).
cnf(c_0_2847,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_2237,
[final] ).
cnf(c_0_2848,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_2238,
[final] ).
cnf(c_0_2849,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_2239,
[final] ).
cnf(c_0_2850,plain,
c_in(X1,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),
c_0_2240,
[final] ).
cnf(c_0_2851,plain,
( c_Relation_Ototal__on(X1,X3,X2)
| ~ c_Relation_Ototal__on(X1,hAPP(c_Relation_Oconverse(X2,X2),X3),X2) ),
c_0_2241,
[final] ).
cnf(c_0_2852,plain,
( c_Relation_Orefl__on(X1,X3,X2)
| ~ c_Relation_Orefl__on(X1,hAPP(c_Relation_Oconverse(X2,X2),X3),X2) ),
c_0_2242,
[final] ).
cnf(c_0_2853,plain,
( c_in(X4,X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
c_0_2243,
[final] ).
cnf(c_0_2854,plain,
( c_in(X4,X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
c_0_2244,
[final] ).
cnf(c_0_2855,plain,
( c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool)) ),
c_0_2245,
[final] ).
cnf(c_0_2856,plain,
( c_in(X4,X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
c_0_2246,
[final] ).
cnf(c_0_2857,plain,
c_Relation_Orefl__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
c_0_2247,
[final] ).
cnf(c_0_2858,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_2248,
[final] ).
cnf(c_0_2859,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_2249,
[final] ).
cnf(c_0_2860,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_2250,
[final] ).
cnf(c_0_2861,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_2251,
[final] ).
cnf(c_0_2862,plain,
c_Relation_OImage(c_Relation_OId(X1),X2,X1,X1) = X2,
c_0_2252,
[final] ).
cnf(c_0_2863,plain,
c_Transitive__Closure_Otrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),
c_0_2253,
[final] ).
cnf(c_0_2864,plain,
( c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
c_0_2254,
[final] ).
cnf(c_0_2865,plain,
( c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
c_0_2255,
[final] ).
cnf(c_0_2866,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
c_0_2256,
[final] ).
cnf(c_0_2867,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X1,tc_fun(X3,tc_bool)) ),
c_0_2257,
[final] ).
cnf(c_0_2868,plain,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
c_0_2258,
[final] ).
cnf(c_0_2869,plain,
( c_in(v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(X1,X2),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_Arrow__Order__Mirabelle_Odictator(X1,X2) ),
c_0_2259,
[final] ).
cnf(c_0_2870,plain,
( c_Wellfounded_Oacyclic(X3,X2)
| ~ c_Wellfounded_Oacyclic(X1,X2)
| ~ c_lessequals(X3,X1,tc_fun(tc_prod(X2,X2),tc_bool)) ),
c_0_2260,
[final] ).
cnf(c_0_2871,plain,
( c_Relation_Oantisym(X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Relation_Oantisym(X2,X3) ),
c_0_2261,
[final] ).
cnf(c_0_2872,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_2262,
[final] ).
cnf(c_0_2873,plain,
( c_lessequals(hAPP(X1,X5),hAPP(X2,X5),X4)
| ~ c_lessequals(X1,X2,tc_fun(X3,X4))
| ~ class_HOL_Oord(X4) ),
c_0_2263,
[final] ).
cnf(c_0_2874,plain,
c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_bool)),X1,X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
c_0_2264,
[final] ).
cnf(c_0_2875,plain,
c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_bool)),X1,X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
c_0_2265,
[final] ).
cnf(c_0_2876,plain,
( c_lessequals(X1,X4,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X4,X3)
| ~ class_Orderings_Opreorder(X3) ),
c_0_2266,
[final] ).
cnf(c_0_2877,plain,
( c_lessequals(X4,X2,X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X4,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_2267,
[final] ).
cnf(c_0_2878,plain,
( c_in(X1,c_Transitive__Closure_Otrancl(X2,X3),tc_prod(X3,X3))
| ~ c_in(X1,X2,tc_prod(X3,X3)) ),
c_0_2268,
[final] ).
cnf(c_0_2879,plain,
( c_in(X1,c_Transitive__Closure_Ortrancl(X2,X3),tc_prod(X3,X3))
| ~ c_in(X1,X2,tc_prod(X3,X3)) ),
c_0_2269,
[final] ).
cnf(c_0_2880,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
c_0_2270,
[final] ).
cnf(c_0_2881,plain,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),
c_0_2271,
[final] ).
cnf(c_0_2882,plain,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
c_0_2272,
[final] ).
cnf(c_0_2883,plain,
c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
c_0_2273,
[final] ).
cnf(c_0_2884,plain,
c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
c_0_2274,
[final] ).
cnf(c_0_2885,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_2275,
[final] ).
cnf(c_0_2886,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_2276,
[final] ).
cnf(c_0_2887,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_2277,
[final] ).
cnf(c_0_2888,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_2278,
[final] ).
cnf(c_0_2889,plain,
( c_Relation_Ototal__on(X1,hAPP(c_Relation_Oconverse(X3,X3),X2),X3)
| ~ c_Relation_Ototal__on(X1,X2,X3) ),
c_0_2279,
[final] ).
cnf(c_0_2890,plain,
( c_Relation_Orefl__on(X1,hAPP(c_Relation_Oconverse(X3,X3),X2),X3)
| ~ c_Relation_Orefl__on(X1,X2,X3) ),
c_0_2280,
[final] ).
cnf(c_0_2891,plain,
c_Set_Oinsert(X1,c_Set_Oinsert(X1,X2,X3),X3) = c_Set_Oinsert(X1,X2,X3),
c_0_2281,
[final] ).
cnf(c_0_2892,plain,
( ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| ~ hBOOL(hAPP(X3,X1)) ),
c_0_2282,
[final] ).
cnf(c_0_2893,plain,
( c_in(v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2(X1),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_Arrow__Order__Mirabelle_Ounanimity(X1) ),
c_0_2283,
[final] ).
cnf(c_0_2894,plain,
( c_in(v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X1),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
c_0_2284,
[final] ).
cnf(c_0_2895,plain,
( c_in(v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X1),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
c_0_2285,
[final] ).
cnf(c_0_2896,plain,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
c_0_2286,
[final] ).
cnf(c_0_2897,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool))
| c_Relation_ORange(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_2287,
[final] ).
cnf(c_0_2898,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool))
| c_Relation_ODomain(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
c_0_2288,
[final] ).
cnf(c_0_2899,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
c_0_2289,
[final] ).
cnf(c_0_2900,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_2290,
[final] ).
cnf(c_0_2901,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_2291,
[final] ).
cnf(c_0_2902,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_2292,
[final] ).
cnf(c_0_2903,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_2293,
[final] ).
cnf(c_0_2904,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_2294,
[final] ).
cnf(c_0_2905,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(X1,X2))
| ~ c_lessequals(X1,X3,tc_fun(X4,tc_bool)) ),
c_0_2295,
[final] ).
cnf(c_0_2906,plain,
( hBOOL(hAPP(X2,X4))
| ~ c_lessequals(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(X1,X4)) ),
c_0_2296,
[final] ).
cnf(c_0_2907,plain,
c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
c_0_2297,
[final] ).
cnf(c_0_2908,plain,
c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
c_0_2298,
[final] ).
cnf(c_0_2909,plain,
( hBOOL(hAPP(X3,X1))
| ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
c_0_2299,
[final] ).
cnf(c_0_2910,plain,
c_Relation_OField(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
c_0_2300,
[final] ).
cnf(c_0_2911,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
c_0_2301,
[final] ).
cnf(c_0_2912,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
c_0_2302,
[final] ).
cnf(c_0_2913,plain,
c_Relation_ODomain(hAPP(c_Relation_Oconverse(X2,X3),X1),X3,X2) = c_Relation_ORange(X1,X2,X3),
c_0_2303,
[final] ).
cnf(c_0_2914,plain,
c_Relation_ODomain(hAPP(c_Relation_Oconverse(X1,X2),X3),X2,X1) = c_Relation_ORange(X3,X1,X2),
c_0_2304,
[final] ).
cnf(c_0_2915,plain,
c_Relation_ORange(hAPP(c_Relation_Oconverse(X1,X2),X3),X2,X1) = c_Relation_ODomain(X3,X1,X2),
c_0_2305,
[final] ).
cnf(c_0_2916,plain,
c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
c_0_2306,
[final] ).
cnf(c_0_2917,plain,
( c_in(X1,X2,X3)
| c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
c_0_2307,
[final] ).
cnf(c_0_2918,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_2308,
[final] ).
cnf(c_0_2919,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_2309,
[final] ).
cnf(c_0_2920,plain,
( X2 = X1
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_2310,
[final] ).
cnf(c_0_2921,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_2311,
[final] ).
cnf(c_0_2922,plain,
( X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3) ),
c_0_2312,
[final] ).
cnf(c_0_2923,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
c_0_2313,
[final] ).
cnf(c_0_2924,plain,
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),
c_0_2314,
[final] ).
cnf(c_0_2925,plain,
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),
c_0_2315,
[final] ).
cnf(c_0_2926,plain,
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),
c_0_2316,
[final] ).
cnf(c_0_2927,plain,
c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1) = c_Relation_OId(X1),
c_0_2317,
[final] ).
cnf(c_0_2928,plain,
c_Relation_Oantisym(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
c_0_2318,
[final] ).
cnf(c_0_2929,plain,
c_Wellfounded_Owf(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
c_0_2319,
[final] ).
cnf(c_0_2930,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_2320,
[final] ).
cnf(c_0_2931,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_2321,
[final] ).
cnf(c_0_2932,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X1,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_2322,
[final] ).
cnf(c_0_2933,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_2323,
[final] ).
cnf(c_0_2934,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X2,X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_2324,
[final] ).
cnf(c_0_2935,plain,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3),X1,X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_2325,
[final] ).
cnf(c_0_2936,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_2326,
[final] ).
cnf(c_0_2937,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X3)
| ~ class_Lattices_Olattice(X3) ),
c_0_2327,
[final] ).
cnf(c_0_2938,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_2328,
[final] ).
cnf(c_0_2939,plain,
( c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3),X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_2329,
[final] ).
cnf(c_0_2940,plain,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
c_0_2330,
[final] ).
cnf(c_0_2941,plain,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
c_0_2331,
[final] ).
cnf(c_0_2942,plain,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
c_0_2332,
[final] ).
cnf(c_0_2943,plain,
c_Relation_ODomain(hAPP(c_Relation_Oconverse(t_a,t_b),v_r),t_b,t_a) = c_Relation_ORange(v_r,t_a,t_b),
c_0_2333,
[final] ).
cnf(c_0_2944,plain,
c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
c_0_2334,
[final] ).
cnf(c_0_2945,plain,
c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
c_0_2335,
[final] ).
cnf(c_0_2946,plain,
c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
c_0_2336,
[final] ).
cnf(c_0_2947,plain,
( c_Relation_Oantisym(X2,X1)
| ~ c_Relation_Oantisym(hAPP(c_Relation_Oconverse(X1,X1),X2),X1) ),
c_0_2337,
[final] ).
cnf(c_0_2948,plain,
( c_Relation_Osym(X2,X1)
| ~ c_Relation_Osym(hAPP(c_Relation_Oconverse(X1,X1),X2),X1) ),
c_0_2338,
[final] ).
cnf(c_0_2949,plain,
( c_Wellfounded_Oacyclic(X2,X1)
| ~ c_Wellfounded_Oacyclic(hAPP(c_Relation_Oconverse(X1,X1),X2),X1) ),
c_0_2339,
[final] ).
cnf(c_0_2950,plain,
c_Transitive__Closure_Ortrancl(hAPP(c_Relation_Oconverse(X1,X1),X2),X1) = hAPP(c_Relation_Oconverse(X1,X1),c_Transitive__Closure_Ortrancl(X2,X1)),
c_0_2340,
[final] ).
cnf(c_0_2951,plain,
c_Transitive__Closure_Otrancl(hAPP(c_Relation_Oconverse(X1,X1),X2),X1) = hAPP(c_Relation_Oconverse(X1,X1),c_Transitive__Closure_Otrancl(X2,X1)),
c_0_2341,
[final] ).
cnf(c_0_2952,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
c_0_2342,
[final] ).
cnf(c_0_2953,plain,
c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
c_0_2343,
[final] ).
cnf(c_0_2954,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),
c_0_2344,
[final] ).
cnf(c_0_2955,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)),
c_0_2345,
[final] ).
cnf(c_0_2956,plain,
( c_lessequals(X1,X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) != X1
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_2346,
[final] ).
cnf(c_0_2957,plain,
( c_lessequals(X1,X2,X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) != X2
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_2347,
[final] ).
cnf(c_0_2958,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X3) = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_2348,
[final] ).
cnf(c_0_2959,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X3) = X1
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Olower__semilattice(X3) ),
c_0_2349,
[final] ).
cnf(c_0_2960,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X3) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_2350,
[final] ).
cnf(c_0_2961,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X3) = X2
| ~ c_lessequals(X1,X2,X3)
| ~ class_Lattices_Oupper__semilattice(X3) ),
c_0_2351,
[final] ).
cnf(c_0_2962,plain,
c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)) = c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
c_0_2352,
[final] ).
cnf(c_0_2963,plain,
( c_Set_Oinsert(X1,X2,X3) = X2
| ~ c_in(X1,X2,X3) ),
c_0_2353,
[final] ).
cnf(c_0_2964,plain,
( c_Relation_Orefl__on(X1,X2,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
c_0_2354,
[final] ).
cnf(c_0_2965,plain,
( c_Arrow__Order__Mirabelle_Odictator(X1,X2)
| hAPP(X1,v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(X1,X2)) != hAPP(v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(X1,X2),X2) ),
c_0_2355,
[final] ).
cnf(c_0_2966,plain,
c_Relation_ORange(c_Transitive__Closure_Otrancl(X1,X2),X2,X2) = c_Relation_ORange(X1,X2,X2),
c_0_2356,
[final] ).
cnf(c_0_2967,plain,
c_Relation_ODomain(c_Transitive__Closure_Otrancl(X1,X2),X2,X2) = c_Relation_ODomain(X1,X2,X2),
c_0_2357,
[final] ).
cnf(c_0_2968,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
c_0_2358,
[final] ).
cnf(c_0_2969,plain,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = X2,
c_0_2359,
[final] ).
cnf(c_0_2970,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
c_0_2360,
[final] ).
cnf(c_0_2971,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oinsert(X2,X3,X1),
c_0_2361,
[final] ).
cnf(c_0_2972,plain,
c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
c_0_2362,
[final] ).
cnf(c_0_2973,plain,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
c_0_2363,
[final] ).
cnf(c_0_2974,plain,
hAPP(c_Relation_Oconverse(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3)) = X3,
c_0_2364,
[final] ).
cnf(c_0_2975,plain,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
c_0_2365,
[final] ).
cnf(c_0_2976,plain,
( hBOOL(hAPP(X2,X1))
| ~ c_in(X1,X2,X3) ),
c_0_2366,
[final] ).
cnf(c_0_2977,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_2367,
[final] ).
cnf(c_0_2978,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_2368,
[final] ).
cnf(c_0_2979,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_2369,
[final] ).
cnf(c_0_2980,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_2370,
[final] ).
cnf(c_0_2981,plain,
( c_Relation_Oantisym(hAPP(c_Relation_Oconverse(X2,X2),X1),X2)
| ~ c_Relation_Oantisym(X1,X2) ),
c_0_2371,
[final] ).
cnf(c_0_2982,plain,
( c_Relation_Osym(hAPP(c_Relation_Oconverse(X2,X2),X1),X2)
| ~ c_Relation_Osym(X1,X2) ),
c_0_2372,
[final] ).
cnf(c_0_2983,plain,
( c_Wellfounded_Oacyclic(hAPP(c_Relation_Oconverse(X2,X2),X1),X2)
| ~ c_Wellfounded_Oacyclic(X1,X2) ),
c_0_2373,
[final] ).
cnf(c_0_2984,plain,
c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1),
c_0_2374,
[final] ).
cnf(c_0_2985,plain,
c_Relation_OField(hAPP(c_Relation_Oconverse(X1,X1),X2),X1) = c_Relation_OField(X2,X1),
c_0_2375,
[final] ).
cnf(c_0_2986,plain,
( X1 = c_Orderings_Obot__class_Obot(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
c_0_2376,
[final] ).
cnf(c_0_2987,plain,
( X1 = c_Orderings_Obot__class_Obot(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
c_0_2377,
[final] ).
cnf(c_0_2988,plain,
( c_in(X3,c_Wellfounded_Oacc(X1,X2),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
c_0_2378,
[final] ).
cnf(c_0_2989,plain,
( c_in(X2,X1,X3)
| ~ hBOOL(hAPP(X1,X2)) ),
c_0_2379,
[final] ).
cnf(c_0_2990,plain,
( c_Relation_Osym(X2,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
c_0_2380,
[final] ).
cnf(c_0_2991,plain,
( X1 = X2
| ~ c_fequal(X1,X2,X3) ),
c_0_2381,
[final] ).
cnf(c_0_2992,plain,
c_Relation_ORange(c_Relation_OId__on(X1,X2),X2,X2) = X1,
c_0_2382,
[final] ).
cnf(c_0_2993,plain,
c_Relation_ODomain(c_Relation_OId__on(X1,X2),X2,X2) = X1,
c_0_2383,
[final] ).
cnf(c_0_2994,plain,
c_Relation_Orefl__on(X1,c_Relation_OId__on(X1,X2),X2),
c_0_2384,
[final] ).
cnf(c_0_2995,plain,
c_Relation_Osingle__valued(c_Relation_OId__on(X1,X2),X2,X2),
c_0_2385,
[final] ).
cnf(c_0_2996,plain,
hAPP(c_Relation_Oconverse(X1,X1),c_Relation_OId__on(X2,X1)) = c_Relation_OId__on(X2,X1),
c_0_2386,
[final] ).
cnf(c_0_2997,plain,
( c_Relation_Osym(X1,X2)
| hAPP(c_Relation_Oconverse(X2,X2),X1) != X1 ),
c_0_2387,
[final] ).
cnf(c_0_2998,plain,
c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_fun(X2,tc_bool)) = X1,
c_0_2388,
[final] ).
cnf(c_0_2999,plain,
c_Lattices_Oupper__semilattice__class_Osup(X1,X1,tc_fun(X2,tc_bool)) = X1,
c_0_2389,
[final] ).
cnf(c_0_3000,plain,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
c_0_2390,
[final] ).
cnf(c_0_3001,plain,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
c_0_2391,
[final] ).
cnf(c_0_3002,plain,
( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X1),X2,X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
c_0_2392,
[final] ).
cnf(c_0_3003,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(X2),X2) = c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
c_0_2393,
[final] ).
cnf(c_0_3004,plain,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X1),X2,X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
c_0_2394,
[final] ).
cnf(c_0_3005,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(X2),X2) = X1
| ~ class_Lattices_Obounded__lattice(X2) ),
c_0_2395,
[final] ).
cnf(c_0_3006,plain,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
c_0_2396,
[final] ).
cnf(c_0_3007,plain,
( hAPP(c_Relation_Oconverse(X2,X2),X1) = X1
| ~ c_Relation_Osym(X1,X2) ),
c_0_2397,
[final] ).
cnf(c_0_3008,plain,
( c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X1,X2),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
c_0_2398,
[final] ).
cnf(c_0_3009,plain,
( c_Relation_Osym(c_Transitive__Closure_Ortrancl(X1,X2),X2)
| ~ c_Relation_Osym(X1,X2) ),
c_0_2399,
[final] ).
cnf(c_0_3010,plain,
( c_Relation_Osym(c_Transitive__Closure_Otrancl(X1,X2),X2)
| ~ c_Relation_Osym(X1,X2) ),
c_0_2400,
[final] ).
cnf(c_0_3011,plain,
( c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X1,X2),X2)
| ~ c_Wellfounded_Oacyclic(X1,X2) ),
c_0_2401,
[final] ).
cnf(c_0_3012,plain,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X1,X2) = X1
| ~ class_Lattices_Olower__semilattice(X2) ),
c_0_2402,
[final] ).
cnf(c_0_3013,plain,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X2) = X1
| ~ class_Lattices_Oupper__semilattice(X2) ),
c_0_2403,
[final] ).
cnf(c_0_3014,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
c_0_2404,
[final] ).
cnf(c_0_3015,plain,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
c_0_2405,
[final] ).
cnf(c_0_3016,plain,
c_Relation_Osingle__valued(c_Relation_OId(X1),X1,X1),
c_0_2406,
[final] ).
cnf(c_0_3017,plain,
c_fequal(X1,X1,X2),
c_0_2407,
[final] ).
cnf(c_0_3018,plain,
c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
c_0_2408,
[final] ).
cnf(c_0_3019,plain,
c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X1,X2),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
c_0_2409,
[final] ).
cnf(c_0_3020,plain,
c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
c_0_2410,
[final] ).
cnf(c_0_3021,plain,
hAPP(c_Relation_Oconverse(X1,X1),c_Relation_OId(X1)) = c_Relation_OId(X1),
c_0_2411,
[final] ).
cnf(c_0_3022,plain,
c_Relation_Osym(c_Relation_OId__on(X1,X2),X2),
c_0_2412,
[final] ).
cnf(c_0_3023,plain,
c_Relation_Oantisym(c_Relation_OId__on(X1,X2),X2),
c_0_2413,
[final] ).
cnf(c_0_3024,plain,
( class_HOL_Oord(tc_fun(X2,X1))
| ~ class_HOL_Oord(X1) ),
c_0_2414,
[final] ).
cnf(c_0_3025,plain,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
c_0_2415,
[final] ).
cnf(c_0_3026,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
c_0_2416,
[final] ).
cnf(c_0_3027,plain,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
c_0_2417,
[final] ).
cnf(c_0_3028,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
c_0_2418,
[final] ).
cnf(c_0_3029,plain,
( class_Lattices_Obounded__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
c_0_2419,
[final] ).
cnf(c_0_3030,plain,
( class_Lattices_Odistrib__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
c_0_2420,
[final] ).
cnf(c_0_3031,plain,
( class_Lattices_Olower__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
c_0_2421,
[final] ).
cnf(c_0_3032,plain,
( class_Lattices_Oupper__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
c_0_2422,
[final] ).
cnf(c_0_3033,plain,
( c_Wellfounded_Oacyclic(X1,X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
c_0_2423,
[final] ).
cnf(c_0_3034,plain,
c_Relation_Oantisym(c_Relation_OId(X1),X1),
c_0_2424,
[final] ).
cnf(c_0_3035,plain,
c_Relation_Osym(c_Relation_OId(X1),X1),
c_0_2425,
[final] ).
cnf(c_0_3036,plain,
class_HOL_Oord(tc_bool),
c_0_2426,
[final] ).
cnf(c_0_3037,plain,
class_Orderings_Obot(tc_bool),
c_0_2427,
[final] ).
cnf(c_0_3038,plain,
class_Orderings_Oorder(tc_bool),
c_0_2428,
[final] ).
cnf(c_0_3039,plain,
class_Lattices_Olattice(tc_bool),
c_0_2429,
[final] ).
cnf(c_0_3040,plain,
class_Orderings_Opreorder(tc_bool),
c_0_2430,
[final] ).
cnf(c_0_3041,plain,
class_Lattices_Obounded__lattice(tc_bool),
c_0_2431,
[final] ).
cnf(c_0_3042,plain,
class_Lattices_Odistrib__lattice(tc_bool),
c_0_2432,
[final] ).
cnf(c_0_3043,plain,
class_Lattices_Olower__semilattice(tc_bool),
c_0_2433,
[final] ).
cnf(c_0_3044,plain,
class_Lattices_Oupper__semilattice(tc_bool),
c_0_2434,
[final] ).
cnf(c_0_3045,plain,
c_Arrow__Order__Mirabelle_OIIA(v_F),
c_0_2435,
[final] ).
cnf(c_0_3046,plain,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
c_0_2436,
[final] ).
cnf(c_0_3047,plain,
v_c____ != v_a____,
c_0_2437,
[final] ).
cnf(c_0_3048,plain,
v_c____ != v_b____,
c_0_2438,
[final] ).
cnf(c_0_3049,plain,
v_b____ != v_a____,
c_0_2439,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_2440_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_2440]) ).
cnf(c_0_2440_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_2440]) ).
cnf(c_0_2441_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_2441]) ).
cnf(c_0_2441_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_2441]) ).
cnf(c_0_2442_0,axiom,
( X1 = X2
| X3 = X4
| X1 = X4
| X2 = X3
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X5,v_sko__local__X1__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X1__1(X5,X6,X1,X3,X2,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2442]) ).
cnf(c_0_2442_1,axiom,
( X3 = X4
| X1 = X2
| X1 = X4
| X2 = X3
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X5,v_sko__local__X1__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X1__1(X5,X6,X1,X3,X2,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2442]) ).
cnf(c_0_2442_2,axiom,
( X1 = X4
| X3 = X4
| X1 = X2
| X2 = X3
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X5,v_sko__local__X1__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X1__1(X5,X6,X1,X3,X2,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2442]) ).
cnf(c_0_2442_3,axiom,
( X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X5,v_sko__local__X1__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X1__1(X5,X6,X1,X3,X2,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2442]) ).
cnf(c_0_2442_4,axiom,
( c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X5,v_sko__local__X1__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X1__1(X5,X6,X1,X3,X2,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2442]) ).
cnf(c_0_2442_5,axiom,
( ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X5,v_sko__local__X1__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X1__1(X5,X6,X1,X3,X2,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2442]) ).
cnf(c_0_2442_6,axiom,
( ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__local__X1__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X1__1(X5,X6,X1,X3,X2,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2442]) ).
cnf(c_0_2442_7,axiom,
( ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__local__X1__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X1__1(X5,X6,X1,X3,X2,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2442]) ).
cnf(c_0_2442_8,axiom,
( ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X1__1(X5,X6,X1,X3,X2,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),hAPP(X5,v_sko__local__X1__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2442]) ).
cnf(c_0_2442_9,axiom,
( ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X1__1(X5,X6,X1,X3,X2,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),hAPP(X5,v_sko__local__X1__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2442]) ).
cnf(c_0_2443_0,axiom,
( X1 = X2
| X3 = X4
| X1 = X4
| X2 = X3
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2443]) ).
cnf(c_0_2443_1,axiom,
( X3 = X4
| X1 = X2
| X1 = X4
| X2 = X3
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2443]) ).
cnf(c_0_2443_2,axiom,
( X1 = X4
| X3 = X4
| X1 = X2
| X2 = X3
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2443]) ).
cnf(c_0_2443_3,axiom,
( X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2443]) ).
cnf(c_0_2443_4,axiom,
( c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2443]) ).
cnf(c_0_2443_5,axiom,
( ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2443]) ).
cnf(c_0_2443_6,axiom,
( ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2443]) ).
cnf(c_0_2443_7,axiom,
( ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2443]) ).
cnf(c_0_2443_8,axiom,
( ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,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),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2443]) ).
cnf(c_0_2443_9,axiom,
( ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,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),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2443]) ).
cnf(c_0_2444_0,axiom,
( X1 = X2
| X3 = X4
| X1 = X4
| X2 = X3
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2444]) ).
cnf(c_0_2444_1,axiom,
( X3 = X4
| X1 = X2
| X1 = X4
| X2 = X3
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2444]) ).
cnf(c_0_2444_2,axiom,
( X1 = X4
| X3 = X4
| X1 = X2
| X2 = X3
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2444]) ).
cnf(c_0_2444_3,axiom,
( X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2444]) ).
cnf(c_0_2444_4,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2444]) ).
cnf(c_0_2444_5,axiom,
( ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2444]) ).
cnf(c_0_2444_6,axiom,
( ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2444]) ).
cnf(c_0_2444_7,axiom,
( ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2444]) ).
cnf(c_0_2444_8,axiom,
( ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,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),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2444]) ).
cnf(c_0_2444_9,axiom,
( ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,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),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2444]) ).
cnf(c_0_2445_0,axiom,
( X1 = X2
| X3 = X4
| X1 = X4
| X2 = X3
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__local__X1__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X1__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2445]) ).
cnf(c_0_2445_1,axiom,
( X3 = X4
| X1 = X2
| X1 = X4
| X2 = X3
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__local__X1__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X1__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2445]) ).
cnf(c_0_2445_2,axiom,
( X1 = X4
| X3 = X4
| X1 = X2
| X2 = X3
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__local__X1__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X1__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2445]) ).
cnf(c_0_2445_3,axiom,
( X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__local__X1__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X1__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2445]) ).
cnf(c_0_2445_4,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__local__X1__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X1__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2445]) ).
cnf(c_0_2445_5,axiom,
( c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X1__1(X5,X6,X1,X3,X2,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),hAPP(X5,v_sko__local__X1__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2445]) ).
cnf(c_0_2445_6,axiom,
( c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X1__1(X5,X6,X1,X3,X2,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),hAPP(X5,v_sko__local__X1__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2445]) ).
cnf(c_0_2445_7,axiom,
( ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X1__1(X5,X6,X1,X3,X2,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),hAPP(X5,v_sko__local__X1__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2445]) ).
cnf(c_0_2445_8,axiom,
( ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X1__1(X5,X6,X1,X3,X2,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),hAPP(X5,v_sko__local__X1__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2445]) ).
cnf(c_0_2445_9,axiom,
( ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X1__1(X5,X6,X1,X3,X2,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),hAPP(X5,v_sko__local__X1__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2445]) ).
cnf(c_0_2446_0,axiom,
( X1 = X2
| X3 = X4
| X1 = X4
| X2 = X3
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2446]) ).
cnf(c_0_2446_1,axiom,
( X3 = X4
| X1 = X2
| X1 = X4
| X2 = X3
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2446]) ).
cnf(c_0_2446_2,axiom,
( X1 = X4
| X3 = X4
| X1 = X2
| X2 = X3
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2446]) ).
cnf(c_0_2446_3,axiom,
( X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2446]) ).
cnf(c_0_2446_4,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2446]) ).
cnf(c_0_2446_5,axiom,
( c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,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),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2446]) ).
cnf(c_0_2446_6,axiom,
( c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,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),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2446]) ).
cnf(c_0_2446_7,axiom,
( ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,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),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2446]) ).
cnf(c_0_2446_8,axiom,
( ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,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),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2446]) ).
cnf(c_0_2446_9,axiom,
( ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,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),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2446]) ).
cnf(c_0_2447_0,axiom,
( X1 = X2
| X3 = X4
| X1 = X4
| X2 = X3
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2447]) ).
cnf(c_0_2447_1,axiom,
( X3 = X4
| X1 = X2
| X1 = X4
| X2 = X3
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2447]) ).
cnf(c_0_2447_2,axiom,
( X1 = X4
| X3 = X4
| X1 = X2
| X2 = X3
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2447]) ).
cnf(c_0_2447_3,axiom,
( X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2447]) ).
cnf(c_0_2447_4,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2447]) ).
cnf(c_0_2447_5,axiom,
( c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,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),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2447]) ).
cnf(c_0_2447_6,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,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),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2447]) ).
cnf(c_0_2447_7,axiom,
( ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,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),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2447]) ).
cnf(c_0_2447_8,axiom,
( ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,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),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2447]) ).
cnf(c_0_2447_9,axiom,
( ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X6),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X5,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X5),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X6,v_sko__local__X2__1(X5,X6,X1,X3,X2,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),hAPP(X5,v_sko__local__X2__1(X5,X6,X1,X3,X2,X4)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X2 = X3
| X1 = X4
| X3 = X4
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2447]) ).
cnf(c_0_2448_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_2448]) ).
cnf(c_0_2448_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_2448]) ).
cnf(c_0_2449_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_2449]) ).
cnf(c_0_2449_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_2449]) ).
cnf(c_0_2450_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_2450]) ).
cnf(c_0_2450_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_2450]) ).
cnf(c_0_2451_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_2451]) ).
cnf(c_0_2451_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_2451]) ).
cnf(c_0_2452_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_2452]) ).
cnf(c_0_2452_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_2452]) ).
cnf(c_0_2453_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_2453]) ).
cnf(c_0_2453_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_2453]) ).
cnf(c_0_2454_0,axiom,
( hAPP(hAPP(X3,X7),X9) = hAPP(hAPP(X3,X8),X10)
| ~ c_Equiv__Relations_Ocongruent2(X1,X2,X3,X4,X5,X6)
| ~ c_in(c_Pair(X7,X8,X4,X4),X1,tc_prod(X4,X4))
| ~ c_in(c_Pair(X9,X10,X5,X5),X2,tc_prod(X5,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2454]) ).
cnf(c_0_2454_1,axiom,
( ~ c_Equiv__Relations_Ocongruent2(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X3,X7),X9) = hAPP(hAPP(X3,X8),X10)
| ~ c_in(c_Pair(X7,X8,X4,X4),X1,tc_prod(X4,X4))
| ~ c_in(c_Pair(X9,X10,X5,X5),X2,tc_prod(X5,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2454]) ).
cnf(c_0_2454_2,axiom,
( ~ c_in(c_Pair(X7,X8,X4,X4),X1,tc_prod(X4,X4))
| ~ c_Equiv__Relations_Ocongruent2(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X3,X7),X9) = hAPP(hAPP(X3,X8),X10)
| ~ c_in(c_Pair(X9,X10,X5,X5),X2,tc_prod(X5,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2454]) ).
cnf(c_0_2454_3,axiom,
( ~ c_in(c_Pair(X9,X10,X5,X5),X2,tc_prod(X5,X5))
| ~ c_in(c_Pair(X7,X8,X4,X4),X1,tc_prod(X4,X4))
| ~ c_Equiv__Relations_Ocongruent2(X1,X2,X3,X4,X5,X6)
| hAPP(hAPP(X3,X7),X9) = hAPP(hAPP(X3,X8),X10) ),
inference(literals_permutation,[status(thm)],[c_0_2454]) ).
cnf(c_0_2455_0,axiom,
( c_Equiv__Relations_Ocongruent(X4,hAPP(X5,X8),X6,X7)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_Equiv__Relations_Ocongruent2(X2,X4,X5,X3,X6,X7)
| ~ c_in(X8,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2455]) ).
cnf(c_0_2455_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Equiv__Relations_Ocongruent(X4,hAPP(X5,X8),X6,X7)
| ~ c_Equiv__Relations_Ocongruent2(X2,X4,X5,X3,X6,X7)
| ~ c_in(X8,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2455]) ).
cnf(c_0_2455_2,axiom,
( ~ c_Equiv__Relations_Ocongruent2(X2,X4,X5,X3,X6,X7)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Equiv__Relations_Ocongruent(X4,hAPP(X5,X8),X6,X7)
| ~ c_in(X8,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2455]) ).
cnf(c_0_2455_3,axiom,
( ~ c_in(X8,X1,X3)
| ~ c_Equiv__Relations_Ocongruent2(X2,X4,X5,X3,X6,X7)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Equiv__Relations_Ocongruent(X4,hAPP(X5,X8),X6,X7) ),
inference(literals_permutation,[status(thm)],[c_0_2455]) ).
cnf(c_0_2458_0,axiom,
( c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2458]) ).
cnf(c_0_2458_1,axiom,
( ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2458]) ).
cnf(c_0_2458_2,axiom,
( ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2458]) ).
cnf(c_0_2458_3,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,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),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2458]) ).
cnf(c_0_2458_4,axiom,
( ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,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),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2458]) ).
cnf(c_0_2458_5,axiom,
( ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,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),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2458]) ).
cnf(c_0_2458_6,axiom,
( ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,X2),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),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2458]) ).
cnf(c_0_2459_0,axiom,
( c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X1,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2459]) ).
cnf(c_0_2459_1,axiom,
( ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X1,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2459]) ).
cnf(c_0_2459_2,axiom,
( ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X1,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2459]) ).
cnf(c_0_2459_3,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,X2),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),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X1,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2459]) ).
cnf(c_0_2459_4,axiom,
( ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,X2),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),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X1,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2459]) ).
cnf(c_0_2459_5,axiom,
( ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,X2),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),hAPP(X1,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2459]) ).
cnf(c_0_2459_6,axiom,
( ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,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),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2459]) ).
cnf(c_0_2460_0,axiom,
( X1 = X2
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,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),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2460]) ).
cnf(c_0_2460_1,axiom,
( c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,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),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2460]) ).
cnf(c_0_2460_2,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,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),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2460]) ).
cnf(c_0_2460_3,axiom,
( ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,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),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,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),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2460]) ).
cnf(c_0_2460_4,axiom,
( ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,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),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2460]) ).
cnf(c_0_2460_5,axiom,
( ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,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),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,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),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2460]) ).
cnf(c_0_2460_6,axiom,
( ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,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),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2460]) ).
cnf(c_0_2461_0,axiom,
( X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2461]) ).
cnf(c_0_2461_1,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2461]) ).
cnf(c_0_2461_2,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2461]) ).
cnf(c_0_2461_3,axiom,
( ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X3),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),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2461]) ).
cnf(c_0_2461_4,axiom,
( ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2461]) ).
cnf(c_0_2461_5,axiom,
( ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,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),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2461]) ).
cnf(c_0_2461_6,axiom,
( ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,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),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2461]) ).
cnf(c_0_2462_0,axiom,
( c_in(c_Pair(X5,X6,X3,X3),X2,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(X4,c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X2,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2462]) ).
cnf(c_0_2462_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_in(c_Pair(X5,X6,X3,X3),X2,tc_prod(X3,X3))
| ~ c_in(X4,c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X2,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2462]) ).
cnf(c_0_2462_2,axiom,
( ~ c_in(X4,c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X2,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool)),X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_in(c_Pair(X5,X6,X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2462]) ).
cnf(c_0_2465_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_2465]) ).
cnf(c_0_2465_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_2465]) ).
cnf(c_0_2465_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_2465]) ).
cnf(c_0_2466_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_2466]) ).
cnf(c_0_2466_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_2466]) ).
cnf(c_0_2467_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_2467]) ).
cnf(c_0_2467_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_2467]) ).
cnf(c_0_2469_0,axiom,
( c_Relation_Orel__comp(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(tc_prod(X4,X4),tc_bool)),X4,X4,X4) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool))
| c_Relation_Orel__comp(X1,X2,X4,X4,X4) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool))
| c_Relation_Orel__comp(X1,X3,X4,X4,X4) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2469]) ).
cnf(c_0_2469_1,axiom,
( c_Relation_Orel__comp(X1,X2,X4,X4,X4) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool))
| c_Relation_Orel__comp(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(tc_prod(X4,X4),tc_bool)),X4,X4,X4) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool))
| c_Relation_Orel__comp(X1,X3,X4,X4,X4) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2469]) ).
cnf(c_0_2469_2,axiom,
( c_Relation_Orel__comp(X1,X3,X4,X4,X4) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool))
| c_Relation_Orel__comp(X1,X2,X4,X4,X4) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool))
| c_Relation_Orel__comp(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(tc_prod(X4,X4),tc_bool)),X4,X4,X4) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2469]) ).
cnf(c_0_2470_0,axiom,
( c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X4,X3,X3,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool))
| c_Relation_Orel__comp(X1,X4,X3,X3,X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool))
| c_Relation_Orel__comp(X2,X4,X3,X3,X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2470]) ).
cnf(c_0_2470_1,axiom,
( c_Relation_Orel__comp(X1,X4,X3,X3,X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool))
| c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X4,X3,X3,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool))
| c_Relation_Orel__comp(X2,X4,X3,X3,X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2470]) ).
cnf(c_0_2470_2,axiom,
( c_Relation_Orel__comp(X2,X4,X3,X3,X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool))
| c_Relation_Orel__comp(X1,X4,X3,X3,X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool))
| c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X4,X3,X3,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2470]) ).
cnf(c_0_2471_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_2471]) ).
cnf(c_0_2471_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_2471]) ).
cnf(c_0_2471_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_2471]) ).
cnf(c_0_2472_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_2472]) ).
cnf(c_0_2472_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_2472]) ).
cnf(c_0_2472_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_2472]) ).
cnf(c_0_2473_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_2473]) ).
cnf(c_0_2473_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_2473]) ).
cnf(c_0_2473_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_2473]) ).
cnf(c_0_2474_0,axiom,
( c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X1,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2474]) ).
cnf(c_0_2474_1,axiom,
( c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X1,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2474]) ).
cnf(c_0_2474_2,axiom,
( c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,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),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2474]) ).
cnf(c_0_2474_3,axiom,
( ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,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),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2474]) ).
cnf(c_0_2474_4,axiom,
( ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,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),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2474]) ).
cnf(c_0_2474_5,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,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),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2474]) ).
cnf(c_0_2474_6,axiom,
( ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,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),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2474]) ).
cnf(c_0_2475_0,axiom,
( c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X1,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2475]) ).
cnf(c_0_2475_1,axiom,
( c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X1,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2475]) ).
cnf(c_0_2475_2,axiom,
( c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,X2),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),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X1,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2475]) ).
cnf(c_0_2475_3,axiom,
( ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,X2),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),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X1,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2475]) ).
cnf(c_0_2475_4,axiom,
( ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,X2),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),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(X1,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2475]) ).
cnf(c_0_2475_5,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,X2),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),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X1,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2475]) ).
cnf(c_0_2475_6,axiom,
( ~ c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_in(c_Pair(X4,X5,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,X2),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),hAPP(X3,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,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),hAPP(X2,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(X4,X5,X2,X3)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2475]) ).
cnf(c_0_2476_0,axiom,
( X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2476]) ).
cnf(c_0_2476_1,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2476]) ).
cnf(c_0_2476_2,axiom,
( c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,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),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2476]) ).
cnf(c_0_2476_3,axiom,
( c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,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),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2476]) ).
cnf(c_0_2476_4,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,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),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2476]) ).
cnf(c_0_2476_5,axiom,
( ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,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),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,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),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2476]) ).
cnf(c_0_2476_6,axiom,
( ~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,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),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2476]) ).
cnf(c_0_2477_0,axiom,
( X1 = X2
| c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,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),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2477]) ).
cnf(c_0_2477_1,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,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),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2477]) ).
cnf(c_0_2477_2,axiom,
( c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,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),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,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),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2477]) ).
cnf(c_0_2477_3,axiom,
( c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,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),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2477]) ).
cnf(c_0_2477_4,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,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),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2477]) ).
cnf(c_0_2477_5,axiom,
( ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,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),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2
| ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2477]) ).
cnf(c_0_2477_6,axiom,
( ~ c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,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),hAPP(v_F,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X4,v_sko__local__X3__1(X3,X4,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),hAPP(X3,v_sko__local__X3__1(X3,X4,X1,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2477]) ).
cnf(c_0_2478_0,axiom,
( hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(c_Fun_Ocomp(X7,X8,X9,X4,X10),X11)
| hAPP(X1,hAPP(X2,X6)) != hAPP(X7,hAPP(X8,X11)) ),
inference(literals_permutation,[status(thm)],[c_0_2478]) ).
cnf(c_0_2478_1,axiom,
( hAPP(X1,hAPP(X2,X6)) != hAPP(X7,hAPP(X8,X11))
| hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(c_Fun_Ocomp(X7,X8,X9,X4,X10),X11) ),
inference(literals_permutation,[status(thm)],[c_0_2478]) ).
cnf(c_0_2479_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_2479]) ).
cnf(c_0_2479_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_2479]) ).
cnf(c_0_2479_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_2479]) ).
cnf(c_0_2480_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_2480]) ).
cnf(c_0_2480_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_2480]) ).
cnf(c_0_2480_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_2480]) ).
cnf(c_0_2481_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_2481]) ).
cnf(c_0_2481_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_2481]) ).
cnf(c_0_2481_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_2481]) ).
cnf(c_0_2481_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_2481]) ).
cnf(c_0_2482_0,axiom,
( hAPP(X1,hAPP(X2,X3)) = hAPP(X4,hAPP(X5,X3))
| c_Fun_Ocomp(X1,X2,X6,X7,X8) != c_Fun_Ocomp(X4,X5,X9,X7,X8) ),
inference(literals_permutation,[status(thm)],[c_0_2482]) ).
cnf(c_0_2482_1,axiom,
( c_Fun_Ocomp(X1,X2,X6,X7,X8) != c_Fun_Ocomp(X4,X5,X9,X7,X8)
| hAPP(X1,hAPP(X2,X3)) = hAPP(X4,hAPP(X5,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2482]) ).
cnf(c_0_2483_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_2483]) ).
cnf(c_0_2483_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_2483]) ).
cnf(c_0_2485_0,axiom,
( c_in(c_Pair(X5,X4,X3,X3),X2,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_lessequals(c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2485]) ).
cnf(c_0_2485_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_in(c_Pair(X5,X4,X3,X3),X2,tc_prod(X3,X3))
| ~ c_lessequals(c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2485]) ).
cnf(c_0_2485_2,axiom,
( ~ c_lessequals(c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_in(c_Pair(X5,X4,X3,X3),X2,tc_prod(X3,X3))
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2485]) ).
cnf(c_0_2485_3,axiom,
( ~ c_in(X4,X1,X3)
| ~ c_lessequals(c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_in(c_Pair(X5,X4,X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2485]) ).
cnf(c_0_2486_0,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X5,X1,X4,X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X5,X1,X4,X3),X3,X3),X4,tc_prod(X3,X3))
| hBOOL(hAPP(X5,X2))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ hBOOL(hAPP(X5,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2486]) ).
cnf(c_0_2486_1,axiom,
( hBOOL(hAPP(X5,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X5,X1,X4,X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X5,X1,X4,X3),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))
| ~ hBOOL(hAPP(X5,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2486]) ).
cnf(c_0_2486_2,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| hBOOL(hAPP(X5,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X5,X1,X4,X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X5,X1,X4,X3),X3,X3),X4,tc_prod(X3,X3))
| ~ hBOOL(hAPP(X5,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2486]) ).
cnf(c_0_2486_3,axiom,
( ~ hBOOL(hAPP(X5,X1))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| hBOOL(hAPP(X5,X2))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X5,X1,X4,X3),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X5,X1,X4,X3),X3,X3),X4,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2486]) ).
cnf(c_0_2487_0,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X5,X2,X4,X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X5,X2,X4,X3),X3,X3),X4,tc_prod(X3,X3))
| hBOOL(hAPP(X5,X1))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ hBOOL(hAPP(X5,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2487]) ).
cnf(c_0_2487_1,axiom,
( hBOOL(hAPP(X5,X1))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X5,X2,X4,X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X5,X2,X4,X3),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))
| ~ hBOOL(hAPP(X5,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2487]) ).
cnf(c_0_2487_2,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| hBOOL(hAPP(X5,X1))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X5,X2,X4,X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X5,X2,X4,X3),X3,X3),X4,tc_prod(X3,X3))
| ~ hBOOL(hAPP(X5,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2487]) ).
cnf(c_0_2487_3,axiom,
( ~ hBOOL(hAPP(X5,X2))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| hBOOL(hAPP(X5,X1))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X5,X2,X4,X3),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X5,X2,X4,X3),X3,X3),X4,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2487]) ).
cnf(c_0_2488_0,axiom,
( c_in(c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1(X2,X3,X1,X4,X5),X2,X4)
| ~ c_in(X1,c_Product__Type_OSigma(X2,X3,X4,X5),tc_prod(X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2488]) ).
cnf(c_0_2488_1,axiom,
( ~ c_in(X1,c_Product__Type_OSigma(X2,X3,X4,X5),tc_prod(X4,X5))
| c_in(c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1(X2,X3,X1,X4,X5),X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2488]) ).
cnf(c_0_2489_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_2489]) ).
cnf(c_0_2489_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_2489]) ).
cnf(c_0_2490_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_2490]) ).
cnf(c_0_2490_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_2490]) ).
cnf(c_0_2491_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_2491]) ).
cnf(c_0_2491_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_2491]) ).
cnf(c_0_2492_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_2492]) ).
cnf(c_0_2492_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_2492]) ).
cnf(c_0_2493_0,axiom,
( c_in(c_Pair(X4,X5,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| c_in(c_Pair(X5,X4,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| ~ c_Relation_Osingle__valued(X1,X2,X2)
| ~ c_in(c_Pair(X3,X4,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X3,X5,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2493]) ).
cnf(c_0_2493_1,axiom,
( c_in(c_Pair(X5,X4,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| c_in(c_Pair(X4,X5,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| ~ c_Relation_Osingle__valued(X1,X2,X2)
| ~ c_in(c_Pair(X3,X4,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X3,X5,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2493]) ).
cnf(c_0_2493_2,axiom,
( ~ c_Relation_Osingle__valued(X1,X2,X2)
| c_in(c_Pair(X5,X4,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| c_in(c_Pair(X4,X5,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X3,X4,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X3,X5,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2493]) ).
cnf(c_0_2493_3,axiom,
( ~ c_in(c_Pair(X3,X4,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| ~ c_Relation_Osingle__valued(X1,X2,X2)
| c_in(c_Pair(X5,X4,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| c_in(c_Pair(X4,X5,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X3,X5,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2493]) ).
cnf(c_0_2493_4,axiom,
( ~ c_in(c_Pair(X3,X5,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X3,X4,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| ~ c_Relation_Osingle__valued(X1,X2,X2)
| c_in(c_Pair(X5,X4,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| c_in(c_Pair(X4,X5,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2493]) ).
cnf(c_0_2494_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__XtranclE__1__1(X1,X2,X4,X3),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_2494]) ).
cnf(c_0_2494_1,axiom,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X1,X2,X4,X3),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_2494]) ).
cnf(c_0_2494_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__XtranclE__1__1(X1,X2,X4,X3),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_2494]) ).
cnf(c_0_2495_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_2495]) ).
cnf(c_0_2495_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_2495]) ).
cnf(c_0_2495_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_2495]) ).
cnf(c_0_2496_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_2496]) ).
cnf(c_0_2496_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_2496]) ).
cnf(c_0_2496_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_2496]) ).
cnf(c_0_2497_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__XtranclE__1__1(X1,X2,X4,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_2497]) ).
cnf(c_0_2497_1,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X1,X2,X4,X3),X2,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_2497]) ).
cnf(c_0_2497_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__XtranclE__1__1(X1,X2,X4,X3),X2,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_2497]) ).
cnf(c_0_2498_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_2498]) ).
cnf(c_0_2498_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_2498]) ).
cnf(c_0_2499_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_2499]) ).
cnf(c_0_2499_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_2499]) ).
cnf(c_0_2501_0,axiom,
( c_lessequals(c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2501]) ).
cnf(c_0_2501_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_lessequals(c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool))
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2501]) ).
cnf(c_0_2501_2,axiom,
( ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_lessequals(c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2501]) ).
cnf(c_0_2503_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_2503]) ).
cnf(c_0_2503_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_2503]) ).
cnf(c_0_2503_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_2503]) ).
cnf(c_0_2504_0,axiom,
( c_lessequals(X2,c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X3,X3),X2),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_2504]) ).
cnf(c_0_2504_1,axiom,
( ~ c_Relation_Orefl__on(X1,X2,X3)
| c_lessequals(X2,c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X3,X3),X2),X2,X3,X3,X3),tc_fun(tc_prod(X3,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2504]) ).
cnf(c_0_2505_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_2505]) ).
cnf(c_0_2505_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_2505]) ).
cnf(c_0_2506_0,axiom,
( ~ c_Wellfounded_Oacyclic(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_2506]) ).
cnf(c_0_2506_1,axiom,
( ~ c_in(c_Pair(X2,X1,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2506]) ).
cnf(c_0_2507_0,axiom,
( c_Relation_Osingle__valued(c_Relation_Orel__comp(X1,X4,X2,X3,X5),X2,X5)
| ~ c_Relation_Osingle__valued(X1,X2,X3)
| ~ c_Relation_Osingle__valued(X4,X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2507]) ).
cnf(c_0_2507_1,axiom,
( ~ c_Relation_Osingle__valued(X1,X2,X3)
| c_Relation_Osingle__valued(c_Relation_Orel__comp(X1,X4,X2,X3,X5),X2,X5)
| ~ c_Relation_Osingle__valued(X4,X3,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2507]) ).
cnf(c_0_2507_2,axiom,
( ~ c_Relation_Osingle__valued(X4,X3,X5)
| ~ c_Relation_Osingle__valued(X1,X2,X3)
| c_Relation_Osingle__valued(c_Relation_Orel__comp(X1,X4,X2,X3,X5),X2,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2507]) ).
cnf(c_0_2508_0,axiom,
( hBOOL(hAPP(X5,X1))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ hBOOL(hAPP(X5,X2))
| ~ hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X5,X2,X4,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2508]) ).
cnf(c_0_2508_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| hBOOL(hAPP(X5,X1))
| ~ hBOOL(hAPP(X5,X2))
| ~ hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X5,X2,X4,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2508]) ).
cnf(c_0_2508_2,axiom,
( ~ hBOOL(hAPP(X5,X2))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| hBOOL(hAPP(X5,X1))
| ~ hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X5,X2,X4,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2508]) ).
cnf(c_0_2508_3,axiom,
( ~ hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X5,X2,X4,X3)))
| ~ hBOOL(hAPP(X5,X2))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| hBOOL(hAPP(X5,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2508]) ).
cnf(c_0_2509_0,axiom,
( hBOOL(hAPP(X5,X2))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ hBOOL(hAPP(X5,X1))
| ~ hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X5,X1,X4,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2509]) ).
cnf(c_0_2509_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| hBOOL(hAPP(X5,X2))
| ~ hBOOL(hAPP(X5,X1))
| ~ hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X5,X1,X4,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2509]) ).
cnf(c_0_2509_2,axiom,
( ~ hBOOL(hAPP(X5,X1))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| hBOOL(hAPP(X5,X2))
| ~ hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X5,X1,X4,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2509]) ).
cnf(c_0_2509_3,axiom,
( ~ hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X5,X1,X4,X3)))
| ~ hBOOL(hAPP(X5,X1))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| hBOOL(hAPP(X5,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2509]) ).
cnf(c_0_2511_0,axiom,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X5,X1,X4,X3),X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| hBOOL(hAPP(X5,X2))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ hBOOL(hAPP(X5,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2511]) ).
cnf(c_0_2511_1,axiom,
( hBOOL(hAPP(X5,X2))
| c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X5,X1,X4,X3),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))
| ~ hBOOL(hAPP(X5,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2511]) ).
cnf(c_0_2511_2,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| hBOOL(hAPP(X5,X2))
| c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X5,X1,X4,X3),X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ hBOOL(hAPP(X5,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2511]) ).
cnf(c_0_2511_3,axiom,
( ~ hBOOL(hAPP(X5,X1))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| hBOOL(hAPP(X5,X2))
| c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X5,X1,X4,X3),X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2511]) ).
cnf(c_0_2512_0,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X5,X2,X4,X3),X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| hBOOL(hAPP(X5,X1))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ hBOOL(hAPP(X5,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2512]) ).
cnf(c_0_2512_1,axiom,
( hBOOL(hAPP(X5,X1))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X5,X2,X4,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_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ hBOOL(hAPP(X5,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2512]) ).
cnf(c_0_2512_2,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| hBOOL(hAPP(X5,X1))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X5,X2,X4,X3),X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ hBOOL(hAPP(X5,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2512]) ).
cnf(c_0_2512_3,axiom,
( ~ hBOOL(hAPP(X5,X2))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| hBOOL(hAPP(X5,X1))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X5,X2,X4,X3),X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2512]) ).
cnf(c_0_2514_0,axiom,
( X1 = X2
| c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X1,X2,X4,X3),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)) ),
inference(literals_permutation,[status(thm)],[c_0_2514]) ).
cnf(c_0_2514_1,axiom,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X1,X2,X4,X3),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_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2514]) ).
cnf(c_0_2514_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,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X1,X2,X4,X3),X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2514]) ).
cnf(c_0_2515_0,axiom,
( X1 = X2
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__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_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2515]) ).
cnf(c_0_2515_1,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X4,X1,X2,X3),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_Ortrancl(X4,X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2515]) ).
cnf(c_0_2515_2,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X4,X1,X2,X3),X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2515]) ).
cnf(c_0_2516_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_2516]) ).
cnf(c_0_2516_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_2516]) ).
cnf(c_0_2517_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_2517]) ).
cnf(c_0_2517_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_2517]) ).
cnf(c_0_2518_0,axiom,
( X1 = X2
| c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X4,X1,X2,X3),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)) ),
inference(literals_permutation,[status(thm)],[c_0_2518]) ).
cnf(c_0_2518_1,axiom,
( c_in(c_Pair(X1,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X4,X1,X2,X3),X3,X3),X4,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_2518]) ).
cnf(c_0_2518_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,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X4,X1,X2,X3),X3,X3),X4,tc_prod(X3,X3))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2518]) ).
cnf(c_0_2519_0,axiom,
( X1 = X2
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X1,X2,X4,X3),X2,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)) ),
inference(literals_permutation,[status(thm)],[c_0_2519]) ).
cnf(c_0_2519_1,axiom,
( c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X1,X2,X4,X3),X2,X3,X3),X4,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_2519]) ).
cnf(c_0_2519_2,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| c_in(c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X1,X2,X4,X3),X2,X3,X3),X4,tc_prod(X3,X3))
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2519]) ).
cnf(c_0_2520_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_2520]) ).
cnf(c_0_2520_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_2520]) ).
cnf(c_0_2521_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_2521]) ).
cnf(c_0_2521_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_2521]) ).
cnf(c_0_2522_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_2522]) ).
cnf(c_0_2522_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_2522]) ).
cnf(c_0_2522_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_2522]) ).
cnf(c_0_2523_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_2523]) ).
cnf(c_0_2523_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_2523]) ).
cnf(c_0_2523_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_2523]) ).
cnf(c_0_2524_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_2524]) ).
cnf(c_0_2524_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_2524]) ).
cnf(c_0_2524_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_2524]) ).
cnf(c_0_2525_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_2525]) ).
cnf(c_0_2525_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_2525]) ).
cnf(c_0_2525_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_2525]) ).
cnf(c_0_2529_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_2529]) ).
cnf(c_0_2529_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_2529]) ).
cnf(c_0_2529_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_2529]) ).
cnf(c_0_2529_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_2529]) ).
cnf(c_0_2530_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_2530]) ).
cnf(c_0_2530_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_2530]) ).
cnf(c_0_2530_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_2530]) ).
cnf(c_0_2531_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_2531]) ).
cnf(c_0_2531_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_2531]) ).
cnf(c_0_2531_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_2531]) ).
cnf(c_0_2532_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_2532]) ).
cnf(c_0_2532_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_2532]) ).
cnf(c_0_2532_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_2532]) ).
cnf(c_0_2533_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_2533]) ).
cnf(c_0_2533_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_2533]) ).
cnf(c_0_2533_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_2533]) ).
cnf(c_0_2534_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_2534]) ).
cnf(c_0_2534_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_2534]) ).
cnf(c_0_2534_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_2534]) ).
cnf(c_0_2535_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_2535]) ).
cnf(c_0_2535_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_2535]) ).
cnf(c_0_2535_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_2535]) ).
cnf(c_0_2536_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_2536]) ).
cnf(c_0_2536_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_2536]) ).
cnf(c_0_2537_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_2537]) ).
cnf(c_0_2537_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_2537]) ).
cnf(c_0_2538_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_2538]) ).
cnf(c_0_2538_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_2538]) ).
cnf(c_0_2538_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_2538]) ).
cnf(c_0_2539_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_2539]) ).
cnf(c_0_2539_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_2539]) ).
cnf(c_0_2542_0,axiom,
( c_in(c_Pair(X1,X2,t_a,t_a),X3,tc_prod(t_a,t_a))
| c_in(c_Pair(X1,v_sko__Transitive__Closure__Xtrancl__Xcases__1(X1,X2,X3),t_a,t_a),c_Transitive__Closure_Otrancl(X3,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X1,X2,t_a,t_a),c_Transitive__Closure_Otrancl(X3,t_a),tc_prod(t_a,t_a)) ),
inference(literals_permutation,[status(thm)],[c_0_2542]) ).
cnf(c_0_2542_1,axiom,
( c_in(c_Pair(X1,v_sko__Transitive__Closure__Xtrancl__Xcases__1(X1,X2,X3),t_a,t_a),c_Transitive__Closure_Otrancl(X3,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(X1,X2,t_a,t_a),X3,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X1,X2,t_a,t_a),c_Transitive__Closure_Otrancl(X3,t_a),tc_prod(t_a,t_a)) ),
inference(literals_permutation,[status(thm)],[c_0_2542]) ).
cnf(c_0_2542_2,axiom,
( ~ c_in(c_Pair(X1,X2,t_a,t_a),c_Transitive__Closure_Otrancl(X3,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(X1,v_sko__Transitive__Closure__Xtrancl__Xcases__1(X1,X2,X3),t_a,t_a),c_Transitive__Closure_Otrancl(X3,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(X1,X2,t_a,t_a),X3,tc_prod(t_a,t_a)) ),
inference(literals_permutation,[status(thm)],[c_0_2542]) ).
cnf(c_0_2543_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X3)
| ~ c_in(X1,X5,X3)
| ~ c_in(X2,X5,X3)
| c_Relation_OImage(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2543]) ).
cnf(c_0_2543_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X5,X4,X3)
| c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(X1,X5,X3)
| ~ c_in(X2,X5,X3)
| c_Relation_OImage(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2543]) ).
cnf(c_0_2543_2,axiom,
( ~ c_in(X1,X5,X3)
| ~ c_Equiv__Relations_Oequiv(X5,X4,X3)
| c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(X2,X5,X3)
| c_Relation_OImage(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2543]) ).
cnf(c_0_2543_3,axiom,
( ~ c_in(X2,X5,X3)
| ~ c_in(X1,X5,X3)
| ~ c_Equiv__Relations_Oequiv(X5,X4,X3)
| c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| c_Relation_OImage(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2543]) ).
cnf(c_0_2543_4,axiom,
( c_Relation_OImage(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X4,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ c_in(X2,X5,X3)
| ~ c_in(X1,X5,X3)
| ~ 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_2543]) ).
cnf(c_0_2544_0,axiom,
( c_in(c_Pair(X1,X4,X3,X3),X5,tc_prod(X3,X3))
| ~ c_in(X1,X2,X3)
| ~ c_in(X4,X2,X3)
| ~ c_Equiv__Relations_Oequiv(X2,X5,X3)
| c_Relation_OImage(X5,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X5,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2544]) ).
cnf(c_0_2544_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(c_Pair(X1,X4,X3,X3),X5,tc_prod(X3,X3))
| ~ c_in(X4,X2,X3)
| ~ c_Equiv__Relations_Oequiv(X2,X5,X3)
| c_Relation_OImage(X5,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X5,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2544]) ).
cnf(c_0_2544_2,axiom,
( ~ c_in(X4,X2,X3)
| ~ c_in(X1,X2,X3)
| c_in(c_Pair(X1,X4,X3,X3),X5,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X2,X5,X3)
| c_Relation_OImage(X5,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X5,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2544]) ).
cnf(c_0_2544_3,axiom,
( ~ c_Equiv__Relations_Oequiv(X2,X5,X3)
| ~ c_in(X4,X2,X3)
| ~ c_in(X1,X2,X3)
| c_in(c_Pair(X1,X4,X3,X3),X5,tc_prod(X3,X3))
| c_Relation_OImage(X5,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X5,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2544]) ).
cnf(c_0_2544_4,axiom,
( c_Relation_OImage(X5,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X5,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ c_Equiv__Relations_Oequiv(X2,X5,X3)
| ~ c_in(X4,X2,X3)
| ~ c_in(X1,X2,X3)
| c_in(c_Pair(X1,X4,X3,X3),X5,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2544]) ).
cnf(c_0_2545_0,axiom,
( c_in(c_Pair(X1,X2,t_a,t_a),X3,tc_prod(t_a,t_a))
| c_in(c_Pair(v_sko__Transitive__Closure__Xtrancl__Xcases__1(X1,X2,X3),X2,t_a,t_a),X3,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X1,X2,t_a,t_a),c_Transitive__Closure_Otrancl(X3,t_a),tc_prod(t_a,t_a)) ),
inference(literals_permutation,[status(thm)],[c_0_2545]) ).
cnf(c_0_2545_1,axiom,
( c_in(c_Pair(v_sko__Transitive__Closure__Xtrancl__Xcases__1(X1,X2,X3),X2,t_a,t_a),X3,tc_prod(t_a,t_a))
| c_in(c_Pair(X1,X2,t_a,t_a),X3,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X1,X2,t_a,t_a),c_Transitive__Closure_Otrancl(X3,t_a),tc_prod(t_a,t_a)) ),
inference(literals_permutation,[status(thm)],[c_0_2545]) ).
cnf(c_0_2545_2,axiom,
( ~ c_in(c_Pair(X1,X2,t_a,t_a),c_Transitive__Closure_Otrancl(X3,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_sko__Transitive__Closure__Xtrancl__Xcases__1(X1,X2,X3),X2,t_a,t_a),X3,tc_prod(t_a,t_a))
| c_in(c_Pair(X1,X2,t_a,t_a),X3,tc_prod(t_a,t_a)) ),
inference(literals_permutation,[status(thm)],[c_0_2545]) ).
cnf(c_0_2546_0,axiom,
( c_in(c_Pair(X5,X4,X3,X3),X2,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(X4,X1,X3)
| c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2546]) ).
cnf(c_0_2546_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_in(c_Pair(X5,X4,X3,X3),X2,tc_prod(X3,X3))
| ~ c_in(X4,X1,X3)
| c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2546]) ).
cnf(c_0_2546_2,axiom,
( ~ c_in(X4,X1,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_in(c_Pair(X5,X4,X3,X3),X2,tc_prod(X3,X3))
| c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2546]) ).
cnf(c_0_2546_3,axiom,
( c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) != c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ c_in(X4,X1,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_in(c_Pair(X5,X4,X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2546]) ).
cnf(c_0_2547_0,axiom,
( c_Equiv__Relations_Oequiv(c_Relation_ODomain(X1,X2,X2),X1,X2)
| c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X2,X2),X1),X1,X2,X2,X2) != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2547]) ).
cnf(c_0_2547_1,axiom,
( c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X2,X2),X1),X1,X2,X2,X2) != X1
| c_Equiv__Relations_Oequiv(c_Relation_ODomain(X1,X2,X2),X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2547]) ).
cnf(c_0_2548_0,axiom,
( c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1(X3,X4,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2548]) ).
cnf(c_0_2548_1,axiom,
( ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1(X3,X4,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2548]) ).
cnf(c_0_2548_2,axiom,
( ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1(X3,X4,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2548]) ).
cnf(c_0_2548_3,axiom,
( ~ c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X2,v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1(X3,X4,X2)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X2,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
| c_in(c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2548]) ).
cnf(c_0_2549_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_2549]) ).
cnf(c_0_2549_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_2549]) ).
cnf(c_0_2550_0,axiom,
( c_in(c_Pair(X3,X1,X4,X5),X2,tc_prod(X4,X5))
| ~ c_in(X1,c_Relation_OImage(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_2550]) ).
cnf(c_0_2550_1,axiom,
( ~ c_in(X1,c_Relation_OImage(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X5),X5)
| c_in(c_Pair(X3,X1,X4,X5),X2,tc_prod(X4,X5)) ),
inference(literals_permutation,[status(thm)],[c_0_2550]) ).
cnf(c_0_2551_0,axiom,
( c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(X4,X1,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_2551]) ).
cnf(c_0_2551_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ c_in(X4,X1,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_2551]) ).
cnf(c_0_2551_2,axiom,
( ~ c_in(X4,X1,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ 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_2551]) ).
cnf(c_0_2551_3,axiom,
( ~ c_in(X5,X1,X3)
| ~ c_in(X4,X1,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2551]) ).
cnf(c_0_2551_4,axiom,
( ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3))
| ~ c_in(X5,X1,X3)
| ~ c_in(X4,X1,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2551]) ).
cnf(c_0_2552_0,axiom,
( hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X5,X1,X4,X3)))
| hBOOL(hAPP(X5,X2))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ hBOOL(hAPP(X5,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2552]) ).
cnf(c_0_2552_1,axiom,
( hBOOL(hAPP(X5,X2))
| hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X5,X1,X4,X3)))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ hBOOL(hAPP(X5,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2552]) ).
cnf(c_0_2552_2,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| hBOOL(hAPP(X5,X2))
| hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X5,X1,X4,X3)))
| ~ hBOOL(hAPP(X5,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2552]) ).
cnf(c_0_2552_3,axiom,
( ~ hBOOL(hAPP(X5,X1))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| hBOOL(hAPP(X5,X2))
| hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X5,X1,X4,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2552]) ).
cnf(c_0_2553_0,axiom,
( hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X5,X2,X4,X3)))
| hBOOL(hAPP(X5,X1))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ hBOOL(hAPP(X5,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2553]) ).
cnf(c_0_2553_1,axiom,
( hBOOL(hAPP(X5,X1))
| hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X5,X2,X4,X3)))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| ~ hBOOL(hAPP(X5,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2553]) ).
cnf(c_0_2553_2,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| hBOOL(hAPP(X5,X1))
| hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X5,X2,X4,X3)))
| ~ hBOOL(hAPP(X5,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2553]) ).
cnf(c_0_2553_3,axiom,
( ~ hBOOL(hAPP(X5,X2))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(X4,X3),tc_prod(X3,X3))
| hBOOL(hAPP(X5,X1))
| hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X5,X2,X4,X3))) ),
inference(literals_permutation,[status(thm)],[c_0_2553]) ).
cnf(c_0_2554_0,axiom,
( c_Wellfounded_Owf(X1,X2)
| c_Relation_Orel__comp(X1,X1,X2,X2,X2) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2554]) ).
cnf(c_0_2554_1,axiom,
( c_Relation_Orel__comp(X1,X1,X2,X2,X2) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool))
| c_Wellfounded_Owf(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2554]) ).
cnf(c_0_2555_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_2555]) ).
cnf(c_0_2555_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_2555]) ).
cnf(c_0_2557_0,axiom,
( c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2557]) ).
cnf(c_0_2557_1,axiom,
( ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2557]) ).
cnf(c_0_2557_2,axiom,
( ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2557]) ).
cnf(c_0_2558_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_2558]) ).
cnf(c_0_2558_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_2558]) ).
cnf(c_0_2558_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_2558]) ).
cnf(c_0_2559_0,axiom,
( c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2559]) ).
cnf(c_0_2559_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2559]) ).
cnf(c_0_2559_2,axiom,
( ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2559]) ).
cnf(c_0_2560_0,axiom,
( c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2560]) ).
cnf(c_0_2560_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2560]) ).
cnf(c_0_2560_2,axiom,
( ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) = c_Relation_OImage(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2560]) ).
cnf(c_0_2561_0,axiom,
( X5 = X6
| ~ c_Relation_Osingle__valued(X1,X2,X3)
| ~ c_in(c_Pair(X4,X5,X2,X3),X1,tc_prod(X2,X3))
| ~ c_in(c_Pair(X4,X6,X2,X3),X1,tc_prod(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2561]) ).
cnf(c_0_2561_1,axiom,
( ~ c_Relation_Osingle__valued(X1,X2,X3)
| X5 = X6
| ~ c_in(c_Pair(X4,X5,X2,X3),X1,tc_prod(X2,X3))
| ~ c_in(c_Pair(X4,X6,X2,X3),X1,tc_prod(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2561]) ).
cnf(c_0_2561_2,axiom,
( ~ c_in(c_Pair(X4,X5,X2,X3),X1,tc_prod(X2,X3))
| ~ c_Relation_Osingle__valued(X1,X2,X3)
| X5 = X6
| ~ c_in(c_Pair(X4,X6,X2,X3),X1,tc_prod(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2561]) ).
cnf(c_0_2561_3,axiom,
( ~ c_in(c_Pair(X4,X6,X2,X3),X1,tc_prod(X2,X3))
| ~ c_in(c_Pair(X4,X5,X2,X3),X1,tc_prod(X2,X3))
| ~ c_Relation_Osingle__valued(X1,X2,X3)
| X5 = X6 ),
inference(literals_permutation,[status(thm)],[c_0_2561]) ).
cnf(c_0_2562_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),hAPP(c_Relation_Oconverse(X3,X3),c_Transitive__Closure_Otrancl(X4,X3)),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(hAPP(c_Relation_Oconverse(X3,X3),X4),X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2562]) ).
cnf(c_0_2562_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(hAPP(c_Relation_Oconverse(X3,X3),X4),X3),tc_prod(X3,X3))
| c_in(c_Pair(X1,X2,X3,X3),hAPP(c_Relation_Oconverse(X3,X3),c_Transitive__Closure_Otrancl(X4,X3)),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2562]) ).
cnf(c_0_2563_0,axiom,
( c_in(X2,c_Relation_OImage(X5,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X4),X4)
| ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2563]) ).
cnf(c_0_2563_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
| c_in(X2,c_Relation_OImage(X5,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2563]) ).
cnf(c_0_2564_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(hAPP(c_Relation_Oconverse(X3,X3),X4),X3),tc_prod(X3,X3))
| ~ c_in(c_Pair(X1,X2,X3,X3),hAPP(c_Relation_Oconverse(X3,X3),c_Transitive__Closure_Otrancl(X4,X3)),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2564]) ).
cnf(c_0_2564_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),hAPP(c_Relation_Oconverse(X3,X3),c_Transitive__Closure_Otrancl(X4,X3)),tc_prod(X3,X3))
| c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Otrancl(hAPP(c_Relation_Oconverse(X3,X3),X4),X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2564]) ).
cnf(c_0_2565_0,axiom,
( X1 = X2
| ~ c_Relation_Orefl__on(c_Relation_OField(X3,X4),X3,X4)
| ~ c_Relation_Oantisym(X3,X4)
| ~ c_in(X1,c_Relation_OField(X3,X4),X4)
| ~ c_in(X2,c_Relation_OField(X3,X4),X4)
| c_Relation_OImage(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4) != c_Relation_OImage(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2565]) ).
cnf(c_0_2565_1,axiom,
( ~ c_Relation_Orefl__on(c_Relation_OField(X3,X4),X3,X4)
| X1 = X2
| ~ c_Relation_Oantisym(X3,X4)
| ~ c_in(X1,c_Relation_OField(X3,X4),X4)
| ~ c_in(X2,c_Relation_OField(X3,X4),X4)
| c_Relation_OImage(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4) != c_Relation_OImage(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2565]) ).
cnf(c_0_2565_2,axiom,
( ~ c_Relation_Oantisym(X3,X4)
| ~ c_Relation_Orefl__on(c_Relation_OField(X3,X4),X3,X4)
| X1 = X2
| ~ c_in(X1,c_Relation_OField(X3,X4),X4)
| ~ c_in(X2,c_Relation_OField(X3,X4),X4)
| c_Relation_OImage(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4) != c_Relation_OImage(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2565]) ).
cnf(c_0_2565_3,axiom,
( ~ c_in(X1,c_Relation_OField(X3,X4),X4)
| ~ c_Relation_Oantisym(X3,X4)
| ~ c_Relation_Orefl__on(c_Relation_OField(X3,X4),X3,X4)
| X1 = X2
| ~ c_in(X2,c_Relation_OField(X3,X4),X4)
| c_Relation_OImage(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4) != c_Relation_OImage(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2565]) ).
cnf(c_0_2565_4,axiom,
( ~ c_in(X2,c_Relation_OField(X3,X4),X4)
| ~ c_in(X1,c_Relation_OField(X3,X4),X4)
| ~ c_Relation_Oantisym(X3,X4)
| ~ c_Relation_Orefl__on(c_Relation_OField(X3,X4),X3,X4)
| X1 = X2
| c_Relation_OImage(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4) != c_Relation_OImage(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2565]) ).
cnf(c_0_2565_5,axiom,
( c_Relation_OImage(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4) != c_Relation_OImage(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4,X4)
| ~ c_in(X2,c_Relation_OField(X3,X4),X4)
| ~ c_in(X1,c_Relation_OField(X3,X4),X4)
| ~ c_Relation_Oantisym(X3,X4)
| ~ c_Relation_Orefl__on(c_Relation_OField(X3,X4),X3,X4)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2565]) ).
cnf(c_0_2566_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_2566]) ).
cnf(c_0_2566_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_2566]) ).
cnf(c_0_2567_0,axiom,
( c_Wellfounded_Oacyclic(X4,X3)
| ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2567]) ).
cnf(c_0_2567_1,axiom,
( ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)),X3)
| c_Wellfounded_Oacyclic(X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2567]) ).
cnf(c_0_2568_0,axiom,
( X3 = X4
| ~ c_Relation_Oantisym(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_2568]) ).
cnf(c_0_2568_1,axiom,
( ~ c_Relation_Oantisym(X1,X2)
| X3 = X4
| ~ 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_2568]) ).
cnf(c_0_2568_2,axiom,
( ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2))
| ~ c_Relation_Oantisym(X1,X2)
| X3 = X4
| ~ c_in(c_Pair(X4,X3,X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2568]) ).
cnf(c_0_2568_3,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_Relation_Oantisym(X1,X2)
| X3 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_2568]) ).
cnf(c_0_2569_0,axiom,
( X3 = X4
| ~ c_Relation_Oantisym(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_2569]) ).
cnf(c_0_2569_1,axiom,
( ~ c_Relation_Oantisym(X1,X2)
| X3 = X4
| ~ 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_2569]) ).
cnf(c_0_2569_2,axiom,
( ~ c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2))
| ~ c_Relation_Oantisym(X1,X2)
| X3 = X4
| ~ c_in(c_Pair(X4,X3,X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2569]) ).
cnf(c_0_2569_3,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_Relation_Oantisym(X1,X2)
| X3 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_2569]) ).
cnf(c_0_2570_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_2570]) ).
cnf(c_0_2570_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_2570]) ).
cnf(c_0_2570_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_2570]) ).
cnf(c_0_2571_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_2571]) ).
cnf(c_0_2571_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_2571]) ).
cnf(c_0_2572_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_2572]) ).
cnf(c_0_2572_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_2572]) ).
cnf(c_0_2573_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_2573]) ).
cnf(c_0_2573_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_2573]) ).
cnf(c_0_2574_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_2574]) ).
cnf(c_0_2574_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_2574]) ).
cnf(c_0_2576_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(hAPP(c_Relation_Oconverse(X3,X3),X4),X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2576]) ).
cnf(c_0_2576_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X3),c_Transitive__Closure_Ortrancl(hAPP(c_Relation_Oconverse(X3,X3),X4),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_2576]) ).
cnf(c_0_2577_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_2577]) ).
cnf(c_0_2577_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_2577]) ).
cnf(c_0_2577_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_2577]) ).
cnf(c_0_2578_0,axiom,
( c_in(c_Pair(X3,X4,X2,X2),c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X4,X3,X2,X2),X1,tc_prod(X2,X2)),X2)
| ~ c_Wellfounded_Oacyclic(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2578]) ).
cnf(c_0_2578_1,axiom,
( c_Wellfounded_Oacyclic(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_Oacyclic(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2578]) ).
cnf(c_0_2578_2,axiom,
( ~ c_Wellfounded_Oacyclic(X1,X2)
| c_Wellfounded_Oacyclic(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_2578]) ).
cnf(c_0_2579_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_2579]) ).
cnf(c_0_2579_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_2579]) ).
cnf(c_0_2580_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_2580]) ).
cnf(c_0_2580_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_2580]) ).
cnf(c_0_2581_0,axiom,
( X2 = X1
| c_in(c_Pair(X1,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X1,X2,X3),t_a,t_a),c_Transitive__Closure_Ortrancl(X3,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X1,X2,t_a,t_a),c_Transitive__Closure_Ortrancl(X3,t_a),tc_prod(t_a,t_a)) ),
inference(literals_permutation,[status(thm)],[c_0_2581]) ).
cnf(c_0_2581_1,axiom,
( c_in(c_Pair(X1,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X1,X2,X3),t_a,t_a),c_Transitive__Closure_Ortrancl(X3,t_a),tc_prod(t_a,t_a))
| X2 = X1
| ~ c_in(c_Pair(X1,X2,t_a,t_a),c_Transitive__Closure_Ortrancl(X3,t_a),tc_prod(t_a,t_a)) ),
inference(literals_permutation,[status(thm)],[c_0_2581]) ).
cnf(c_0_2581_2,axiom,
( ~ c_in(c_Pair(X1,X2,t_a,t_a),c_Transitive__Closure_Ortrancl(X3,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(X1,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X1,X2,X3),t_a,t_a),c_Transitive__Closure_Ortrancl(X3,t_a),tc_prod(t_a,t_a))
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2581]) ).
cnf(c_0_2582_0,axiom,
( c_in(c_Pair(X2,X1,X3,X3),c_Transitive__Closure_Ortrancl(hAPP(c_Relation_Oconverse(X3,X3),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_2582]) ).
cnf(c_0_2582_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(hAPP(c_Relation_Oconverse(X3,X3),X4),X3),tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2582]) ).
cnf(c_0_2583_0,axiom,
( X2 = X1
| c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X1,X2,X3),X2,t_a,t_a),X3,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X1,X2,t_a,t_a),c_Transitive__Closure_Ortrancl(X3,t_a),tc_prod(t_a,t_a)) ),
inference(literals_permutation,[status(thm)],[c_0_2583]) ).
cnf(c_0_2583_1,axiom,
( c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X1,X2,X3),X2,t_a,t_a),X3,tc_prod(t_a,t_a))
| X2 = X1
| ~ c_in(c_Pair(X1,X2,t_a,t_a),c_Transitive__Closure_Ortrancl(X3,t_a),tc_prod(t_a,t_a)) ),
inference(literals_permutation,[status(thm)],[c_0_2583]) ).
cnf(c_0_2583_2,axiom,
( ~ c_in(c_Pair(X1,X2,t_a,t_a),c_Transitive__Closure_Ortrancl(X3,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X1,X2,X3),X2,t_a,t_a),X3,tc_prod(t_a,t_a))
| X2 = X1 ),
inference(literals_permutation,[status(thm)],[c_0_2583]) ).
cnf(c_0_2584_0,axiom,
( c_Equiv__Relations_Oquotient(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,X3) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(X4,X1,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_2584]) ).
cnf(c_0_2584_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Equiv__Relations_Oquotient(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,X3) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,X3)
| ~ c_in(X4,X1,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_2584]) ).
cnf(c_0_2584_2,axiom,
( ~ c_in(X4,X1,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Equiv__Relations_Oquotient(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,X3) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,X3)
| ~ 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_2584]) ).
cnf(c_0_2584_3,axiom,
( ~ c_in(X5,X1,X3)
| ~ c_in(X4,X1,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Equiv__Relations_Oquotient(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,X3) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,X3)
| ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2584]) ).
cnf(c_0_2584_4,axiom,
( ~ c_in(c_Pair(X4,X5,X3,X3),X2,tc_prod(X3,X3))
| ~ c_in(X5,X1,X3)
| ~ c_in(X4,X1,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Equiv__Relations_Oquotient(c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,X3) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2584]) ).
cnf(c_0_2585_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X3,X4,X1,X2),c_Relation_OImage(X3,X5,X1,X2),tc_fun(X2,tc_bool)) = c_Relation_OImage(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X1,tc_bool)),X1,X2)
| ~ c_Relation_Osingle__valued(hAPP(c_Relation_Oconverse(X1,X2),X3),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2585]) ).
cnf(c_0_2585_1,axiom,
( ~ c_Relation_Osingle__valued(hAPP(c_Relation_Oconverse(X1,X2),X3),X2,X1)
| c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X3,X4,X1,X2),c_Relation_OImage(X3,X5,X1,X2),tc_fun(X2,tc_bool)) = c_Relation_OImage(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_fun(X1,tc_bool)),X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2585]) ).
cnf(c_0_2586_0,axiom,
( c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Oequiv(X5,X4,X3)
| ~ c_in(X1,X5,X3)
| ~ c_in(X2,X5,X3)
| c_Equiv__Relations_Oquotient(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X4,X3) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2586]) ).
cnf(c_0_2586_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X5,X4,X3)
| c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(X1,X5,X3)
| ~ c_in(X2,X5,X3)
| c_Equiv__Relations_Oquotient(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X4,X3) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2586]) ).
cnf(c_0_2586_2,axiom,
( ~ c_in(X1,X5,X3)
| ~ c_Equiv__Relations_Oequiv(X5,X4,X3)
| c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| ~ c_in(X2,X5,X3)
| c_Equiv__Relations_Oquotient(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X4,X3) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2586]) ).
cnf(c_0_2586_3,axiom,
( ~ c_in(X2,X5,X3)
| ~ c_in(X1,X5,X3)
| ~ c_Equiv__Relations_Oequiv(X5,X4,X3)
| c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3))
| c_Equiv__Relations_Oquotient(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X4,X3) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X4,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2586]) ).
cnf(c_0_2586_4,axiom,
( c_Equiv__Relations_Oquotient(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X4,X3) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X4,X3)
| ~ c_in(X2,X5,X3)
| ~ c_in(X1,X5,X3)
| ~ 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_2586]) ).
cnf(c_0_2587_0,axiom,
( c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X1),X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X1),X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2587]) ).
cnf(c_0_2587_1,axiom,
( c_Arrow__Order__Mirabelle_OIIA(X1)
| c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X1),X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X1),X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2587]) ).
cnf(c_0_2587_2,axiom,
( ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X1),X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_Arrow__Order__Mirabelle_OIIA(X1)
| c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X1),X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2587]) ).
cnf(c_0_2588_0,axiom,
( c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X1),X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X1),X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2588]) ).
cnf(c_0_2588_1,axiom,
( c_Arrow__Order__Mirabelle_OIIA(X1)
| c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X1),X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X1),X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2588]) ).
cnf(c_0_2588_2,axiom,
( ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X1),X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_Arrow__Order__Mirabelle_OIIA(X1)
| c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X1),X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2588]) ).
cnf(c_0_2589_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_2589]) ).
cnf(c_0_2589_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_2589]) ).
cnf(c_0_2590_0,axiom,
( c_in(c_Pair(X2,X1,X4,X3),X5,tc_prod(X4,X3))
| ~ c_in(c_Pair(X1,X2,X3,X4),hAPP(c_Relation_Oconverse(X4,X3),X5),tc_prod(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2590]) ).
cnf(c_0_2590_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X4),hAPP(c_Relation_Oconverse(X4,X3),X5),tc_prod(X3,X4))
| c_in(c_Pair(X2,X1,X4,X3),X5,tc_prod(X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2590]) ).
cnf(c_0_2592_0,axiom,
( c_in(c_Pair(X2,X1,X4,X3),hAPP(c_Relation_Oconverse(X3,X4),X5),tc_prod(X4,X3))
| ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2592]) ).
cnf(c_0_2592_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
| c_in(c_Pair(X2,X1,X4,X3),hAPP(c_Relation_Oconverse(X3,X4),X5),tc_prod(X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2592]) ).
cnf(c_0_2593_0,axiom,
( c_in(c_Pair(X2,X1,X4,X3),hAPP(c_Relation_Oconverse(X3,X4),X5),tc_prod(X4,X3))
| ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2593]) ).
cnf(c_0_2593_1,axiom,
( ~ c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))
| c_in(c_Pair(X2,X1,X4,X3),hAPP(c_Relation_Oconverse(X3,X4),X5),tc_prod(X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2593]) ).
cnf(c_0_2594_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_2594]) ).
cnf(c_0_2594_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_2594]) ).
cnf(c_0_2594_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_2594]) ).
cnf(c_0_2595_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_2595]) ).
cnf(c_0_2595_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_2595]) ).
cnf(c_0_2595_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_2595]) ).
cnf(c_0_2596_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_2596]) ).
cnf(c_0_2596_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_2596]) ).
cnf(c_0_2596_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_2596]) ).
cnf(c_0_2597_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_2597]) ).
cnf(c_0_2597_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_2597]) ).
cnf(c_0_2597_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_2597]) ).
cnf(c_0_2598_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_2598]) ).
cnf(c_0_2598_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_2598]) ).
cnf(c_0_2599_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_2599]) ).
cnf(c_0_2599_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_2599]) ).
cnf(c_0_2599_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_2599]) ).
cnf(c_0_2600_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_2600]) ).
cnf(c_0_2600_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_2600]) ).
cnf(c_0_2600_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_2600]) ).
cnf(c_0_2603_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_2603]) ).
cnf(c_0_2603_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_2603]) ).
cnf(c_0_2604_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_2604]) ).
cnf(c_0_2604_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_2604]) ).
cnf(c_0_2604_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_2604]) ).
cnf(c_0_2605_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_2605]) ).
cnf(c_0_2605_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_2605]) ).
cnf(c_0_2605_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_2605]) ).
cnf(c_0_2606_0,axiom,
( c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2606]) ).
cnf(c_0_2606_1,axiom,
( ~ c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2606]) ).
cnf(c_0_2607_0,axiom,
( c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2607]) ).
cnf(c_0_2607_1,axiom,
( ~ c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2607]) ).
cnf(c_0_2608_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_2608]) ).
cnf(c_0_2608_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_2608]) ).
cnf(c_0_2608_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_2608]) ).
cnf(c_0_2609_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_2609]) ).
cnf(c_0_2609_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_2609]) ).
cnf(c_0_2609_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_2609]) ).
cnf(c_0_2610_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_2610]) ).
cnf(c_0_2610_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_2610]) ).
cnf(c_0_2610_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_2610]) ).
cnf(c_0_2610_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_2610]) ).
cnf(c_0_2611_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_2611]) ).
cnf(c_0_2611_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_2611]) ).
cnf(c_0_2611_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_2611]) ).
cnf(c_0_2611_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_2611]) ).
cnf(c_0_2612_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_2612]) ).
cnf(c_0_2612_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_2612]) ).
cnf(c_0_2612_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_2612]) ).
cnf(c_0_2612_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_2612]) ).
cnf(c_0_2613_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_2613]) ).
cnf(c_0_2613_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_2613]) ).
cnf(c_0_2613_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_2613]) ).
cnf(c_0_2613_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_2613]) ).
cnf(c_0_2617_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_2617]) ).
cnf(c_0_2617_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_2617]) ).
cnf(c_0_2617_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_2617]) ).
cnf(c_0_2617_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_2617]) ).
cnf(c_0_2618_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_2618]) ).
cnf(c_0_2618_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_2618]) ).
cnf(c_0_2618_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_2618]) ).
cnf(c_0_2618_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_2618]) ).
cnf(c_0_2619_0,axiom,
( ~ c_in(c_Pair(X1,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2))
| c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Relation_Oconverse(X2,X2),X3),c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2619]) ).
cnf(c_0_2619_1,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Relation_Oconverse(X2,X2),X3),c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_in(c_Pair(X1,X1,X2,X2),c_Transitive__Closure_Otrancl(X3,X2),tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2619]) ).
cnf(c_0_2620_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_2620]) ).
cnf(c_0_2620_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_2620]) ).
cnf(c_0_2620_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_2620]) ).
cnf(c_0_2620_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_2620]) ).
cnf(c_0_2621_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_2621]) ).
cnf(c_0_2621_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_2621]) ).
cnf(c_0_2621_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_2621]) ).
cnf(c_0_2621_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_2621]) ).
cnf(c_0_2622_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_2622]) ).
cnf(c_0_2622_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_2622]) ).
cnf(c_0_2622_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_2622]) ).
cnf(c_0_2622_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_2622]) ).
cnf(c_0_2622_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_2622]) ).
cnf(c_0_2622_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_2622]) ).
cnf(c_0_2623_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_2623]) ).
cnf(c_0_2623_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_2623]) ).
cnf(c_0_2623_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_2623]) ).
cnf(c_0_2624_0,axiom,
( c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X3,X3),X2),X2,X3,X3,X3) = X2
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2624]) ).
cnf(c_0_2624_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X3,X3),X2),X2,X3,X3,X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2624]) ).
cnf(c_0_2627_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_2627]) ).
cnf(c_0_2627_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_2627]) ).
cnf(c_0_2627_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_2627]) ).
cnf(c_0_2628_0,axiom,
( hBOOL(hAPP(X4,X3))
| hBOOL(hAPP(X4,X5))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2628]) ).
cnf(c_0_2628_1,axiom,
( hBOOL(hAPP(X4,X5))
| hBOOL(hAPP(X4,X3))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2628]) ).
cnf(c_0_2628_2,axiom,
( ~ c_Wellfounded_Owf(X1,X2)
| hBOOL(hAPP(X4,X5))
| hBOOL(hAPP(X4,X3))
| ~ c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2628]) ).
cnf(c_0_2628_3,axiom,
( ~ c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2))
| ~ c_Wellfounded_Owf(X1,X2)
| hBOOL(hAPP(X4,X5))
| hBOOL(hAPP(X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2628]) ).
cnf(c_0_2629_0,axiom,
( hBOOL(hAPP(X4,X3))
| hBOOL(hAPP(X4,X5))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_Pair(X3,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2629]) ).
cnf(c_0_2629_1,axiom,
( hBOOL(hAPP(X4,X5))
| hBOOL(hAPP(X4,X3))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_Pair(X3,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2629]) ).
cnf(c_0_2629_2,axiom,
( ~ c_Wellfounded_Owf(X1,X2)
| hBOOL(hAPP(X4,X5))
| hBOOL(hAPP(X4,X3))
| ~ c_in(c_Pair(X3,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2629]) ).
cnf(c_0_2629_3,axiom,
( ~ c_in(c_Pair(X3,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2))
| ~ c_Wellfounded_Owf(X1,X2)
| hBOOL(hAPP(X4,X5))
| hBOOL(hAPP(X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2629]) ).
cnf(c_0_2630_0,axiom,
( hBOOL(hAPP(X4,X3))
| hBOOL(hAPP(X4,X5))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2630]) ).
cnf(c_0_2630_1,axiom,
( hBOOL(hAPP(X4,X5))
| hBOOL(hAPP(X4,X3))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2630]) ).
cnf(c_0_2630_2,axiom,
( ~ c_Wellfounded_Owf(X1,X2)
| hBOOL(hAPP(X4,X5))
| hBOOL(hAPP(X4,X3))
| ~ c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2630]) ).
cnf(c_0_2630_3,axiom,
( ~ c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2))
| ~ c_Wellfounded_Owf(X1,X2)
| hBOOL(hAPP(X4,X5))
| hBOOL(hAPP(X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2630]) ).
cnf(c_0_2631_0,axiom,
( hBOOL(hAPP(X4,X3))
| hBOOL(hAPP(X4,X5))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2631]) ).
cnf(c_0_2631_1,axiom,
( hBOOL(hAPP(X4,X5))
| hBOOL(hAPP(X4,X3))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2631]) ).
cnf(c_0_2631_2,axiom,
( ~ c_Wellfounded_Owf(X1,X2)
| hBOOL(hAPP(X4,X5))
| hBOOL(hAPP(X4,X3))
| ~ c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2631]) ).
cnf(c_0_2631_3,axiom,
( ~ c_in(c_Pair(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X4,X1,X2),X2,X2),X1,tc_prod(X2,X2))
| ~ c_Wellfounded_Owf(X1,X2)
| hBOOL(hAPP(X4,X5))
| hBOOL(hAPP(X4,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2631]) ).
cnf(c_0_2632_0,axiom,
( hAPP(X2,X5) = hAPP(X2,X6)
| ~ c_Equiv__Relations_Ocongruent(X1,X2,X3,X4)
| ~ c_in(c_Pair(X5,X6,X3,X3),X1,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2632]) ).
cnf(c_0_2632_1,axiom,
( ~ c_Equiv__Relations_Ocongruent(X1,X2,X3,X4)
| hAPP(X2,X5) = hAPP(X2,X6)
| ~ c_in(c_Pair(X5,X6,X3,X3),X1,tc_prod(X3,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_2632]) ).
cnf(c_0_2632_2,axiom,
( ~ c_in(c_Pair(X5,X6,X3,X3),X1,tc_prod(X3,X3))
| ~ c_Equiv__Relations_Ocongruent(X1,X2,X3,X4)
| hAPP(X2,X5) = hAPP(X2,X6) ),
inference(literals_permutation,[status(thm)],[c_0_2632]) ).
cnf(c_0_2633_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_2633]) ).
cnf(c_0_2633_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_2633]) ).
cnf(c_0_2633_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_2633]) ).
cnf(c_0_2634_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_2634]) ).
cnf(c_0_2634_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_2634]) ).
cnf(c_0_2634_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_2634]) ).
cnf(c_0_2638_0,axiom,
( c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2638]) ).
cnf(c_0_2638_1,axiom,
( c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2638]) ).
cnf(c_0_2638_2,axiom,
( c_Arrow__Order__Mirabelle_OIIA(X1)
| c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__XIIA__def__4(X1),v_sko__Arrow__Order__Mirabelle__XIIA__def__5(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2638]) ).
cnf(c_0_2643_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_2643]) ).
cnf(c_0_2643_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_2643]) ).
cnf(c_0_2643_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_2643]) ).
cnf(c_0_2643_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_2643]) ).
cnf(c_0_2644_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_2644]) ).
cnf(c_0_2644_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_2644]) ).
cnf(c_0_2644_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_2644]) ).
cnf(c_0_2644_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_2644]) ).
cnf(c_0_2645_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_2645]) ).
cnf(c_0_2645_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_2645]) ).
cnf(c_0_2645_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_2645]) ).
cnf(c_0_2646_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_2646]) ).
cnf(c_0_2646_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_2646]) ).
cnf(c_0_2646_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_2646]) ).
cnf(c_0_2647_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_2647]) ).
cnf(c_0_2647_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_2647]) ).
cnf(c_0_2647_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_2647]) ).
cnf(c_0_2647_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_2647]) ).
cnf(c_0_2648_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_2648]) ).
cnf(c_0_2648_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_2648]) ).
cnf(c_0_2648_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_2648]) ).
cnf(c_0_2648_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_2648]) ).
cnf(c_0_2649_0,axiom,
( c_in(X4,c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2649]) ).
cnf(c_0_2649_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_in(X4,c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),X3)
| ~ c_in(X4,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2649]) ).
cnf(c_0_2649_2,axiom,
( ~ c_in(X4,X1,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_in(X4,c_Relation_OImage(X2,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2649]) ).
cnf(c_0_2650_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_2650]) ).
cnf(c_0_2650_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_2650]) ).
cnf(c_0_2650_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_2650]) ).
cnf(c_0_2651_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_2651]) ).
cnf(c_0_2651_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_2651]) ).
cnf(c_0_2651_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_2651]) ).
cnf(c_0_2653_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_2653]) ).
cnf(c_0_2653_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_2653]) ).
cnf(c_0_2653_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_2653]) ).
cnf(c_0_2654_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_2654]) ).
cnf(c_0_2654_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_2654]) ).
cnf(c_0_2654_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_2654]) ).
cnf(c_0_2655_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_2655]) ).
cnf(c_0_2655_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_2655]) ).
cnf(c_0_2655_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_2655]) ).
cnf(c_0_2656_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_2656]) ).
cnf(c_0_2656_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_2656]) ).
cnf(c_0_2657_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_2657]) ).
cnf(c_0_2657_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_2657]) ).
cnf(c_0_2658_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_2658]) ).
cnf(c_0_2658_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_2658]) ).
cnf(c_0_2659_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_2659]) ).
cnf(c_0_2659_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_2659]) ).
cnf(c_0_2660_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_2660]) ).
cnf(c_0_2660_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_2660]) ).
cnf(c_0_2661_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_2661]) ).
cnf(c_0_2661_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_2661]) ).
cnf(c_0_2661_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_2661]) ).
cnf(c_0_2662_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_2662]) ).
cnf(c_0_2662_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_2662]) ).
cnf(c_0_2662_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_2662]) ).
cnf(c_0_2663_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_2663]) ).
cnf(c_0_2663_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_2663]) ).
cnf(c_0_2663_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_2663]) ).
cnf(c_0_2664_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_2664]) ).
cnf(c_0_2664_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_2664]) ).
cnf(c_0_2664_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_2664]) ).
cnf(c_0_2666_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_2666]) ).
cnf(c_0_2666_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_2666]) ).
cnf(c_0_2667_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_2667]) ).
cnf(c_0_2667_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_2667]) ).
cnf(c_0_2668_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_2668]) ).
cnf(c_0_2668_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_2668]) ).
cnf(c_0_2669_0,axiom,
( c_Arrow__Order__Mirabelle_Ounanimity(X1)
| ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3(X1),v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2(X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2669]) ).
cnf(c_0_2669_1,axiom,
( ~ c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3(X1),v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2(X1)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_Arrow__Order__Mirabelle_Ounanimity(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2669]) ).
cnf(c_0_2670_0,axiom,
( ~ c_Wellfounded_Oacyclic(X1,X2)
| ~ c_in(c_Pair(X3,X3,X2,X2),c_Transitive__Closure_Otrancl(X1,X2),tc_prod(X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2670]) ).
cnf(c_0_2670_1,axiom,
( ~ c_in(c_Pair(X3,X3,X2,X2),c_Transitive__Closure_Otrancl(X1,X2),tc_prod(X2,X2))
| ~ c_Wellfounded_Oacyclic(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2670]) ).
cnf(c_0_2672_0,axiom,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ c_lessequals(X3,c_Relation_OImage(X1,X3,X2,X2),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2672]) ).
cnf(c_0_2672_1,axiom,
( ~ c_Wellfounded_Owf(X1,X2)
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X3,c_Relation_OImage(X1,X3,X2,X2),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2672]) ).
cnf(c_0_2672_2,axiom,
( ~ c_lessequals(X3,c_Relation_OImage(X1,X3,X2,X2),tc_fun(X2,tc_bool))
| ~ c_Wellfounded_Owf(X1,X2)
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2672]) ).
cnf(c_0_2673_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_2673]) ).
cnf(c_0_2673_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_2673]) ).
cnf(c_0_2674_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_2674]) ).
cnf(c_0_2674_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_2674]) ).
cnf(c_0_2679_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_2679]) ).
cnf(c_0_2679_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_2679]) ).
cnf(c_0_2680_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_2680]) ).
cnf(c_0_2680_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_2680]) ).
cnf(c_0_2681_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_2681]) ).
cnf(c_0_2681_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_2681]) ).
cnf(c_0_2682_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_2682]) ).
cnf(c_0_2682_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_2682]) ).
cnf(c_0_2683_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_2683]) ).
cnf(c_0_2683_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_2683]) ).
cnf(c_0_2685_0,axiom,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_2685]) ).
cnf(c_0_2685_1,axiom,
( X1 = X3
| X1 = X2
| c_Set_Oinsert(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_2685]) ).
cnf(c_0_2685_2,axiom,
( c_Set_Oinsert(X4,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X3,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5)
| X1 = X3
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2685]) ).
cnf(c_0_2686_0,axiom,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2686]) ).
cnf(c_0_2686_1,axiom,
( X3 = X2
| X1 = X2
| c_Set_Oinsert(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2686]) ).
cnf(c_0_2686_2,axiom,
( c_Set_Oinsert(X3,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X5,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)
| X3 = X2
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2686]) ).
cnf(c_0_2687_0,axiom,
( X1 = X2
| X3 = X2
| c_Set_Oinsert(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2687]) ).
cnf(c_0_2687_1,axiom,
( X3 = X2
| X1 = X2
| c_Set_Oinsert(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) ),
inference(literals_permutation,[status(thm)],[c_0_2687]) ).
cnf(c_0_2687_2,axiom,
( c_Set_Oinsert(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4) != c_Set_Oinsert(X2,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X4)
| X3 = X2
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2687]) ).
cnf(c_0_2688_0,axiom,
( X1 = X2
| X1 = X3
| c_Set_Oinsert(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_2688]) ).
cnf(c_0_2688_1,axiom,
( X1 = X3
| X1 = X2
| c_Set_Oinsert(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
inference(literals_permutation,[status(thm)],[c_0_2688]) ).
cnf(c_0_2688_2,axiom,
( c_Set_Oinsert(X1,c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5)
| X1 = X3
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2688]) ).
cnf(c_0_2689_0,axiom,
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Wellfounded_Owf(X1,X3)
| ~ c_Wellfounded_Owf(X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X1,X3,X3),c_Relation_ORange(X2,X3,X3),tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2689]) ).
cnf(c_0_2689_1,axiom,
( ~ c_Wellfounded_Owf(X1,X3)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| ~ c_Wellfounded_Owf(X2,X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X1,X3,X3),c_Relation_ORange(X2,X3,X3),tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2689]) ).
cnf(c_0_2689_2,axiom,
( ~ c_Wellfounded_Owf(X2,X3)
| ~ c_Wellfounded_Owf(X1,X3)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3)
| c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X1,X3,X3),c_Relation_ORange(X2,X3,X3),tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2689]) ).
cnf(c_0_2689_3,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X1,X3,X3),c_Relation_ORange(X2,X3,X3),tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_Wellfounded_Owf(X2,X3)
| ~ c_Wellfounded_Owf(X1,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_2689]) ).
cnf(c_0_2690_0,axiom,
( c_lessequals(X1,X2,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_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2690]) ).
cnf(c_0_2690_1,axiom,
( 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_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_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2690]) ).
cnf(c_0_2691_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_2691]) ).
cnf(c_0_2691_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_2691]) ).
cnf(c_0_2692_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_2692]) ).
cnf(c_0_2692_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_2692]) ).
cnf(c_0_2693_0,axiom,
( X1 = X2
| c_Pair(X1,X3,X4,X5) != c_Pair(X2,X6,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2693]) ).
cnf(c_0_2693_1,axiom,
( c_Pair(X1,X3,X4,X5) != c_Pair(X2,X6,X4,X5)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2693]) ).
cnf(c_0_2694_0,axiom,
( X1 = X2
| c_Pair(X3,X1,X4,X5) != c_Pair(X6,X2,X4,X5) ),
inference(literals_permutation,[status(thm)],[c_0_2694]) ).
cnf(c_0_2694_1,axiom,
( c_Pair(X3,X1,X4,X5) != c_Pair(X6,X2,X4,X5)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2694]) ).
cnf(c_0_2695_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_2695]) ).
cnf(c_0_2695_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_2695]) ).
cnf(c_0_2696_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_2696]) ).
cnf(c_0_2696_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_2696]) ).
cnf(c_0_2696_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_2696]) ).
cnf(c_0_2697_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_2697]) ).
cnf(c_0_2697_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_2697]) ).
cnf(c_0_2697_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_2697]) ).
cnf(c_0_2698_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_2698]) ).
cnf(c_0_2698_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_2698]) ).
cnf(c_0_2700_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_2700]) ).
cnf(c_0_2700_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_2700]) ).
cnf(c_0_2700_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_2700]) ).
cnf(c_0_2701_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_2701]) ).
cnf(c_0_2701_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_2701]) ).
cnf(c_0_2701_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_2701]) ).
cnf(c_0_2702_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_2702]) ).
cnf(c_0_2702_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_2702]) ).
cnf(c_0_2703_0,axiom,
( c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3(X1),v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2(X1),X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| c_Arrow__Order__Mirabelle_Ounanimity(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2703]) ).
cnf(c_0_2703_1,axiom,
( c_Arrow__Order__Mirabelle_Ounanimity(X1)
| c_in(c_Pair(v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3(X1),v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4(X1),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2(X1),X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(literals_permutation,[status(thm)],[c_0_2703]) ).
cnf(c_0_2704_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_2704]) ).
cnf(c_0_2704_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_2704]) ).
cnf(c_0_2704_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_2704]) ).
cnf(c_0_2705_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_2705]) ).
cnf(c_0_2705_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_2705]) ).
cnf(c_0_2705_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_2705]) ).
cnf(c_0_2714_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_2714]) ).
cnf(c_0_2714_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_2714]) ).
cnf(c_0_2715_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_2715]) ).
cnf(c_0_2715_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_2715]) ).
cnf(c_0_2715_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_2715]) ).
cnf(c_0_2716_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_2716]) ).
cnf(c_0_2716_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_2716]) ).
cnf(c_0_2716_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_2716]) ).
cnf(c_0_2717_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_2717]) ).
cnf(c_0_2717_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_2717]) ).
cnf(c_0_2718_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X1 = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| ~ c_lessequals(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2718]) ).
cnf(c_0_2718_1,axiom,
( X1 = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_lessequals(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2718]) ).
cnf(c_0_2718_2,axiom,
( ~ c_lessequals(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool))
| X1 = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2718]) ).
cnf(c_0_2719_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_2719]) ).
cnf(c_0_2719_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_2719]) ).
cnf(c_0_2719_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_2719]) ).
cnf(c_0_2721_0,axiom,
( 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_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_lessequals(X1,X2,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2721]) ).
cnf(c_0_2721_1,axiom,
( ~ c_lessequals(X1,X2,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_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2721]) ).
cnf(c_0_2726_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_2726]) ).
cnf(c_0_2726_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_2726]) ).
cnf(c_0_2727_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_2727]) ).
cnf(c_0_2727_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_2727]) ).
cnf(c_0_2728_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_2728]) ).
cnf(c_0_2728_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_2728]) ).
cnf(c_0_2728_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_2728]) ).
cnf(c_0_2729_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_2729]) ).
cnf(c_0_2729_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_2729]) ).
cnf(c_0_2729_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_2729]) ).
cnf(c_0_2731_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_2731]) ).
cnf(c_0_2731_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_2731]) ).
cnf(c_0_2732_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_2732]) ).
cnf(c_0_2732_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_2732]) ).
cnf(c_0_2734_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_2734]) ).
cnf(c_0_2734_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_2734]) ).
cnf(c_0_2735_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_2735]) ).
cnf(c_0_2735_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_2735]) ).
cnf(c_0_2735_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_2735]) ).
cnf(c_0_2736_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_2736]) ).
cnf(c_0_2736_1,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_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2736]) ).
cnf(c_0_2737_0,axiom,
( 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(literals_permutation,[status(thm)],[c_0_2737]) ).
cnf(c_0_2737_1,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_Set_Oinsert(X1,c_Lattices_Olower__semilattice__class_Oinf(X4,X2,tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2737]) ).
cnf(c_0_2738_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_2738]) ).
cnf(c_0_2738_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_2738]) ).
cnf(c_0_2738_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_2738]) ).
cnf(c_0_2739_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_2739]) ).
cnf(c_0_2739_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_2739]) ).
cnf(c_0_2739_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_2739]) ).
cnf(c_0_2740_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_2740]) ).
cnf(c_0_2740_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_2740]) ).
cnf(c_0_2740_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_2740]) ).
cnf(c_0_2741_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_2741]) ).
cnf(c_0_2741_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_2741]) ).
cnf(c_0_2741_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_2741]) ).
cnf(c_0_2742_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_2742]) ).
cnf(c_0_2742_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_2742]) ).
cnf(c_0_2742_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_2742]) ).
cnf(c_0_2747_0,axiom,
( c_Relation_Oantisym(X1,X2)
| ~ c_Relation_Oantisym(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_2747]) ).
cnf(c_0_2747_1,axiom,
( ~ c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| c_Relation_Oantisym(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2747]) ).
cnf(c_0_2748_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_2748]) ).
cnf(c_0_2748_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_2748]) ).
cnf(c_0_2749_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_2749]) ).
cnf(c_0_2749_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_2749]) ).
cnf(c_0_2750_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_2750]) ).
cnf(c_0_2750_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_2750]) ).
cnf(c_0_2751_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_2751]) ).
cnf(c_0_2751_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_2751]) ).
cnf(c_0_2752_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_2752]) ).
cnf(c_0_2752_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_2752]) ).
cnf(c_0_2753_0,axiom,
( hBOOL(hAPP(X3,X4))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2753]) ).
cnf(c_0_2753_1,axiom,
( ~ c_Wellfounded_Owf(X1,X2)
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2753]) ).
cnf(c_0_2753_2,axiom,
( ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X3,X1,X2)))
| ~ c_Wellfounded_Owf(X1,X2)
| hBOOL(hAPP(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2753]) ).
cnf(c_0_2754_0,axiom,
( hBOOL(hAPP(X3,X4))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2754]) ).
cnf(c_0_2754_1,axiom,
( ~ c_Wellfounded_Owf(X1,X2)
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2754]) ).
cnf(c_0_2754_2,axiom,
( ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X3,X1,X2)))
| ~ c_Wellfounded_Owf(X1,X2)
| hBOOL(hAPP(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2754]) ).
cnf(c_0_2755_0,axiom,
( hBOOL(hAPP(X3,X4))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2755]) ).
cnf(c_0_2755_1,axiom,
( ~ c_Wellfounded_Owf(X1,X2)
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2755]) ).
cnf(c_0_2755_2,axiom,
( ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X3,X1,X2)))
| ~ c_Wellfounded_Owf(X1,X2)
| hBOOL(hAPP(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2755]) ).
cnf(c_0_2756_0,axiom,
( hBOOL(hAPP(X3,X4))
| ~ c_Wellfounded_Owf(X1,X2)
| ~ hBOOL(hAPP(X3,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2756]) ).
cnf(c_0_2756_1,axiom,
( ~ c_Wellfounded_Owf(X1,X2)
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(X3,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X3,X1,X2))) ),
inference(literals_permutation,[status(thm)],[c_0_2756]) ).
cnf(c_0_2756_2,axiom,
( ~ hBOOL(hAPP(X3,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X3,X1,X2)))
| ~ c_Wellfounded_Owf(X1,X2)
| hBOOL(hAPP(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2756]) ).
cnf(c_0_2757_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_2757]) ).
cnf(c_0_2757_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_2757]) ).
cnf(c_0_2758_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_2758]) ).
cnf(c_0_2758_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_2758]) ).
cnf(c_0_2759_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_2759]) ).
cnf(c_0_2759_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_2759]) ).
cnf(c_0_2760_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_2760]) ).
cnf(c_0_2760_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_2760]) ).
cnf(c_0_2761_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_2761]) ).
cnf(c_0_2761_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_2761]) ).
cnf(c_0_2761_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_2761]) ).
cnf(c_0_2762_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_2762]) ).
cnf(c_0_2762_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_2762]) ).
cnf(c_0_2762_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_2762]) ).
cnf(c_0_2765_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_2765]) ).
cnf(c_0_2765_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_2765]) ).
cnf(c_0_2766_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_2766]) ).
cnf(c_0_2766_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_2766]) ).
cnf(c_0_2766_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_2766]) ).
cnf(c_0_2767_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_2767]) ).
cnf(c_0_2767_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_2767]) ).
cnf(c_0_2767_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_2767]) ).
cnf(c_0_2768_0,axiom,
( X1 = X2
| ~ c_in(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2768]) ).
cnf(c_0_2768_1,axiom,
( ~ c_in(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2768]) ).
cnf(c_0_2769_0,axiom,
( X1 = X4
| hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2769]) ).
cnf(c_0_2769_1,axiom,
( hBOOL(hAPP(X2,X4))
| X1 = X4
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
inference(literals_permutation,[status(thm)],[c_0_2769]) ).
cnf(c_0_2769_2,axiom,
( ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4))
| hBOOL(hAPP(X2,X4))
| X1 = X4 ),
inference(literals_permutation,[status(thm)],[c_0_2769]) ).
cnf(c_0_2770_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_2770]) ).
cnf(c_0_2770_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_2770]) ).
cnf(c_0_2772_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_2772]) ).
cnf(c_0_2772_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_2772]) ).
cnf(c_0_2772_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_2772]) ).
cnf(c_0_2775_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_2775]) ).
cnf(c_0_2775_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_2775]) ).
cnf(c_0_2776_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_2776]) ).
cnf(c_0_2776_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_2776]) ).
cnf(c_0_2777_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_2777]) ).
cnf(c_0_2777_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_2777]) ).
cnf(c_0_2778_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_2778]) ).
cnf(c_0_2778_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_2778]) ).
cnf(c_0_2779_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_2779]) ).
cnf(c_0_2779_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_2779]) ).
cnf(c_0_2780_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_2780]) ).
cnf(c_0_2780_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_2780]) ).
cnf(c_0_2780_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_2780]) ).
cnf(c_0_2781_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_2781]) ).
cnf(c_0_2781_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_2781]) ).
cnf(c_0_2781_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_2781]) ).
cnf(c_0_2783_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_2783]) ).
cnf(c_0_2783_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_2783]) ).
cnf(c_0_2784_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_2784]) ).
cnf(c_0_2784_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_2784]) ).
cnf(c_0_2785_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_2785]) ).
cnf(c_0_2785_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_2785]) ).
cnf(c_0_2786_0,axiom,
( hAPP(X1,X3) = hAPP(X3,X2)
| ~ c_Arrow__Order__Mirabelle_Odictator(X1,X2)
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
inference(literals_permutation,[status(thm)],[c_0_2786]) ).
cnf(c_0_2786_1,axiom,
( ~ c_Arrow__Order__Mirabelle_Odictator(X1,X2)
| hAPP(X1,X3) = hAPP(X3,X2)
| ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
inference(literals_permutation,[status(thm)],[c_0_2786]) ).
cnf(c_0_2786_2,axiom,
( ~ c_in(X3,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| ~ c_Arrow__Order__Mirabelle_Odictator(X1,X2)
| hAPP(X1,X3) = hAPP(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2786]) ).
cnf(c_0_2787_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_2787]) ).
cnf(c_0_2787_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_2787]) ).
cnf(c_0_2787_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_2787]) ).
cnf(c_0_2788_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_2788]) ).
cnf(c_0_2788_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_2788]) ).
cnf(c_0_2788_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_2788]) ).
cnf(c_0_2790_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_2790]) ).
cnf(c_0_2790_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_2790]) ).
cnf(c_0_2790_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_2790]) ).
cnf(c_0_2791_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_2791]) ).
cnf(c_0_2791_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_2791]) ).
cnf(c_0_2791_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_2791]) ).
cnf(c_0_2792_0,axiom,
( c_Relation_Osingle__valued(X1,X3,X4)
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool))
| ~ c_Relation_Osingle__valued(X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2792]) ).
cnf(c_0_2792_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool))
| c_Relation_Osingle__valued(X1,X3,X4)
| ~ c_Relation_Osingle__valued(X2,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2792]) ).
cnf(c_0_2792_2,axiom,
( ~ c_Relation_Osingle__valued(X2,X3,X4)
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool))
| c_Relation_Osingle__valued(X1,X3,X4) ),
inference(literals_permutation,[status(thm)],[c_0_2792]) ).
cnf(c_0_2793_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_2793]) ).
cnf(c_0_2793_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_2793]) ).
cnf(c_0_2795_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_2795]) ).
cnf(c_0_2795_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_2795]) ).
cnf(c_0_2795_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_2795]) ).
cnf(c_0_2795_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_2795]) ).
cnf(c_0_2796_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_2796]) ).
cnf(c_0_2796_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_2796]) ).
cnf(c_0_2796_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_2796]) ).
cnf(c_0_2796_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_2796]) ).
cnf(c_0_2797_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_2797]) ).
cnf(c_0_2797_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_2797]) ).
cnf(c_0_2797_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_2797]) ).
cnf(c_0_2797_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_2797]) ).
cnf(c_0_2798_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_2798]) ).
cnf(c_0_2798_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_2798]) ).
cnf(c_0_2798_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_2798]) ).
cnf(c_0_2798_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_2798]) ).
cnf(c_0_2799_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_2799]) ).
cnf(c_0_2799_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_2799]) ).
cnf(c_0_2799_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_2799]) ).
cnf(c_0_2799_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_2799]) ).
cnf(c_0_2800_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_2800]) ).
cnf(c_0_2800_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_2800]) ).
cnf(c_0_2800_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_2800]) ).
cnf(c_0_2800_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_2800]) ).
cnf(c_0_2801_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_in(X4,X1,X3)
| ~ c_in(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2801]) ).
cnf(c_0_2801_1,axiom,
( ~ c_in(X4,X1,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_in(X4,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2801]) ).
cnf(c_0_2801_2,axiom,
( ~ c_in(X4,X2,X3)
| ~ c_in(X4,X1,X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2801]) ).
cnf(c_0_2802_0,axiom,
( X1 = X2
| c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) != c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2802]) ).
cnf(c_0_2802_1,axiom,
( c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3) != c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2802]) ).
cnf(c_0_2803_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_2803]) ).
cnf(c_0_2803_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_2803]) ).
cnf(c_0_2804_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_2804]) ).
cnf(c_0_2804_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_2804]) ).
cnf(c_0_2805_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_2805]) ).
cnf(c_0_2805_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_2805]) ).
cnf(c_0_2806_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_2806]) ).
cnf(c_0_2806_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_2806]) ).
cnf(c_0_2807_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_2807]) ).
cnf(c_0_2807_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_2807]) ).
cnf(c_0_2808_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_2808]) ).
cnf(c_0_2808_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_2808]) ).
cnf(c_0_2809_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_2809]) ).
cnf(c_0_2809_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_2809]) ).
cnf(c_0_2810_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_2810]) ).
cnf(c_0_2810_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_2810]) ).
cnf(c_0_2811_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_2811]) ).
cnf(c_0_2811_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_2811]) ).
cnf(c_0_2812_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_2812]) ).
cnf(c_0_2812_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_2812]) ).
cnf(c_0_2813_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_2813]) ).
cnf(c_0_2813_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_2813]) ).
cnf(c_0_2816_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_2816]) ).
cnf(c_0_2816_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_2816]) ).
cnf(c_0_2816_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_2816]) ).
cnf(c_0_2817_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_2817]) ).
cnf(c_0_2817_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_2817]) ).
cnf(c_0_2818_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_2818]) ).
cnf(c_0_2818_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_2818]) ).
cnf(c_0_2819_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_2819]) ).
cnf(c_0_2819_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_2819]) ).
cnf(c_0_2819_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_2819]) ).
cnf(c_0_2820_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_2820]) ).
cnf(c_0_2820_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_2820]) ).
cnf(c_0_2820_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_2820]) ).
cnf(c_0_2821_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_2821]) ).
cnf(c_0_2821_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_2821]) ).
cnf(c_0_2821_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_2821]) ).
cnf(c_0_2822_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_2822]) ).
cnf(c_0_2822_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_2822]) ).
cnf(c_0_2822_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_2822]) ).
cnf(c_0_2823_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_2823]) ).
cnf(c_0_2823_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_2823]) ).
cnf(c_0_2823_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_2823]) ).
cnf(c_0_2824_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_2824]) ).
cnf(c_0_2824_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_2824]) ).
cnf(c_0_2824_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_2824]) ).
cnf(c_0_2825_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_2825]) ).
cnf(c_0_2825_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_2825]) ).
cnf(c_0_2825_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_2825]) ).
cnf(c_0_2826_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_2826]) ).
cnf(c_0_2826_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_2826]) ).
cnf(c_0_2826_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_2826]) ).
cnf(c_0_2827_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_2827]) ).
cnf(c_0_2827_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_2827]) ).
cnf(c_0_2827_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_2827]) ).
cnf(c_0_2828_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_2828]) ).
cnf(c_0_2828_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_2828]) ).
cnf(c_0_2828_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_2828]) ).
cnf(c_0_2829_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_2829]) ).
cnf(c_0_2829_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_2829]) ).
cnf(c_0_2829_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_2829]) ).
cnf(c_0_2832_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_2832]) ).
cnf(c_0_2832_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_2832]) ).
cnf(c_0_2833_0,axiom,
( c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X1,c_Relation_OId(X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ c_Relation_Oantisym(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2833]) ).
cnf(c_0_2833_1,axiom,
( ~ c_Relation_Oantisym(X1,X2)
| c_Relation_Oantisym(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_2833]) ).
cnf(c_0_2837_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_2837]) ).
cnf(c_0_2837_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_2837]) ).
cnf(c_0_2838_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_2838]) ).
cnf(c_0_2838_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_2838]) ).
cnf(c_0_2839_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_2839]) ).
cnf(c_0_2839_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_2839]) ).
cnf(c_0_2840_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_2840]) ).
cnf(c_0_2840_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_2840]) ).
cnf(c_0_2841_0,axiom,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2841]) ).
cnf(c_0_2841_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2841]) ).
cnf(c_0_2842_0,axiom,
( c_Wellfounded_Owf(hAPP(c_Relation_Oconverse(X1,X1),c_Transitive__Closure_Otrancl(X2,X1)),X1)
| ~ c_Wellfounded_Owf(hAPP(c_Relation_Oconverse(X1,X1),X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2842]) ).
cnf(c_0_2842_1,axiom,
( ~ c_Wellfounded_Owf(hAPP(c_Relation_Oconverse(X1,X1),X2),X1)
| c_Wellfounded_Owf(hAPP(c_Relation_Oconverse(X1,X1),c_Transitive__Closure_Otrancl(X2,X1)),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2842]) ).
cnf(c_0_2844_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_2844]) ).
cnf(c_0_2844_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_2844]) ).
cnf(c_0_2844_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_2844]) ).
cnf(c_0_2844_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_2844]) ).
cnf(c_0_2846_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_2846]) ).
cnf(c_0_2846_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_2846]) ).
cnf(c_0_2846_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_2846]) ).
cnf(c_0_2847_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_2847]) ).
cnf(c_0_2847_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_2847]) ).
cnf(c_0_2847_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_2847]) ).
cnf(c_0_2848_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_2848]) ).
cnf(c_0_2848_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_2848]) ).
cnf(c_0_2848_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_2848]) ).
cnf(c_0_2849_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_2849]) ).
cnf(c_0_2849_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_2849]) ).
cnf(c_0_2849_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_2849]) ).
cnf(c_0_2851_0,axiom,
( c_Relation_Ototal__on(X1,X3,X2)
| ~ c_Relation_Ototal__on(X1,hAPP(c_Relation_Oconverse(X2,X2),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2851]) ).
cnf(c_0_2851_1,axiom,
( ~ c_Relation_Ototal__on(X1,hAPP(c_Relation_Oconverse(X2,X2),X3),X2)
| c_Relation_Ototal__on(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2851]) ).
cnf(c_0_2852_0,axiom,
( c_Relation_Orefl__on(X1,X3,X2)
| ~ c_Relation_Orefl__on(X1,hAPP(c_Relation_Oconverse(X2,X2),X3),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2852]) ).
cnf(c_0_2852_1,axiom,
( ~ c_Relation_Orefl__on(X1,hAPP(c_Relation_Oconverse(X2,X2),X3),X2)
| c_Relation_Orefl__on(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2852]) ).
cnf(c_0_2853_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_2853]) ).
cnf(c_0_2853_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_2853]) ).
cnf(c_0_2853_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_2853]) ).
cnf(c_0_2854_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_2854]) ).
cnf(c_0_2854_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_2854]) ).
cnf(c_0_2854_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_2854]) ).
cnf(c_0_2855_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_2855]) ).
cnf(c_0_2855_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_2855]) ).
cnf(c_0_2855_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_2855]) ).
cnf(c_0_2856_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_2856]) ).
cnf(c_0_2856_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_2856]) ).
cnf(c_0_2856_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_2856]) ).
cnf(c_0_2858_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_2858]) ).
cnf(c_0_2858_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_2858]) ).
cnf(c_0_2858_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_2858]) ).
cnf(c_0_2859_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_2859]) ).
cnf(c_0_2859_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_2859]) ).
cnf(c_0_2859_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_2859]) ).
cnf(c_0_2860_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_2860]) ).
cnf(c_0_2860_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_2860]) ).
cnf(c_0_2860_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_2860]) ).
cnf(c_0_2861_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_2861]) ).
cnf(c_0_2861_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_2861]) ).
cnf(c_0_2861_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_2861]) ).
cnf(c_0_2864_0,axiom,
( c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2864]) ).
cnf(c_0_2864_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(X1,c_Set_Oinsert(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2864]) ).
cnf(c_0_2865_0,axiom,
( c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2865]) ).
cnf(c_0_2865_1,axiom,
( ~ c_in(X1,X2,X3)
| c_in(X1,c_Set_Oinsert(X4,X2,X3),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2865]) ).
cnf(c_0_2866_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_2866]) ).
cnf(c_0_2866_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_2866]) ).
cnf(c_0_2866_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_2866]) ).
cnf(c_0_2867_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_2867]) ).
cnf(c_0_2867_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_2867]) ).
cnf(c_0_2867_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_2867]) ).
cnf(c_0_2869_0,axiom,
( c_in(v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(X1,X2),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_Arrow__Order__Mirabelle_Odictator(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2869]) ).
cnf(c_0_2869_1,axiom,
( c_Arrow__Order__Mirabelle_Odictator(X1,X2)
| c_in(v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(X1,X2),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
inference(literals_permutation,[status(thm)],[c_0_2869]) ).
cnf(c_0_2870_0,axiom,
( c_Wellfounded_Oacyclic(X3,X2)
| ~ c_Wellfounded_Oacyclic(X1,X2)
| ~ c_lessequals(X3,X1,tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2870]) ).
cnf(c_0_2870_1,axiom,
( ~ c_Wellfounded_Oacyclic(X1,X2)
| c_Wellfounded_Oacyclic(X3,X2)
| ~ c_lessequals(X3,X1,tc_fun(tc_prod(X2,X2),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2870]) ).
cnf(c_0_2870_2,axiom,
( ~ c_lessequals(X3,X1,tc_fun(tc_prod(X2,X2),tc_bool))
| ~ c_Wellfounded_Oacyclic(X1,X2)
| c_Wellfounded_Oacyclic(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2870]) ).
cnf(c_0_2871_0,axiom,
( c_Relation_Oantisym(X1,X3)
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool))
| ~ c_Relation_Oantisym(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2871]) ).
cnf(c_0_2871_1,axiom,
( ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool))
| c_Relation_Oantisym(X1,X3)
| ~ c_Relation_Oantisym(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2871]) ).
cnf(c_0_2871_2,axiom,
( ~ c_Relation_Oantisym(X2,X3)
| ~ c_lessequals(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool))
| c_Relation_Oantisym(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2871]) ).
cnf(c_0_2872_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_2872]) ).
cnf(c_0_2872_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_2872]) ).
cnf(c_0_2872_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_2872]) ).
cnf(c_0_2873_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_2873]) ).
cnf(c_0_2873_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_2873]) ).
cnf(c_0_2873_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_2873]) ).
cnf(c_0_2876_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_2876]) ).
cnf(c_0_2876_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_2876]) ).
cnf(c_0_2876_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_2876]) ).
cnf(c_0_2876_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_2876]) ).
cnf(c_0_2877_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_2877]) ).
cnf(c_0_2877_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_2877]) ).
cnf(c_0_2877_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_2877]) ).
cnf(c_0_2877_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_2877]) ).
cnf(c_0_2878_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_2878]) ).
cnf(c_0_2878_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_2878]) ).
cnf(c_0_2879_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_2879]) ).
cnf(c_0_2879_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_2879]) ).
cnf(c_0_2880_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2880]) ).
cnf(c_0_2880_1,axiom,
( ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2880]) ).
cnf(c_0_2885_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_2885]) ).
cnf(c_0_2885_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_2885]) ).
cnf(c_0_2886_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_2886]) ).
cnf(c_0_2886_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_2886]) ).
cnf(c_0_2887_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_2887]) ).
cnf(c_0_2887_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_2887]) ).
cnf(c_0_2888_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_2888]) ).
cnf(c_0_2888_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_2888]) ).
cnf(c_0_2889_0,axiom,
( c_Relation_Ototal__on(X1,hAPP(c_Relation_Oconverse(X3,X3),X2),X3)
| ~ c_Relation_Ototal__on(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2889]) ).
cnf(c_0_2889_1,axiom,
( ~ c_Relation_Ototal__on(X1,X2,X3)
| c_Relation_Ototal__on(X1,hAPP(c_Relation_Oconverse(X3,X3),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2889]) ).
cnf(c_0_2890_0,axiom,
( c_Relation_Orefl__on(X1,hAPP(c_Relation_Oconverse(X3,X3),X2),X3)
| ~ c_Relation_Orefl__on(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2890]) ).
cnf(c_0_2890_1,axiom,
( ~ c_Relation_Orefl__on(X1,X2,X3)
| c_Relation_Orefl__on(X1,hAPP(c_Relation_Oconverse(X3,X3),X2),X3) ),
inference(literals_permutation,[status(thm)],[c_0_2890]) ).
cnf(c_0_2892_0,axiom,
( ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2892]) ).
cnf(c_0_2892_1,axiom,
( ~ hBOOL(hAPP(X3,X1))
| ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2892]) ).
cnf(c_0_2893_0,axiom,
( c_in(v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2(X1),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_Arrow__Order__Mirabelle_Ounanimity(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2893]) ).
cnf(c_0_2893_1,axiom,
( c_Arrow__Order__Mirabelle_Ounanimity(X1)
| c_in(v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2(X1),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
inference(literals_permutation,[status(thm)],[c_0_2893]) ).
cnf(c_0_2894_0,axiom,
( c_in(v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X1),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2894]) ).
cnf(c_0_2894_1,axiom,
( c_Arrow__Order__Mirabelle_OIIA(X1)
| c_in(v_sko__Arrow__Order__Mirabelle__XIIA__def__2(X1),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
inference(literals_permutation,[status(thm)],[c_0_2894]) ).
cnf(c_0_2895_0,axiom,
( c_in(v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X1),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(literals_permutation,[status(thm)],[c_0_2895]) ).
cnf(c_0_2895_1,axiom,
( c_Arrow__Order__Mirabelle_OIIA(X1)
| c_in(v_sko__Arrow__Order__Mirabelle__XIIA__def__3(X1),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
inference(literals_permutation,[status(thm)],[c_0_2895]) ).
cnf(c_0_2897_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool))
| c_Relation_ORange(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2897]) ).
cnf(c_0_2897_1,axiom,
( c_Relation_ORange(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2897]) ).
cnf(c_0_2898_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool))
| c_Relation_ODomain(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2898]) ).
cnf(c_0_2898_1,axiom,
( c_Relation_ODomain(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2898]) ).
cnf(c_0_2900_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_2900]) ).
cnf(c_0_2900_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_2900]) ).
cnf(c_0_2901_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_2901]) ).
cnf(c_0_2901_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_2901]) ).
cnf(c_0_2902_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_2902]) ).
cnf(c_0_2902_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_2902]) ).
cnf(c_0_2903_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_2903]) ).
cnf(c_0_2903_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_2903]) ).
cnf(c_0_2904_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_2904]) ).
cnf(c_0_2904_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_2904]) ).
cnf(c_0_2905_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_2905]) ).
cnf(c_0_2905_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_2905]) ).
cnf(c_0_2905_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_2905]) ).
cnf(c_0_2906_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_2906]) ).
cnf(c_0_2906_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_2906]) ).
cnf(c_0_2906_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_2906]) ).
cnf(c_0_2909_0,axiom,
( hBOOL(hAPP(X3,X1))
| ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2909]) ).
cnf(c_0_2909_1,axiom,
( ~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| hBOOL(hAPP(X3,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2909]) ).
cnf(c_0_2911_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2911]) ).
cnf(c_0_2911_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2911]) ).
cnf(c_0_2912_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2912]) ).
cnf(c_0_2912_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X3,X1,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2912]) ).
cnf(c_0_2917_0,axiom,
( c_in(X1,X2,X3)
| c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(literals_permutation,[status(thm)],[c_0_2917]) ).
cnf(c_0_2917_1,axiom,
( c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2917]) ).
cnf(c_0_2918_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_2918]) ).
cnf(c_0_2918_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_2918]) ).
cnf(c_0_2919_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_2919]) ).
cnf(c_0_2919_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_2919]) ).
cnf(c_0_2920_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_2920]) ).
cnf(c_0_2920_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_2920]) ).
cnf(c_0_2920_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_2920]) ).
cnf(c_0_2920_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_2920]) ).
cnf(c_0_2921_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_2921]) ).
cnf(c_0_2921_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_2921]) ).
cnf(c_0_2921_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_2921]) ).
cnf(c_0_2921_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_2921]) ).
cnf(c_0_2922_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_2922]) ).
cnf(c_0_2922_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_2922]) ).
cnf(c_0_2922_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_2922]) ).
cnf(c_0_2922_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_2922]) ).
cnf(c_0_2930_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_2930]) ).
cnf(c_0_2930_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_2930]) ).
cnf(c_0_2931_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_2931]) ).
cnf(c_0_2931_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_2931]) ).
cnf(c_0_2932_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_2932]) ).
cnf(c_0_2932_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_2932]) ).
cnf(c_0_2933_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_2933]) ).
cnf(c_0_2933_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_2933]) ).
cnf(c_0_2934_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_2934]) ).
cnf(c_0_2934_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_2934]) ).
cnf(c_0_2935_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_2935]) ).
cnf(c_0_2935_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_2935]) ).
cnf(c_0_2936_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_2936]) ).
cnf(c_0_2936_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_2936]) ).
cnf(c_0_2937_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_2937]) ).
cnf(c_0_2937_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_2937]) ).
cnf(c_0_2938_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_2938]) ).
cnf(c_0_2938_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_2938]) ).
cnf(c_0_2939_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_2939]) ).
cnf(c_0_2939_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_2939]) ).
cnf(c_0_2947_0,axiom,
( c_Relation_Oantisym(X2,X1)
| ~ c_Relation_Oantisym(hAPP(c_Relation_Oconverse(X1,X1),X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2947]) ).
cnf(c_0_2947_1,axiom,
( ~ c_Relation_Oantisym(hAPP(c_Relation_Oconverse(X1,X1),X2),X1)
| c_Relation_Oantisym(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2947]) ).
cnf(c_0_2948_0,axiom,
( c_Relation_Osym(X2,X1)
| ~ c_Relation_Osym(hAPP(c_Relation_Oconverse(X1,X1),X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2948]) ).
cnf(c_0_2948_1,axiom,
( ~ c_Relation_Osym(hAPP(c_Relation_Oconverse(X1,X1),X2),X1)
| c_Relation_Osym(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2948]) ).
cnf(c_0_2949_0,axiom,
( c_Wellfounded_Oacyclic(X2,X1)
| ~ c_Wellfounded_Oacyclic(hAPP(c_Relation_Oconverse(X1,X1),X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_2949]) ).
cnf(c_0_2949_1,axiom,
( ~ c_Wellfounded_Oacyclic(hAPP(c_Relation_Oconverse(X1,X1),X2),X1)
| c_Wellfounded_Oacyclic(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_2949]) ).
cnf(c_0_2956_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_2956]) ).
cnf(c_0_2956_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_2956]) ).
cnf(c_0_2956_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_2956]) ).
cnf(c_0_2957_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_2957]) ).
cnf(c_0_2957_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_2957]) ).
cnf(c_0_2957_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_2957]) ).
cnf(c_0_2958_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_2958]) ).
cnf(c_0_2958_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_2958]) ).
cnf(c_0_2958_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_2958]) ).
cnf(c_0_2959_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_2959]) ).
cnf(c_0_2959_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_2959]) ).
cnf(c_0_2959_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_2959]) ).
cnf(c_0_2960_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_2960]) ).
cnf(c_0_2960_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_2960]) ).
cnf(c_0_2960_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_2960]) ).
cnf(c_0_2961_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_2961]) ).
cnf(c_0_2961_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_2961]) ).
cnf(c_0_2961_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_2961]) ).
cnf(c_0_2963_0,axiom,
( c_Set_Oinsert(X1,X2,X3) = X2
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2963]) ).
cnf(c_0_2963_1,axiom,
( ~ c_in(X1,X2,X3)
| c_Set_Oinsert(X1,X2,X3) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2963]) ).
cnf(c_0_2964_0,axiom,
( c_Relation_Orefl__on(X1,X2,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2964]) ).
cnf(c_0_2964_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Relation_Orefl__on(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2964]) ).
cnf(c_0_2965_0,axiom,
( c_Arrow__Order__Mirabelle_Odictator(X1,X2)
| hAPP(X1,v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(X1,X2)) != hAPP(v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2965]) ).
cnf(c_0_2965_1,axiom,
( hAPP(X1,v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(X1,X2)) != hAPP(v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(X1,X2),X2)
| c_Arrow__Order__Mirabelle_Odictator(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2965]) ).
cnf(c_0_2975_0,axiom,
( c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2975]) ).
cnf(c_0_2975_1,axiom,
( c_lessequals(X2,X1,X3)
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) ),
inference(literals_permutation,[status(thm)],[c_0_2975]) ).
cnf(c_0_2975_2,axiom,
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X2,X1,X3)
| c_lessequals(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2975]) ).
cnf(c_0_2976_0,axiom,
( hBOOL(hAPP(X2,X1))
| ~ c_in(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2976]) ).
cnf(c_0_2976_1,axiom,
( ~ c_in(X1,X2,X3)
| hBOOL(hAPP(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_2976]) ).
cnf(c_0_2977_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_2977]) ).
cnf(c_0_2977_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_2977]) ).
cnf(c_0_2978_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_2978]) ).
cnf(c_0_2978_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_2978]) ).
cnf(c_0_2979_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_2979]) ).
cnf(c_0_2979_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_2979]) ).
cnf(c_0_2980_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_2980]) ).
cnf(c_0_2980_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_2980]) ).
cnf(c_0_2981_0,axiom,
( c_Relation_Oantisym(hAPP(c_Relation_Oconverse(X2,X2),X1),X2)
| ~ c_Relation_Oantisym(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2981]) ).
cnf(c_0_2981_1,axiom,
( ~ c_Relation_Oantisym(X1,X2)
| c_Relation_Oantisym(hAPP(c_Relation_Oconverse(X2,X2),X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2981]) ).
cnf(c_0_2982_0,axiom,
( c_Relation_Osym(hAPP(c_Relation_Oconverse(X2,X2),X1),X2)
| ~ c_Relation_Osym(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2982]) ).
cnf(c_0_2982_1,axiom,
( ~ c_Relation_Osym(X1,X2)
| c_Relation_Osym(hAPP(c_Relation_Oconverse(X2,X2),X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2982]) ).
cnf(c_0_2983_0,axiom,
( c_Wellfounded_Oacyclic(hAPP(c_Relation_Oconverse(X2,X2),X1),X2)
| ~ c_Wellfounded_Oacyclic(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2983]) ).
cnf(c_0_2983_1,axiom,
( ~ c_Wellfounded_Oacyclic(X1,X2)
| c_Wellfounded_Oacyclic(hAPP(c_Relation_Oconverse(X2,X2),X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2983]) ).
cnf(c_0_2986_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2986]) ).
cnf(c_0_2986_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2) != c_Orderings_Obot__class_Obot(X2)
| X1 = c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2986]) ).
cnf(c_0_2986_2,axiom,
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2) != c_Orderings_Obot__class_Obot(X2)
| X1 = c_Orderings_Obot__class_Obot(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2986]) ).
cnf(c_0_2987_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2) != c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2987]) ).
cnf(c_0_2987_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2) != c_Orderings_Obot__class_Obot(X2)
| X1 = c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2987]) ).
cnf(c_0_2987_2,axiom,
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2) != c_Orderings_Obot__class_Obot(X2)
| X1 = c_Orderings_Obot__class_Obot(X2) ),
inference(literals_permutation,[status(thm)],[c_0_2987]) ).
cnf(c_0_2988_0,axiom,
( c_in(X3,c_Wellfounded_Oacc(X1,X2),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2988]) ).
cnf(c_0_2988_1,axiom,
( ~ c_Wellfounded_Owf(X1,X2)
| c_in(X3,c_Wellfounded_Oacc(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_2988]) ).
cnf(c_0_2989_0,axiom,
( c_in(X2,X1,X3)
| ~ hBOOL(hAPP(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_2989]) ).
cnf(c_0_2989_1,axiom,
( ~ hBOOL(hAPP(X1,X2))
| c_in(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2989]) ).
cnf(c_0_2990_0,axiom,
( c_Relation_Osym(X2,X3)
| ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2990]) ).
cnf(c_0_2990_1,axiom,
( ~ c_Equiv__Relations_Oequiv(X1,X2,X3)
| c_Relation_Osym(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2990]) ).
cnf(c_0_2991_0,axiom,
( X1 = X2
| ~ c_fequal(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_2991]) ).
cnf(c_0_2991_1,axiom,
( ~ c_fequal(X1,X2,X3)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_2991]) ).
cnf(c_0_2997_0,axiom,
( c_Relation_Osym(X1,X2)
| hAPP(c_Relation_Oconverse(X2,X2),X1) != X1 ),
inference(literals_permutation,[status(thm)],[c_0_2997]) ).
cnf(c_0_2997_1,axiom,
( hAPP(c_Relation_Oconverse(X2,X2),X1) != X1
| c_Relation_Osym(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_2997]) ).
cnf(c_0_3002_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X1),X2,X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3002]) ).
cnf(c_0_3002_1,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X1),X2,X1) = c_Orderings_Obot__class_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3002]) ).
cnf(c_0_3003_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(X2),X2) = c_Orderings_Obot__class_Obot(X2)
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3003]) ).
cnf(c_0_3003_1,axiom,
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(X2),X2) = c_Orderings_Obot__class_Obot(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3003]) ).
cnf(c_0_3004_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X1),X2,X1) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3004]) ).
cnf(c_0_3004_1,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X1),X2,X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_3004]) ).
cnf(c_0_3005_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(X2),X2) = X1
| ~ class_Lattices_Obounded__lattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3005]) ).
cnf(c_0_3005_1,axiom,
( ~ class_Lattices_Obounded__lattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(X2),X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3005]) ).
cnf(c_0_3006_0,axiom,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3006]) ).
cnf(c_0_3006_1,axiom,
( ~ class_Orderings_Obot(X1)
| c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_3006]) ).
cnf(c_0_3007_0,axiom,
( hAPP(c_Relation_Oconverse(X2,X2),X1) = X1
| ~ c_Relation_Osym(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3007]) ).
cnf(c_0_3007_1,axiom,
( ~ c_Relation_Osym(X1,X2)
| hAPP(c_Relation_Oconverse(X2,X2),X1) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3007]) ).
cnf(c_0_3008_0,axiom,
( c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X1,X2),X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3008]) ).
cnf(c_0_3008_1,axiom,
( ~ c_Wellfounded_Owf(X1,X2)
| c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3008]) ).
cnf(c_0_3009_0,axiom,
( c_Relation_Osym(c_Transitive__Closure_Ortrancl(X1,X2),X2)
| ~ c_Relation_Osym(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3009]) ).
cnf(c_0_3009_1,axiom,
( ~ c_Relation_Osym(X1,X2)
| c_Relation_Osym(c_Transitive__Closure_Ortrancl(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3009]) ).
cnf(c_0_3010_0,axiom,
( c_Relation_Osym(c_Transitive__Closure_Otrancl(X1,X2),X2)
| ~ c_Relation_Osym(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3010]) ).
cnf(c_0_3010_1,axiom,
( ~ c_Relation_Osym(X1,X2)
| c_Relation_Osym(c_Transitive__Closure_Otrancl(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3010]) ).
cnf(c_0_3011_0,axiom,
( c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X1,X2),X2)
| ~ c_Wellfounded_Oacyclic(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3011]) ).
cnf(c_0_3011_1,axiom,
( ~ c_Wellfounded_Oacyclic(X1,X2)
| c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_3011]) ).
cnf(c_0_3012_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1,X1,X2) = X1
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3012]) ).
cnf(c_0_3012_1,axiom,
( ~ class_Lattices_Olower__semilattice(X2)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X1,X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3012]) ).
cnf(c_0_3013_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X2) = X1
| ~ class_Lattices_Oupper__semilattice(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3013]) ).
cnf(c_0_3013_1,axiom,
( ~ class_Lattices_Oupper__semilattice(X2)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X2) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_3013]) ).
cnf(c_0_3014_0,axiom,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Opreorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3014]) ).
cnf(c_0_3014_1,axiom,
( ~ class_Orderings_Opreorder(X2)
| c_lessequals(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3014]) ).
cnf(c_0_3015_0,axiom,
( c_lessequals(X1,X1,X2)
| ~ class_Orderings_Oorder(X2) ),
inference(literals_permutation,[status(thm)],[c_0_3015]) ).
cnf(c_0_3015_1,axiom,
( ~ class_Orderings_Oorder(X2)
| c_lessequals(X1,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3015]) ).
cnf(c_0_3024_0,axiom,
( class_HOL_Oord(tc_fun(X2,X1))
| ~ class_HOL_Oord(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3024]) ).
cnf(c_0_3024_1,axiom,
( ~ class_HOL_Oord(X1)
| class_HOL_Oord(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3024]) ).
cnf(c_0_3025_0,axiom,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3025]) ).
cnf(c_0_3025_1,axiom,
( ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3025]) ).
cnf(c_0_3026_0,axiom,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3026]) ).
cnf(c_0_3026_1,axiom,
( ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3026]) ).
cnf(c_0_3027_0,axiom,
( class_Lattices_Olattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3027]) ).
cnf(c_0_3027_1,axiom,
( ~ class_Lattices_Olattice(X1)
| class_Lattices_Olattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3027]) ).
cnf(c_0_3028_0,axiom,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3028]) ).
cnf(c_0_3028_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3028]) ).
cnf(c_0_3029_0,axiom,
( class_Lattices_Obounded__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3029]) ).
cnf(c_0_3029_1,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| class_Lattices_Obounded__lattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3029]) ).
cnf(c_0_3030_0,axiom,
( class_Lattices_Odistrib__lattice(tc_fun(X2,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3030]) ).
cnf(c_0_3030_1,axiom,
( ~ class_Lattices_Odistrib__lattice(X1)
| class_Lattices_Odistrib__lattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3030]) ).
cnf(c_0_3031_0,axiom,
( class_Lattices_Olower__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3031]) ).
cnf(c_0_3031_1,axiom,
( ~ class_Lattices_Olattice(X1)
| class_Lattices_Olower__semilattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3031]) ).
cnf(c_0_3032_0,axiom,
( class_Lattices_Oupper__semilattice(tc_fun(X2,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(literals_permutation,[status(thm)],[c_0_3032]) ).
cnf(c_0_3032_1,axiom,
( ~ class_Lattices_Olattice(X1)
| class_Lattices_Oupper__semilattice(tc_fun(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_3032]) ).
cnf(c_0_3033_0,axiom,
( c_Wellfounded_Oacyclic(X1,X2)
| ~ c_Wellfounded_Owf(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3033]) ).
cnf(c_0_3033_1,axiom,
( ~ c_Wellfounded_Owf(X1,X2)
| c_Wellfounded_Oacyclic(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_3033]) ).
cnf(c_0_2675_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(literals_permutation,[status(thm)],[c_0_2675]) ).
cnf(c_0_2676_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(literals_permutation,[status(thm)],[c_0_2676]) ).
cnf(c_0_2677_0,axiom,
~ c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X3,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(literals_permutation,[status(thm)],[c_0_2677]) ).
cnf(c_0_2678_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(literals_permutation,[status(thm)],[c_0_2678]) ).
cnf(c_0_2896_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
inference(literals_permutation,[status(thm)],[c_0_2896]) ).
cnf(c_0_2940_0,axiom,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
inference(literals_permutation,[status(thm)],[c_0_2940]) ).
cnf(c_0_2941_0,axiom,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
inference(literals_permutation,[status(thm)],[c_0_2941]) ).
cnf(c_0_2942_0,axiom,
~ c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
inference(literals_permutation,[status(thm)],[c_0_2942]) ).
cnf(c_0_2971_0,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oinsert(X2,X3,X1),
inference(literals_permutation,[status(thm)],[c_0_2971]) ).
cnf(c_0_2972_0,axiom,
c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2972]) ).
cnf(c_0_3047_0,axiom,
v_c____ != v_a____,
inference(literals_permutation,[status(thm)],[c_0_3047]) ).
cnf(c_0_3048_0,axiom,
v_c____ != v_b____,
inference(literals_permutation,[status(thm)],[c_0_3048]) ).
cnf(c_0_3049_0,axiom,
v_b____ != v_a____,
inference(literals_permutation,[status(thm)],[c_0_3049]) ).
cnf(c_0_2456_0,axiom,
c_Fun_Ocomp(X1,c_Fun_Ocomp(X2,X3,X4,X5,X6),X5,X7,X6) = c_Fun_Ocomp(c_Fun_Ocomp(X1,X2,X5,X7,X4),X3,X4,X7,X6),
inference(literals_permutation,[status(thm)],[c_0_2456]) ).
cnf(c_0_2457_0,axiom,
c_Relation_Orel__comp(c_Relation_Orel__comp(X1,X2,X3,X4,X5),X6,X3,X5,X7) = c_Relation_Orel__comp(X1,c_Relation_Orel__comp(X2,X6,X4,X5,X7),X3,X4,X7),
inference(literals_permutation,[status(thm)],[c_0_2457]) ).
cnf(c_0_2463_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,X2,X6,X4,X5),c_Relation_Orel__comp(X1,X3,X6,X4,X5),tc_fun(tc_prod(X6,X5),tc_bool)) = c_Relation_Orel__comp(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(tc_prod(X4,X5),tc_bool)),X6,X4,X5),
inference(literals_permutation,[status(thm)],[c_0_2463]) ).
cnf(c_0_2464_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X1,X5,X3,X4,X6),c_Relation_Orel__comp(X2,X5,X3,X4,X6),tc_fun(tc_prod(X3,X6),tc_bool)) = c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X5,X3,X4,X6),
inference(literals_permutation,[status(thm)],[c_0_2464]) ).
cnf(c_0_2468_0,axiom,
c_Set_Oinsert(c_Pair(X1,X4,X3,X6),c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X2,c_COMBK(c_Set_Oinsert(X4,X5,X6),tc_fun(X6,tc_bool),X3),X3,X6),c_Product__Type_OSigma(c_Set_Oinsert(X1,X2,X3),c_COMBK(X5,tc_fun(X6,tc_bool),X3),X3,X6),tc_fun(tc_prod(X3,X6),tc_bool)),tc_prod(X3,X6)) = c_Product__Type_OSigma(c_Set_Oinsert(X1,X2,X3),c_COMBK(c_Set_Oinsert(X4,X5,X6),tc_fun(X6,tc_bool),X3),X3,X6),
inference(literals_permutation,[status(thm)],[c_0_2468]) ).
cnf(c_0_2484_0,axiom,
c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(X5,X2),X4),hAPP(c_Relation_Oconverse(X1,X5),X3),X2,X5,X1) = hAPP(c_Relation_Oconverse(X1,X2),c_Relation_Orel__comp(X3,X4,X1,X5,X2)),
inference(literals_permutation,[status(thm)],[c_0_2484]) ).
cnf(c_0_2500_0,axiom,
c_lessequals(c_Relation_OImage(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),X4,X5),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X1,X2,X4,X5),c_Relation_OImage(X1,X3,X4,X5),tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2500]) ).
cnf(c_0_2502_0,axiom,
c_in(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
inference(literals_permutation,[status(thm)],[c_0_2502]) ).
cnf(c_0_2510_0,axiom,
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)) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_2510]) ).
cnf(c_0_2513_0,axiom,
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)) = c_Transitive__Closure_Otrancl(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_2513]) ).
cnf(c_0_2526_0,axiom,
hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
inference(literals_permutation,[status(thm)],[c_0_2526]) ).
cnf(c_0_2527_0,axiom,
hAPP(c_Fun_Ocomp(X1,X2,X4,X5,X6),X3) = hAPP(X1,hAPP(X2,X3)),
inference(literals_permutation,[status(thm)],[c_0_2527]) ).
cnf(c_0_2528_0,axiom,
c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),X1,X2,X2,X2) = c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2),
inference(literals_permutation,[status(thm)],[c_0_2528]) ).
cnf(c_0_2540_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X1,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),c_Product__Type_OSigma(X2,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),tc_fun(tc_prod(X3,X5),tc_bool)) = c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),
inference(literals_permutation,[status(thm)],[c_0_2540]) ).
cnf(c_0_2541_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(X1,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),c_Product__Type_OSigma(X2,c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),tc_fun(tc_prod(X3,X5),tc_bool)) = c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_COMBK(X4,tc_fun(X5,tc_bool),X3),X3,X5),
inference(literals_permutation,[status(thm)],[c_0_2541]) ).
cnf(c_0_2556_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2556]) ).
cnf(c_0_2575_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),c_Relation_OField(X4,X3),tc_fun(X3,tc_bool)) = c_Relation_OField(c_Set_Oinsert(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)),X3),
inference(literals_permutation,[status(thm)],[c_0_2575]) ).
cnf(c_0_2591_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X1,X5,X3,X4),c_Relation_OImage(X2,X5,X3,X4),tc_fun(X4,tc_bool)) = c_Relation_OImage(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X5,X3,X4),
inference(literals_permutation,[status(thm)],[c_0_2591]) ).
cnf(c_0_2601_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X1,X4,X3,X5),c_Product__Type_OSigma(X2,X4,X3,X5),tc_fun(tc_prod(X3,X5),tc_bool)) = c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,X3,X5),
inference(literals_permutation,[status(thm)],[c_0_2601]) ).
cnf(c_0_2602_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Product__Type_OSigma(X1,X4,X3,X5),c_Product__Type_OSigma(X2,X4,X3,X5),tc_fun(tc_prod(X3,X5),tc_bool)) = c_Product__Type_OSigma(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,X3,X5),
inference(literals_permutation,[status(thm)],[c_0_2602]) ).
cnf(c_0_2614_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X1,X2,X4,X5),c_Relation_OImage(X1,X3,X4,X5),tc_fun(X5,tc_bool)) = c_Relation_OImage(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),X4,X5),
inference(literals_permutation,[status(thm)],[c_0_2614]) ).
cnf(c_0_2615_0,axiom,
c_Relation_Orel__comp(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_bool)),X4,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X3),tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2615]) ).
cnf(c_0_2616_0,axiom,
c_Relation_Orel__comp(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_bool)),X3,X1,X2,X4) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X4),tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2616]) ).
cnf(c_0_2625_0,axiom,
c_Relation_ORange(c_Set_Oinsert(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)),X3,X4) = c_Set_Oinsert(X2,c_Relation_ORange(X5,X3,X4),X4),
inference(literals_permutation,[status(thm)],[c_0_2625]) ).
cnf(c_0_2626_0,axiom,
c_Relation_ODomain(c_Set_Oinsert(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)),X3,X4) = c_Set_Oinsert(X1,c_Relation_ODomain(X5,X3,X4),X3),
inference(literals_permutation,[status(thm)],[c_0_2626]) ).
cnf(c_0_2635_0,axiom,
c_lessequals(c_Relation_ORange(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(X1,X3,X4),c_Relation_ORange(X2,X3,X4),tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2635]) ).
cnf(c_0_2636_0,axiom,
c_lessequals(c_Relation_ODomain(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X1,X3,X4),c_Relation_ODomain(X2,X3,X4),tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2636]) ).
cnf(c_0_2637_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(literals_permutation,[status(thm)],[c_0_2637]) ).
cnf(c_0_2639_0,axiom,
c_Relation_Orel__comp(X1,c_Transitive__Closure_Ortrancl(X1,X2),X2,X2,X2) = c_Transitive__Closure_Otrancl(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_2639]) ).
cnf(c_0_2640_0,axiom,
c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X1,X2),X1,X2,X2,X2) = c_Transitive__Closure_Otrancl(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_2640]) ).
cnf(c_0_2641_0,axiom,
c_Relation_Orel__comp(X1,c_Relation_OId(X2),X3,X2,X2) = X1,
inference(literals_permutation,[status(thm)],[c_0_2641]) ).
cnf(c_0_2642_0,axiom,
c_Relation_Orel__comp(c_Relation_OId(X1),X2,X1,X1,X3) = X2,
inference(literals_permutation,[status(thm)],[c_0_2642]) ).
cnf(c_0_2652_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(literals_permutation,[status(thm)],[c_0_2652]) ).
cnf(c_0_2665_0,axiom,
c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2),tc_fun(tc_prod(X2,X2),tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2665]) ).
cnf(c_0_2671_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(literals_permutation,[status(thm)],[c_0_2671]) ).
cnf(c_0_2684_0,axiom,
hAPP(c_Relation_Oconverse(X1,X1),c_Relation_Oinv__image(X2,X3,X4,X1)) = c_Relation_Oinv__image(hAPP(c_Relation_Oconverse(X4,X4),X2),X3,X4,X1),
inference(literals_permutation,[status(thm)],[c_0_2684]) ).
cnf(c_0_2699_0,axiom,
c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X1,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_fun(tc_prod(X2,X2),tc_bool)),X2) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(tc_prod(X2,X2),tc_bool)),X2),
inference(literals_permutation,[status(thm)],[c_0_2699]) ).
cnf(c_0_2706_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2706]) ).
cnf(c_0_2707_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X4,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(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_2707]) ).
cnf(c_0_2708_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X4,tc_fun(X3,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(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_2708]) ).
cnf(c_0_2709_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,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(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2709]) ).
cnf(c_0_2710_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X1,X3,X4),c_Relation_ORange(X2,X3,X4),tc_fun(X4,tc_bool)) = c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4),
inference(literals_permutation,[status(thm)],[c_0_2710]) ).
cnf(c_0_2711_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X1,X3,X4),c_Relation_ODomain(X2,X3,X4),tc_fun(X3,tc_bool)) = c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X4),tc_bool)),X3,X4),
inference(literals_permutation,[status(thm)],[c_0_2711]) ).
cnf(c_0_2712_0,axiom,
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_2712]) ).
cnf(c_0_2713_0,axiom,
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_2713]) ).
cnf(c_0_2720_0,axiom,
c_Product__Type_OSigma(X1,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool),X3),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X2),tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2720]) ).
cnf(c_0_2722_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Relation_Oconverse(X1,X2),X3),hAPP(c_Relation_Oconverse(X1,X2),X4),tc_fun(tc_prod(X2,X1),tc_bool)) = hAPP(c_Relation_Oconverse(X1,X2),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,tc_fun(tc_prod(X1,X2),tc_bool))),
inference(literals_permutation,[status(thm)],[c_0_2722]) ).
cnf(c_0_2723_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Relation_Oconverse(X1,X2),X3),hAPP(c_Relation_Oconverse(X1,X2),X4),tc_fun(tc_prod(X2,X1),tc_bool)) = hAPP(c_Relation_Oconverse(X1,X2),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,tc_fun(tc_prod(X1,X2),tc_bool))),
inference(literals_permutation,[status(thm)],[c_0_2723]) ).
cnf(c_0_2724_0,axiom,
c_in(c_Pair(X1,X1,X2,X2),c_Relation_OId(X2),tc_prod(X2,X2)),
inference(literals_permutation,[status(thm)],[c_0_2724]) ).
cnf(c_0_2725_0,axiom,
c_in(c_Pair(X1,X1,X2,X2),c_Relation_OId(X2),tc_prod(X2,X2)),
inference(literals_permutation,[status(thm)],[c_0_2725]) ).
cnf(c_0_2730_0,axiom,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),
inference(literals_permutation,[status(thm)],[c_0_2730]) ).
cnf(c_0_2733_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X1,X2,X3),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),
inference(literals_permutation,[status(thm)],[c_0_2733]) ).
cnf(c_0_2743_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2743]) ).
cnf(c_0_2744_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(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_2744]) ).
cnf(c_0_2745_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2745]) ).
cnf(c_0_2746_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X4,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2746]) ).
cnf(c_0_2763_0,axiom,
c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X1,hAPP(c_Relation_Oconverse(X2,X2),X1),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
inference(literals_permutation,[status(thm)],[c_0_2763]) ).
cnf(c_0_2764_0,axiom,
c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X1,hAPP(c_Relation_Oconverse(X2,X2),X1),tc_fun(tc_prod(X2,X2),tc_bool)),X2),
inference(literals_permutation,[status(thm)],[c_0_2764]) ).
cnf(c_0_2771_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OField(X1,X3),c_Relation_OField(X2,X3),tc_fun(X3,tc_bool)) = c_Relation_OField(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(tc_prod(X3,X3),tc_bool)),X3),
inference(literals_permutation,[status(thm)],[c_0_2771]) ).
cnf(c_0_2773_0,axiom,
c_Set_Oinsert(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X4,tc_bool)),X4) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Set_Oinsert(X2,X3,X4),tc_fun(X4,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2773]) ).
cnf(c_0_2774_0,axiom,
c_Set_Oinsert(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X4,tc_fun(X3,tc_bool)),X3) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2774]) ).
cnf(c_0_2782_0,axiom,
c_Product__Type_OSigma(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X3),tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2782]) ).
cnf(c_0_2789_0,axiom,
c_Relation_OImage(c_Relation_OId__on(X1,X2),X3,X2,X2) = c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2789]) ).
cnf(c_0_2794_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X2,tc_fun(X3,tc_bool)) = c_Set_Oinsert(X1,X2,X3),
inference(literals_permutation,[status(thm)],[c_0_2794]) ).
cnf(c_0_2814_0,axiom,
c_Relation_OImage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2814]) ).
cnf(c_0_2815_0,axiom,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,X3,X4),X4) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,X3,X4),X4),
inference(literals_permutation,[status(thm)],[c_0_2815]) ).
cnf(c_0_2830_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2830]) ).
cnf(c_0_2831_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2831]) ).
cnf(c_0_2834_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X1,X2,X2),c_Relation_ORange(X1,X2,X2),tc_fun(X2,tc_bool)) = c_Relation_OField(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_2834]) ).
cnf(c_0_2835_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(literals_permutation,[status(thm)],[c_0_2835]) ).
cnf(c_0_2836_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(literals_permutation,[status(thm)],[c_0_2836]) ).
cnf(c_0_2843_0,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X2,tc_fun(tc_prod(X1,X1),tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2843]) ).
cnf(c_0_2845_0,axiom,
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)) = c_Relation_OField(v_r,t_a),
inference(literals_permutation,[status(thm)],[c_0_2845]) ).
cnf(c_0_2850_0,axiom,
c_in(X1,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),
inference(literals_permutation,[status(thm)],[c_0_2850]) ).
cnf(c_0_2857_0,axiom,
c_Relation_Orefl__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
inference(literals_permutation,[status(thm)],[c_0_2857]) ).
cnf(c_0_2862_0,axiom,
c_Relation_OImage(c_Relation_OId(X1),X2,X1,X1) = X2,
inference(literals_permutation,[status(thm)],[c_0_2862]) ).
cnf(c_0_2863_0,axiom,
c_Transitive__Closure_Otrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2863]) ).
cnf(c_0_2868_0,axiom,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
inference(literals_permutation,[status(thm)],[c_0_2868]) ).
cnf(c_0_2874_0,axiom,
c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_bool)),X1,X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2874]) ).
cnf(c_0_2875_0,axiom,
c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_bool)),X1,X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2875]) ).
cnf(c_0_2881_0,axiom,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X2,tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2881]) ).
cnf(c_0_2882_0,axiom,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)),X1,tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2882]) ).
cnf(c_0_2883_0,axiom,
c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2883]) ).
cnf(c_0_2884_0,axiom,
c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2884]) ).
cnf(c_0_2891_0,axiom,
c_Set_Oinsert(X1,c_Set_Oinsert(X1,X2,X3),X3) = c_Set_Oinsert(X1,X2,X3),
inference(literals_permutation,[status(thm)],[c_0_2891]) ).
cnf(c_0_2899_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2899]) ).
cnf(c_0_2907_0,axiom,
c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
inference(literals_permutation,[status(thm)],[c_0_2907]) ).
cnf(c_0_2908_0,axiom,
c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
inference(literals_permutation,[status(thm)],[c_0_2908]) ).
cnf(c_0_2910_0,axiom,
c_Relation_OField(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2910]) ).
cnf(c_0_2913_0,axiom,
c_Relation_ODomain(hAPP(c_Relation_Oconverse(X2,X3),X1),X3,X2) = c_Relation_ORange(X1,X2,X3),
inference(literals_permutation,[status(thm)],[c_0_2913]) ).
cnf(c_0_2914_0,axiom,
c_Relation_ODomain(hAPP(c_Relation_Oconverse(X1,X2),X3),X2,X1) = c_Relation_ORange(X3,X1,X2),
inference(literals_permutation,[status(thm)],[c_0_2914]) ).
cnf(c_0_2915_0,axiom,
c_Relation_ORange(hAPP(c_Relation_Oconverse(X1,X2),X3),X2,X1) = c_Relation_ODomain(X3,X1,X2),
inference(literals_permutation,[status(thm)],[c_0_2915]) ).
cnf(c_0_2916_0,axiom,
c_lessequals(X1,c_Set_Oinsert(X2,X1,X3),tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2916]) ).
cnf(c_0_2923_0,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2923]) ).
cnf(c_0_2924_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(literals_permutation,[status(thm)],[c_0_2924]) ).
cnf(c_0_2925_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(literals_permutation,[status(thm)],[c_0_2925]) ).
cnf(c_0_2926_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(literals_permutation,[status(thm)],[c_0_2926]) ).
cnf(c_0_2927_0,axiom,
c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1) = c_Relation_OId(X1),
inference(literals_permutation,[status(thm)],[c_0_2927]) ).
cnf(c_0_2928_0,axiom,
c_Relation_Oantisym(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
inference(literals_permutation,[status(thm)],[c_0_2928]) ).
cnf(c_0_2929_0,axiom,
c_Wellfounded_Owf(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
inference(literals_permutation,[status(thm)],[c_0_2929]) ).
cnf(c_0_2943_0,axiom,
c_Relation_ODomain(hAPP(c_Relation_Oconverse(t_a,t_b),v_r),t_b,t_a) = c_Relation_ORange(v_r,t_a,t_b),
inference(literals_permutation,[status(thm)],[c_0_2943]) ).
cnf(c_0_2944_0,axiom,
c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
inference(literals_permutation,[status(thm)],[c_0_2944]) ).
cnf(c_0_2945_0,axiom,
c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
inference(literals_permutation,[status(thm)],[c_0_2945]) ).
cnf(c_0_2946_0,axiom,
c_in(X1,c_Set_Oinsert(X1,X2,X3),X3),
inference(literals_permutation,[status(thm)],[c_0_2946]) ).
cnf(c_0_2950_0,axiom,
c_Transitive__Closure_Ortrancl(hAPP(c_Relation_Oconverse(X1,X1),X2),X1) = hAPP(c_Relation_Oconverse(X1,X1),c_Transitive__Closure_Ortrancl(X2,X1)),
inference(literals_permutation,[status(thm)],[c_0_2950]) ).
cnf(c_0_2951_0,axiom,
c_Transitive__Closure_Otrancl(hAPP(c_Relation_Oconverse(X1,X1),X2),X1) = hAPP(c_Relation_Oconverse(X1,X1),c_Transitive__Closure_Otrancl(X2,X1)),
inference(literals_permutation,[status(thm)],[c_0_2951]) ).
cnf(c_0_2952_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2952]) ).
cnf(c_0_2953_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2953]) ).
cnf(c_0_2954_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2954]) ).
cnf(c_0_2955_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_fun(X3,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_fun(X3,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2955]) ).
cnf(c_0_2962_0,axiom,
c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)) = c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
inference(literals_permutation,[status(thm)],[c_0_2962]) ).
cnf(c_0_2966_0,axiom,
c_Relation_ORange(c_Transitive__Closure_Otrancl(X1,X2),X2,X2) = c_Relation_ORange(X1,X2,X2),
inference(literals_permutation,[status(thm)],[c_0_2966]) ).
cnf(c_0_2967_0,axiom,
c_Relation_ODomain(c_Transitive__Closure_Otrancl(X1,X2),X2,X2) = c_Relation_ODomain(X1,X2,X2),
inference(literals_permutation,[status(thm)],[c_0_2967]) ).
cnf(c_0_2968_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
inference(literals_permutation,[status(thm)],[c_0_2968]) ).
cnf(c_0_2969_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) = X2,
inference(literals_permutation,[status(thm)],[c_0_2969]) ).
cnf(c_0_2970_0,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_2970]) ).
cnf(c_0_2973_0,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
inference(literals_permutation,[status(thm)],[c_0_2973]) ).
cnf(c_0_2974_0,axiom,
hAPP(c_Relation_Oconverse(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3)) = X3,
inference(literals_permutation,[status(thm)],[c_0_2974]) ).
cnf(c_0_2984_0,axiom,
c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1),
inference(literals_permutation,[status(thm)],[c_0_2984]) ).
cnf(c_0_2985_0,axiom,
c_Relation_OField(hAPP(c_Relation_Oconverse(X1,X1),X2),X1) = c_Relation_OField(X2,X1),
inference(literals_permutation,[status(thm)],[c_0_2985]) ).
cnf(c_0_2992_0,axiom,
c_Relation_ORange(c_Relation_OId__on(X1,X2),X2,X2) = X1,
inference(literals_permutation,[status(thm)],[c_0_2992]) ).
cnf(c_0_2993_0,axiom,
c_Relation_ODomain(c_Relation_OId__on(X1,X2),X2,X2) = X1,
inference(literals_permutation,[status(thm)],[c_0_2993]) ).
cnf(c_0_2994_0,axiom,
c_Relation_Orefl__on(X1,c_Relation_OId__on(X1,X2),X2),
inference(literals_permutation,[status(thm)],[c_0_2994]) ).
cnf(c_0_2995_0,axiom,
c_Relation_Osingle__valued(c_Relation_OId__on(X1,X2),X2,X2),
inference(literals_permutation,[status(thm)],[c_0_2995]) ).
cnf(c_0_2996_0,axiom,
hAPP(c_Relation_Oconverse(X1,X1),c_Relation_OId__on(X2,X1)) = c_Relation_OId__on(X2,X1),
inference(literals_permutation,[status(thm)],[c_0_2996]) ).
cnf(c_0_2998_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_fun(X2,tc_bool)) = X1,
inference(literals_permutation,[status(thm)],[c_0_2998]) ).
cnf(c_0_2999_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(X1,X1,tc_fun(X2,tc_bool)) = X1,
inference(literals_permutation,[status(thm)],[c_0_2999]) ).
cnf(c_0_3000_0,axiom,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_3000]) ).
cnf(c_0_3001_0,axiom,
c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
inference(literals_permutation,[status(thm)],[c_0_3001]) ).
cnf(c_0_3016_0,axiom,
c_Relation_Osingle__valued(c_Relation_OId(X1),X1,X1),
inference(literals_permutation,[status(thm)],[c_0_3016]) ).
cnf(c_0_3017_0,axiom,
c_fequal(X1,X1,X2),
inference(literals_permutation,[status(thm)],[c_0_3017]) ).
cnf(c_0_3018_0,axiom,
c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X1,X2),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_3018]) ).
cnf(c_0_3019_0,axiom,
c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X1,X2),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_3019]) ).
cnf(c_0_3020_0,axiom,
c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X1,X2),X2) = c_Transitive__Closure_Ortrancl(X1,X2),
inference(literals_permutation,[status(thm)],[c_0_3020]) ).
cnf(c_0_3021_0,axiom,
hAPP(c_Relation_Oconverse(X1,X1),c_Relation_OId(X1)) = c_Relation_OId(X1),
inference(literals_permutation,[status(thm)],[c_0_3021]) ).
cnf(c_0_3022_0,axiom,
c_Relation_Osym(c_Relation_OId__on(X1,X2),X2),
inference(literals_permutation,[status(thm)],[c_0_3022]) ).
cnf(c_0_3023_0,axiom,
c_Relation_Oantisym(c_Relation_OId__on(X1,X2),X2),
inference(literals_permutation,[status(thm)],[c_0_3023]) ).
cnf(c_0_3034_0,axiom,
c_Relation_Oantisym(c_Relation_OId(X1),X1),
inference(literals_permutation,[status(thm)],[c_0_3034]) ).
cnf(c_0_3035_0,axiom,
c_Relation_Osym(c_Relation_OId(X1),X1),
inference(literals_permutation,[status(thm)],[c_0_3035]) ).
cnf(c_0_3036_0,axiom,
class_HOL_Oord(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_3036]) ).
cnf(c_0_3037_0,axiom,
class_Orderings_Obot(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_3037]) ).
cnf(c_0_3038_0,axiom,
class_Orderings_Oorder(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_3038]) ).
cnf(c_0_3039_0,axiom,
class_Lattices_Olattice(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_3039]) ).
cnf(c_0_3040_0,axiom,
class_Orderings_Opreorder(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_3040]) ).
cnf(c_0_3041_0,axiom,
class_Lattices_Obounded__lattice(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_3041]) ).
cnf(c_0_3042_0,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_3042]) ).
cnf(c_0_3043_0,axiom,
class_Lattices_Olower__semilattice(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_3043]) ).
cnf(c_0_3044_0,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
inference(literals_permutation,[status(thm)],[c_0_3044]) ).
cnf(c_0_3045_0,axiom,
c_Arrow__Order__Mirabelle_OIIA(v_F),
inference(literals_permutation,[status(thm)],[c_0_3045]) ).
cnf(c_0_3046_0,axiom,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
inference(literals_permutation,[status(thm)],[c_0_3046]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,negated_conjecture,
! [X1] :
( c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi),X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_conjecture_1) ).
fof(c_0_1_002,negated_conjecture,
! [X1] :
( c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi),X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('<stdin>',cls_conjecture_2) ).
fof(c_0_2_003,negated_conjecture,
v_b____ = v_a____,
file('<stdin>',cls_conjecture_0) ).
fof(c_0_3_004,negated_conjecture,
! [X1] :
( c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi),X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_4_005,negated_conjecture,
! [X1] :
( c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi),X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_5_006,negated_conjecture,
v_b____ = v_a____,
c_0_2 ).
fof(c_0_6_007,negated_conjecture,
! [X2] :
( c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi),X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(variable_rename,[status(thm)],[c_0_3]) ).
fof(c_0_7_008,negated_conjecture,
! [X2] :
( c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi),X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(variable_rename,[status(thm)],[c_0_4]) ).
fof(c_0_8_009,negated_conjecture,
v_b____ = v_a____,
c_0_5 ).
cnf(c_0_9_010,negated_conjecture,
( c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi),X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10_011,negated_conjecture,
( c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi),X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11_012,negated_conjecture,
v_b____ = v_a____,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12_013,negated_conjecture,
( c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi),X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_9,
[final] ).
cnf(c_0_13_014,negated_conjecture,
( c_in(c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi),X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Pair(v_b____,v_c____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P_H____,X1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
c_0_10,
[final] ).
cnf(c_0_14_015,negated_conjecture,
v_b____ = v_a____,
c_0_11,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_150,plain,
v_b____ != v_a____,
file('/export/starexec/sandbox2/tmp/iprover_modulo_ad6231.p',c_0_3049_0) ).
cnf(c_1422,negated_conjecture,
v_b____ = v_a____,
file('/export/starexec/sandbox2/tmp/iprover_modulo_ad6231.p',c_0_14) ).
cnf(contradiction,plain,
$false,
inference(minisat,[status(thm)],[c_150,c_1422]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SCT061-1 : TPTP v8.1.0. Released v4.1.0.
% 0.13/0.14 % Command : iprover_modulo %s %d
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sat Jul 2 06:30:05 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Running in mono-core mode
% 0.21/0.55 % Orienting using strategy Equiv(ClausalAll)
% 0.21/0.55 % Orientation found
% 0.21/0.55 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_e4690c.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_ad6231.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_9d9591 | grep -v "SZS"
% 0.40/0.58
% 0.40/0.58 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.40/0.58
% 0.40/0.58 %
% 0.40/0.58 % ------ iProver source info
% 0.40/0.58
% 0.40/0.58 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.40/0.58 % git: non_committed_changes: true
% 0.40/0.58 % git: last_make_outside_of_git: true
% 0.40/0.58
% 0.40/0.58 %
% 0.40/0.58 % ------ Input Options
% 0.40/0.58
% 0.40/0.58 % --out_options all
% 0.40/0.58 % --tptp_safe_out true
% 0.40/0.58 % --problem_path ""
% 0.40/0.58 % --include_path ""
% 0.40/0.58 % --clausifier .//eprover
% 0.40/0.58 % --clausifier_options --tstp-format
% 0.40/0.58 % --stdin false
% 0.40/0.58 % --dbg_backtrace false
% 0.40/0.58 % --dbg_dump_prop_clauses false
% 0.40/0.58 % --dbg_dump_prop_clauses_file -
% 0.40/0.58 % --dbg_out_stat false
% 0.40/0.58
% 0.40/0.58 % ------ General Options
% 0.40/0.58
% 0.40/0.58 % --fof false
% 0.40/0.58 % --time_out_real 150.
% 0.40/0.58 % --time_out_prep_mult 0.2
% 0.40/0.58 % --time_out_virtual -1.
% 0.40/0.58 % --schedule none
% 0.40/0.58 % --ground_splitting input
% 0.40/0.58 % --splitting_nvd 16
% 0.40/0.58 % --non_eq_to_eq false
% 0.40/0.58 % --prep_gs_sim true
% 0.40/0.58 % --prep_unflatten false
% 0.40/0.58 % --prep_res_sim true
% 0.40/0.58 % --prep_upred true
% 0.40/0.58 % --res_sim_input true
% 0.40/0.58 % --clause_weak_htbl true
% 0.40/0.58 % --gc_record_bc_elim false
% 0.40/0.58 % --symbol_type_check false
% 0.40/0.58 % --clausify_out false
% 0.40/0.58 % --large_theory_mode false
% 0.40/0.58 % --prep_sem_filter none
% 0.40/0.58 % --prep_sem_filter_out false
% 0.40/0.58 % --preprocessed_out false
% 0.40/0.58 % --sub_typing false
% 0.40/0.58 % --brand_transform false
% 0.40/0.58 % --pure_diseq_elim true
% 0.40/0.58 % --min_unsat_core false
% 0.40/0.58 % --pred_elim true
% 0.40/0.58 % --add_important_lit false
% 0.40/0.58 % --soft_assumptions false
% 0.40/0.58 % --reset_solvers false
% 0.40/0.58 % --bc_imp_inh []
% 0.40/0.58 % --conj_cone_tolerance 1.5
% 0.40/0.58 % --prolific_symb_bound 500
% 0.40/0.58 % --lt_threshold 2000
% 0.40/0.58
% 0.40/0.58 % ------ SAT Options
% 0.40/0.58
% 0.40/0.58 % --sat_mode false
% 0.40/0.58 % --sat_fm_restart_options ""
% 0.40/0.58 % --sat_gr_def false
% 0.40/0.58 % --sat_epr_types true
% 0.40/0.58 % --sat_non_cyclic_types false
% 0.40/0.58 % --sat_finite_models false
% 0.40/0.58 % --sat_fm_lemmas false
% 0.40/0.58 % --sat_fm_prep false
% 0.40/0.58 % --sat_fm_uc_incr true
% 0.40/0.58 % --sat_out_model small
% 0.40/0.58 % --sat_out_clauses false
% 0.40/0.58
% 0.40/0.58 % ------ QBF Options
% 0.40/0.58
% 0.40/0.58 % --qbf_mode false
% 0.40/0.58 % --qbf_elim_univ true
% 0.40/0.58 % --qbf_sk_in true
% 0.40/0.58 % --qbf_pred_elim true
% 0.40/0.58 % --qbf_split 32
% 0.40/0.58
% 0.40/0.58 % ------ BMC1 Options
% 0.40/0.58
% 0.40/0.58 % --bmc1_incremental false
% 0.40/0.58 % --bmc1_axioms reachable_all
% 0.40/0.58 % --bmc1_min_bound 0
% 0.40/0.58 % --bmc1_max_bound -1
% 0.40/0.58 % --bmc1_max_bound_default -1
% 0.40/0.58 % --bmc1_symbol_reachability true
% 0.40/0.58 % --bmc1_property_lemmas false
% 0.40/0.58 % --bmc1_k_induction false
% 0.40/0.58 % --bmc1_non_equiv_states false
% 0.40/0.58 % --bmc1_deadlock false
% 0.40/0.58 % --bmc1_ucm false
% 0.40/0.58 % --bmc1_add_unsat_core none
% 0.40/0.58 % --bmc1_unsat_core_children false
% 0.40/0.58 % --bmc1_unsat_core_extrapolate_axioms false
% 0.40/0.58 % --bmc1_out_stat full
% 0.40/0.58 % --bmc1_ground_init false
% 0.40/0.58 % --bmc1_pre_inst_next_state false
% 0.40/0.58 % --bmc1_pre_inst_state false
% 0.40/0.58 % --bmc1_pre_inst_reach_state false
% 0.40/0.58 % --bmc1_out_unsat_core false
% 0.40/0.58 % --bmc1_aig_witness_out false
% 0.40/0.58 % --bmc1_verbose false
% 0.40/0.58 % --bmc1_dump_clauses_tptp false
% 6.94/7.81 % --bmc1_dump_unsat_core_tptp false
% 6.94/7.81 % --bmc1_dump_file -
% 6.94/7.81 % --bmc1_ucm_expand_uc_limit 128
% 6.94/7.81 % --bmc1_ucm_n_expand_iterations 6
% 6.94/7.81 % --bmc1_ucm_extend_mode 1
% 6.94/7.81 % --bmc1_ucm_init_mode 2
% 6.94/7.81 % --bmc1_ucm_cone_mode none
% 6.94/7.81 % --bmc1_ucm_reduced_relation_type 0
% 6.94/7.81 % --bmc1_ucm_relax_model 4
% 6.94/7.81 % --bmc1_ucm_full_tr_after_sat true
% 6.94/7.81 % --bmc1_ucm_expand_neg_assumptions false
% 6.94/7.81 % --bmc1_ucm_layered_model none
% 6.94/7.81 % --bmc1_ucm_max_lemma_size 10
% 6.94/7.81
% 6.94/7.81 % ------ AIG Options
% 6.94/7.81
% 6.94/7.81 % --aig_mode false
% 6.94/7.81
% 6.94/7.81 % ------ Instantiation Options
% 6.94/7.81
% 6.94/7.81 % --instantiation_flag true
% 6.94/7.81 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 6.94/7.81 % --inst_solver_per_active 750
% 6.94/7.81 % --inst_solver_calls_frac 0.5
% 6.94/7.81 % --inst_passive_queue_type priority_queues
% 6.94/7.81 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 6.94/7.81 % --inst_passive_queues_freq [25;2]
% 6.94/7.81 % --inst_dismatching true
% 6.94/7.81 % --inst_eager_unprocessed_to_passive true
% 6.94/7.81 % --inst_prop_sim_given true
% 6.94/7.81 % --inst_prop_sim_new false
% 6.94/7.81 % --inst_orphan_elimination true
% 6.94/7.81 % --inst_learning_loop_flag true
% 6.94/7.81 % --inst_learning_start 3000
% 6.94/7.81 % --inst_learning_factor 2
% 6.94/7.81 % --inst_start_prop_sim_after_learn 3
% 6.94/7.81 % --inst_sel_renew solver
% 6.94/7.81 % --inst_lit_activity_flag true
% 6.94/7.81 % --inst_out_proof true
% 6.94/7.81
% 6.94/7.81 % ------ Resolution Options
% 6.94/7.81
% 6.94/7.81 % --resolution_flag true
% 6.94/7.81 % --res_lit_sel kbo_max
% 6.94/7.81 % --res_to_prop_solver none
% 6.94/7.81 % --res_prop_simpl_new false
% 6.94/7.81 % --res_prop_simpl_given false
% 6.94/7.81 % --res_passive_queue_type priority_queues
% 6.94/7.81 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 6.94/7.81 % --res_passive_queues_freq [15;5]
% 6.94/7.81 % --res_forward_subs full
% 6.94/7.81 % --res_backward_subs full
% 6.94/7.81 % --res_forward_subs_resolution true
% 6.94/7.81 % --res_backward_subs_resolution true
% 6.94/7.81 % --res_orphan_elimination false
% 6.94/7.81 % --res_time_limit 1000.
% 6.94/7.81 % --res_out_proof true
% 6.94/7.81 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_e4690c.s
% 6.94/7.81 % --modulo true
% 6.94/7.81
% 6.94/7.81 % ------ Combination Options
% 6.94/7.81
% 6.94/7.81 % --comb_res_mult 1000
% 6.94/7.81 % --comb_inst_mult 300
% 6.94/7.81 % ------
% 6.94/7.81
% 6.94/7.81 % ------ Parsing...% successful
% 6.94/7.81
% 6.94/7.81 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe_e snvd_s sp: 0 0s snvd_e %
% 6.94/7.81
% 6.94/7.81 % ------ Proving...
% 6.94/7.81 % ------ Problem Properties
% 6.94/7.81
% 6.94/7.81 %
% 6.94/7.81 % EPR false
% 6.94/7.81 % Horn false
% 6.94/7.81 % Has equality true
% 6.94/7.81
% 6.94/7.81 % % ------ Input Options Time Limit: Unbounded
% 6.94/7.81
% 6.94/7.81
% 6.94/7.81 Compiling...
% 6.94/7.81 Loading plugin: done.
% 6.94/7.81 Compiling...
% 6.94/7.81 Loading plugin: done.
% 6.94/7.81 Compiling...
% 6.94/7.81 Loading plugin: done.
% 6.94/7.81 Compiling...
% 6.94/7.81 Loading plugin: done.
% 6.94/7.81 Compiling...
% 6.94/7.81 Loading plugin: done.
% 6.94/7.81 Compiling...
% 6.94/7.81 Loading plugin: done.
% 6.94/7.81 Compiling...
% 6.94/7.81 Loading plugin: done.
% 6.94/7.81 Compiling...
% 6.94/7.81 Loading plugin: done.
% 6.94/7.81 Compiling...
% 6.94/7.81 Loading plugin: done.
% 6.94/7.81 Compiling...
% 6.94/7.81 Loading plugin: done.
% 6.94/7.81 Compiling...
% 6.94/7.81 Loading plugin: done.
% 6.94/7.81 Compiling...
% 6.94/7.81 Loading plugin: done.
% 6.94/7.81 Compiling...
% 6.94/7.81 Loading plugin: done.
% 6.94/7.81 Compiling...
% 6.94/7.81 Loading plugin: done.
% 6.94/7.81 Compiling...
% 6.94/7.81 Loading plugin: done.
% 6.94/7.81 Compiling...
% 6.94/7.81 Loading plugin: done.
% 6.94/7.81 Compiling...
% 6.94/7.81 Loading plugin: done.
% 6.94/7.81 Compiling...
% 6.94/7.81 Loading plugin: done.
% 6.94/7.81 Compiling...
% 6.94/7.81 Loading plugin: done.
% 6.94/7.81 Compiling...
% 6.94/7.81 Loading plugin: done.
% 6.94/7.81 Compiling...
% 6.94/7.81 Loading plugin: done.
% 6.94/7.81 Compiling...
% 6.94/7.81 Loading plugin: done.
% 6.94/7.81 Compiling...
% 6.94/7.81 Loading plugin: done.
% 6.94/7.81 Compiling...
% 6.94/7.81 Loading plugin: done.
% 6.94/7.81 Compiling...
% 6.94/7.81 Loading plugin: done.
% 6.94/7.81 % % ------ Current options:
% 6.94/7.81
% 6.94/7.81 % ------ Input Options
% 6.94/7.81
% 6.94/7.81 % --out_options all
% 6.94/7.81 % --tptp_safe_out true
% 6.94/7.81 % --problem_path ""
% 6.94/7.81 % --include_path ""
% 6.94/7.81 % --clausifier .//eprover
% 6.94/7.81 % --clausifier_options --tstp-format
% 6.94/7.81 % --stdin false
% 6.94/7.81 % --dbg_backtrace false
% 6.94/7.81 % --dbg_dump_prop_clauses false
% 6.94/7.81 % --dbg_dump_prop_clauses_file -
% 6.94/7.81 % --dbg_out_stat false
% 6.94/7.81
% 6.94/7.81 % ------ General Options
% 6.94/7.81
% 6.94/7.81 % --fof false
% 6.94/7.81 % --time_out_real 150.
% 6.94/7.81 % --time_out_prep_mult 0.2
% 6.94/7.81 % --time_out_virtual -1.
% 6.94/7.81 % --schedule none
% 6.94/7.81 % --ground_splitting input
% 6.94/7.81 % --splitting_nvd 16
% 6.94/7.81 % --non_eq_to_eq false
% 6.94/7.81 % --prep_gs_sim true
% 6.94/7.81 % --prep_unflatten false
% 6.94/7.81 % --prep_res_sim true
% 6.94/7.81 % --prep_upred true
% 6.94/7.81 % --res_sim_input true
% 6.94/7.81 % --clause_weak_htbl true
% 6.94/7.81 % --gc_record_bc_elim false
% 6.94/7.81 % --symbol_type_check false
% 6.94/7.81 % --clausify_out false
% 6.94/7.81 % --large_theory_mode false
% 6.94/7.81 % --prep_sem_filter none
% 6.94/7.81 % --prep_sem_filter_out false
% 6.94/7.81 % --preprocessed_out false
% 6.94/7.81 % --sub_typing false
% 6.94/7.81 % --brand_transform false
% 6.94/7.81 % --pure_diseq_elim true
% 6.94/7.81 % --min_unsat_core false
% 6.94/7.81 % --pred_elim true
% 6.94/7.81 % --add_important_lit false
% 6.94/7.81 % --soft_assumptions false
% 6.94/7.81 % --reset_solvers false
% 6.94/7.81 % --bc_imp_inh []
% 6.94/7.81 % --conj_cone_tolerance 1.5
% 6.94/7.81 % --prolific_symb_bound 500
% 6.94/7.81 % --lt_threshold 2000
% 6.94/7.81
% 6.94/7.81 % ------ SAT Options
% 6.94/7.81
% 6.94/7.81 % --sat_mode false
% 6.94/7.81 % --sat_fm_restart_options ""
% 6.94/7.81 % --sat_gr_def false
% 6.94/7.81 % --sat_epr_types true
% 6.94/7.81 % --sat_non_cyclic_types false
% 6.94/7.81 % --sat_finite_models false
% 6.94/7.81 % --sat_fm_lemmas false
% 6.94/7.81 % --sat_fm_prep false
% 6.94/7.81 % --sat_fm_uc_incr true
% 6.94/7.81 % --sat_out_model small
% 6.94/7.81 % --sat_out_clauses false
% 6.94/7.81
% 6.94/7.81 % ------ QBF Options
% 6.94/7.81
% 6.94/7.81 % --qbf_mode false
% 6.94/7.81 % --qbf_elim_univ true
% 6.94/7.81 % --qbf_sk_in true
% 6.94/7.81 % --qbf_pred_elim true
% 6.94/7.81 % --qbf_split 32
% 6.94/7.81
% 6.94/7.81 % ------ BMC1 Options
% 6.94/7.81
% 6.94/7.81 % --bmc1_incremental false
% 6.94/7.81 % --bmc1_axioms reachable_all
% 6.94/7.81 % --bmc1_min_bound 0
% 6.94/7.81 % --bmc1_max_bound -1
% 6.94/7.81 % --bmc1_max_bound_default -1
% 6.94/7.81 % --bmc1_symbol_reachability true
% 6.94/7.81 % --bmc1_property_lemmas false
% 6.94/7.81 % --bmc1_k_induction false
% 6.94/7.81 % --bmc1_non_equiv_states false
% 6.94/7.81 % --bmc1_deadlock false
% 6.94/7.81 % --bmc1_ucm false
% 6.94/7.81 % --bmc1_add_unsat_core none
% 6.94/7.81 % --bmc1_unsat_core_children false
% 6.94/7.81 % --bmc1_unsat_core_extrapolate_axioms false
% 6.94/7.81 % --bmc1_out_stat full
% 6.94/7.81 % --bmc1_ground_init false
% 6.94/7.81 % --bmc1_pre_inst_next_state false
% 6.94/7.81 % --bmc1_pre_inst_state false
% 6.94/7.81 % --bmc1_pre_inst_reach_state false
% 6.94/7.81 % --bmc1_out_unsat_core false
% 6.94/7.81 % --bmc1_aig_witness_out false
% 6.94/7.81 % --bmc1_verbose false
% 6.94/7.81 % --bmc1_dump_clauses_tptp false
% 6.94/7.81 % --bmc1_dump_unsat_core_tptp false
% 6.94/7.81 % --bmc1_dump_file -
% 6.94/7.81 % --bmc1_ucm_expand_uc_limit 128
% 6.94/7.81 % --bmc1_ucm_n_expand_iterations 6
% 6.94/7.81 % --bmc1_ucm_extend_mode 1
% 6.94/7.81 % --bmc1_ucm_init_mode 2
% 6.94/7.81 % --bmc1_ucm_cone_mode none
% 6.94/7.81 % --bmc1_ucm_reduced_relation_type 0
% 149.75/150.58 % --bmc1_ucm_relax_model 4
% 149.75/150.58 % --bmc1_ucm_full_tr_after_sat true
% 149.75/150.58 % --bmc1_ucm_expand_neg_assumptions false
% 149.75/150.58 % --bmc1_ucm_layered_model none
% 149.75/150.58 % --bmc1_ucm_max_lemma_size 10
% 149.75/150.58
% 149.75/150.58 % ------ AIG Options
% 149.75/150.58
% 149.75/150.58 % --aig_mode false
% 149.75/150.58
% 149.75/150.58 % ------ Instantiation Options
% 149.75/150.58
% 149.75/150.58 % --instantiation_flag true
% 149.75/150.58 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 149.75/150.58 % --inst_solver_per_active 750
% 149.75/150.58 % --inst_solver_calls_frac 0.5
% 149.75/150.58 % --inst_passive_queue_type priority_queues
% 149.75/150.58 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 149.75/150.58 % --inst_passive_queues_freq [25;2]
% 149.75/150.58 % --inst_dismatching true
% 149.75/150.58 % --inst_eager_unprocessed_to_passive true
% 149.75/150.58 % --inst_prop_sim_given true
% 149.75/150.58 % --inst_prop_sim_new false
% 149.75/150.58 % --inst_orphan_elimination true
% 149.75/150.58 % --inst_learning_loop_flag true
% 149.75/150.58 % --inst_learning_start 3000
% 149.75/150.58 % --inst_learning_factor 2
% 149.75/150.58 % --inst_start_prop_sim_after_learn 3
% 149.75/150.58 % --inst_sel_renew solver
% 149.75/150.58 % --inst_lit_activity_flag true
% 149.75/150.58 % --inst_out_proof true
% 149.75/150.58
% 149.75/150.58 % ------ Resolution Options
% 149.75/150.58
% 149.75/150.58 % --resolution_flag true
% 149.75/150.58 % --res_lit_sel kbo_max
% 149.75/150.58 % --res_to_prop_solver none
% 149.75/150.58 % --res_prop_simpl_new false
% 149.75/150.58 % --res_prop_simpl_given false
% 149.75/150.58 % --res_passive_queue_type priority_queues
% 149.75/150.58 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 149.75/150.58 % --res_passive_queues_freq [15;5]
% 149.75/150.58 % --res_forward_subs full
% 149.75/150.58 % --res_backward_subs full
% 149.75/150.58 % --res_forward_subs_resolution true
% 149.75/150.58 % --res_backward_subs_resolution true
% 149.75/150.58 % --res_orphan_elimination false
% 149.75/150.58 % --res_time_limit 1000.
% 149.75/150.58 % --res_out_proof true
% 149.75/150.58 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_e4690c.s
% 149.75/150.58 % --modulo true
% 149.75/150.58
% 149.75/150.58 % ------ Combination Options
% 149.75/150.58
% 149.75/150.58 % --comb_res_mult 1000
% 149.75/150.58 % --comb_inst_mult 300
% 149.75/150.58 % ------
% 149.75/150.58
% 149.75/150.58
% 149.75/150.58
% 149.75/150.58 % ------ Proving...
% 149.75/150.58 %
% 149.75/150.58
% 149.75/150.58
% 149.75/150.58 % Time Out Real
% 149.75/150.58
% 149.75/150.58 % ------ Statistics
% 149.75/150.58
% 149.75/150.58 % ------ General
% 149.75/150.58
% 149.75/150.58 % num_of_input_clauses: 1423
% 149.75/150.58 % num_of_input_neg_conjectures: 3
% 149.75/150.58 % num_of_splits: 0
% 149.75/150.58 % num_of_split_atoms: 0
% 149.75/150.58 % num_of_sem_filtered_clauses: 0
% 149.75/150.58 % num_of_subtypes: 0
% 149.75/150.58 % monotx_restored_types: 0
% 149.75/150.58 % sat_num_of_epr_types: 0
% 149.75/150.58 % sat_num_of_non_cyclic_types: 0
% 149.75/150.58 % sat_guarded_non_collapsed_types: 0
% 149.75/150.58 % is_epr: 0
% 149.75/150.58 % is_horn: 0
% 149.75/150.58 % has_eq: 1
% 149.75/150.58 % num_pure_diseq_elim: 0
% 149.75/150.58 % simp_replaced_by: 0
% 149.75/150.58 % res_preprocessed: 6
% 149.75/150.58 % prep_upred: 0
% 149.75/150.58 % prep_unflattend: 0
% 149.75/150.58 % pred_elim_cands: 0
% 149.75/150.58 % pred_elim: 0
% 149.75/150.58 % pred_elim_cl: 0
% 149.75/150.58 % pred_elim_cycles: 0
% 149.75/150.58 % forced_gc_time: 0
% 149.75/150.58 % gc_basic_clause_elim: 0
% 149.75/150.58 % parsing_time: 0.078
% 149.75/150.58 % sem_filter_time: 0.
% 149.75/150.58 % pred_elim_time: 0.
% 149.75/150.58 % out_proof_time: 0.
% 149.75/150.58 % monotx_time: 0.
% 149.75/150.58 % subtype_inf_time: 0.
% 149.75/150.58 % unif_index_cands_time: 0.078
% 149.75/150.58 % unif_index_add_time: 0.02
% 149.75/150.58 % total_time: 150.017
% 149.75/150.58 % num_of_symbols: 149
% 149.75/150.58 % num_of_terms: 187246
% 149.75/150.58
% 149.75/150.58 % ------ Propositional Solver
% 149.75/150.58
% 149.75/150.58 % prop_solver_calls: 2
% 149.75/150.58 % prop_fast_solver_calls: 15
% 149.75/150.58 % prop_num_of_clauses: 1655
% 149.75/150.58 % prop_preprocess_simplified: 7182
% 149.75/150.58 % prop_fo_subsumed: 0
% 149.75/150.58 % prop_solver_time: 0.
% 149.75/150.58 % prop_fast_solver_time: 0.
% 149.75/150.58 % prop_unsat_core_time: 0.
% 149.75/150.58
% 149.75/150.58 % ------ QBF
% 149.75/150.58
% 149.75/150.58 % qbf_q_res: 0
% 149.75/150.58 % qbf_num_tautologies: 0
% 149.75/150.58 % qbf_prep_cycles: 0
% 149.75/150.58
% 149.75/150.58 % ------ BMC1
% 149.75/150.58
% 149.75/150.58 % bmc1_current_bound: -1
% 149.75/150.58 % bmc1_last_solved_bound: -1
% 149.75/150.58 % bmc1_unsat_core_size: -1
% 149.75/150.58 % bmc1_unsat_core_parents_size: -1
% 149.75/150.58 % bmc1_merge_next_fun: 0
% 149.75/150.58 % bmc1_unsat_core_clauses_time: 0.
% 149.75/150.58
% 149.75/150.58 % ------ Instantiation
% 149.75/150.58
% 149.75/150.58 % inst_num_of_clauses: 1483
% 149.75/150.58 % inst_num_in_passive: 1020
% 149.75/150.58 % inst_num_in_active: 299
% 149.75/150.58 % inst_num_in_unprocessed: 164
% 149.75/150.58 % inst_num_of_loops: 300
% 149.75/150.58 % inst_num_of_learning_restarts: 0
% 149.75/150.58 % inst_num_moves_active_passive: 0
% 149.75/150.58 % inst_lit_activity: 28
% 149.75/150.58 % inst_lit_activity_moves: 0
% 149.75/150.58 % inst_num_tautologies: 0
% 149.75/150.58 % inst_num_prop_implied: 0
% 149.75/150.58 % inst_num_existing_simplified: 0
% 149.75/150.58 % inst_num_eq_res_simplified: 0
% 149.75/150.58 % inst_num_child_elim: 0
% 149.75/150.58 % inst_num_of_dismatching_blockings: 11
% 149.75/150.58 % inst_num_of_non_proper_insts: 194
% 149.75/150.58 % inst_num_of_duplicates: 263
% 149.75/150.58 % inst_inst_num_from_inst_to_res: 0
% 149.75/150.58 % inst_dismatching_checking_time: 0.
% 149.75/150.58
% 149.75/150.58 % ------ Resolution
% 149.75/150.58
% 149.75/150.58 % res_num_of_clauses: 99202
% 149.75/150.58 % res_num_in_passive: 96443
% 149.75/150.58 % res_num_in_active: 2102
% 149.75/150.58 % res_num_of_loops: 1793
% 149.75/150.58 % res_forward_subset_subsumed: 9467
% 149.75/150.58 % res_backward_subset_subsumed: 261
% 149.75/150.58 % res_forward_subsumed: 305
% 149.75/150.58 % res_backward_subsumed: 3
% 149.75/150.58 % res_forward_subsumption_resolution: 415
% 149.75/150.58 % res_backward_subsumption_resolution: 0
% 149.75/150.58 % res_clause_to_clause_subsumption: 127381
% 149.75/150.58 % res_orphan_elimination: 0
% 149.75/150.58 % res_tautology_del: 55589
% 149.75/150.58 % res_num_eq_res_simplified: 0
% 149.75/150.58 % res_num_sel_changes: 0
% 149.75/150.58 % res_moves_from_active_to_pass: 0
% 149.75/150.58
% 149.75/150.59 % Status Unknown
% 149.81/150.76 % Orienting using strategy ClausalAll
% 149.81/150.76 % Orientation found
% 149.81/150.76 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_e4690c.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_ad6231.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_c783e0 | grep -v "SZS"
% 149.81/150.78
% 149.81/150.78 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 149.81/150.78
% 149.81/150.78 %
% 149.81/150.78 % ------ iProver source info
% 149.81/150.78
% 149.81/150.78 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 149.81/150.78 % git: non_committed_changes: true
% 149.81/150.78 % git: last_make_outside_of_git: true
% 149.81/150.78
% 149.81/150.78 %
% 149.81/150.78 % ------ Input Options
% 149.81/150.78
% 149.81/150.78 % --out_options all
% 149.81/150.78 % --tptp_safe_out true
% 149.81/150.78 % --problem_path ""
% 149.81/150.78 % --include_path ""
% 149.81/150.78 % --clausifier .//eprover
% 149.81/150.78 % --clausifier_options --tstp-format
% 149.81/150.78 % --stdin false
% 149.81/150.78 % --dbg_backtrace false
% 149.81/150.78 % --dbg_dump_prop_clauses false
% 149.81/150.78 % --dbg_dump_prop_clauses_file -
% 149.81/150.78 % --dbg_out_stat false
% 149.81/150.78
% 149.81/150.78 % ------ General Options
% 149.81/150.78
% 149.81/150.78 % --fof false
% 149.81/150.78 % --time_out_real 150.
% 149.81/150.78 % --time_out_prep_mult 0.2
% 149.81/150.78 % --time_out_virtual -1.
% 149.81/150.78 % --schedule none
% 149.81/150.78 % --ground_splitting input
% 149.81/150.78 % --splitting_nvd 16
% 149.81/150.78 % --non_eq_to_eq false
% 149.81/150.78 % --prep_gs_sim true
% 149.81/150.78 % --prep_unflatten false
% 149.81/150.78 % --prep_res_sim true
% 149.81/150.78 % --prep_upred true
% 149.81/150.78 % --res_sim_input true
% 149.81/150.78 % --clause_weak_htbl true
% 149.81/150.78 % --gc_record_bc_elim false
% 149.81/150.78 % --symbol_type_check false
% 149.81/150.78 % --clausify_out false
% 149.81/150.78 % --large_theory_mode false
% 149.81/150.78 % --prep_sem_filter none
% 149.81/150.78 % --prep_sem_filter_out false
% 149.81/150.78 % --preprocessed_out false
% 149.81/150.78 % --sub_typing false
% 149.81/150.78 % --brand_transform false
% 149.81/150.78 % --pure_diseq_elim true
% 149.81/150.78 % --min_unsat_core false
% 149.81/150.78 % --pred_elim true
% 149.81/150.78 % --add_important_lit false
% 149.81/150.78 % --soft_assumptions false
% 149.81/150.78 % --reset_solvers false
% 149.81/150.78 % --bc_imp_inh []
% 149.81/150.78 % --conj_cone_tolerance 1.5
% 149.81/150.78 % --prolific_symb_bound 500
% 149.81/150.78 % --lt_threshold 2000
% 149.81/150.78
% 149.81/150.78 % ------ SAT Options
% 149.81/150.78
% 149.81/150.78 % --sat_mode false
% 149.81/150.78 % --sat_fm_restart_options ""
% 149.81/150.78 % --sat_gr_def false
% 149.81/150.78 % --sat_epr_types true
% 149.81/150.78 % --sat_non_cyclic_types false
% 149.81/150.78 % --sat_finite_models false
% 149.81/150.78 % --sat_fm_lemmas false
% 149.81/150.78 % --sat_fm_prep false
% 149.81/150.78 % --sat_fm_uc_incr true
% 149.81/150.78 % --sat_out_model small
% 149.81/150.78 % --sat_out_clauses false
% 149.81/150.78
% 149.81/150.78 % ------ QBF Options
% 149.81/150.78
% 149.81/150.78 % --qbf_mode false
% 149.81/150.78 % --qbf_elim_univ true
% 149.81/150.78 % --qbf_sk_in true
% 149.81/150.78 % --qbf_pred_elim true
% 149.81/150.78 % --qbf_split 32
% 149.81/150.78
% 149.81/150.78 % ------ BMC1 Options
% 149.81/150.78
% 149.81/150.78 % --bmc1_incremental false
% 149.81/150.78 % --bmc1_axioms reachable_all
% 149.81/150.78 % --bmc1_min_bound 0
% 149.81/150.78 % --bmc1_max_bound -1
% 149.81/150.78 % --bmc1_max_bound_default -1
% 149.81/150.78 % --bmc1_symbol_reachability true
% 149.81/150.78 % --bmc1_property_lemmas false
% 149.81/150.78 % --bmc1_k_induction false
% 149.81/150.78 % --bmc1_non_equiv_states false
% 149.81/150.78 % --bmc1_deadlock false
% 149.81/150.78 % --bmc1_ucm false
% 149.81/150.78 % --bmc1_add_unsat_core none
% 149.81/150.78 % --bmc1_unsat_core_children false
% 149.81/150.78 % --bmc1_unsat_core_extrapolate_axioms false
% 149.81/150.78 % --bmc1_out_stat full
% 149.81/150.78 % --bmc1_ground_init false
% 149.81/150.78 % --bmc1_pre_inst_next_state false
% 149.81/150.78 % --bmc1_pre_inst_state false
% 149.81/150.78 % --bmc1_pre_inst_reach_state false
% 149.81/150.78 % --bmc1_out_unsat_core false
% 149.81/150.78 % --bmc1_aig_witness_out false
% 149.81/150.78 % --bmc1_verbose false
% 149.81/150.78 % --bmc1_dump_clauses_tptp false
% 150.04/150.85 % --bmc1_dump_unsat_core_tptp false
% 150.04/150.85 % --bmc1_dump_file -
% 150.04/150.85 % --bmc1_ucm_expand_uc_limit 128
% 150.04/150.85 % --bmc1_ucm_n_expand_iterations 6
% 150.04/150.85 % --bmc1_ucm_extend_mode 1
% 150.04/150.85 % --bmc1_ucm_init_mode 2
% 150.04/150.85 % --bmc1_ucm_cone_mode none
% 150.04/150.85 % --bmc1_ucm_reduced_relation_type 0
% 150.04/150.85 % --bmc1_ucm_relax_model 4
% 150.04/150.85 % --bmc1_ucm_full_tr_after_sat true
% 150.04/150.85 % --bmc1_ucm_expand_neg_assumptions false
% 150.04/150.85 % --bmc1_ucm_layered_model none
% 150.04/150.85 % --bmc1_ucm_max_lemma_size 10
% 150.04/150.85
% 150.04/150.85 % ------ AIG Options
% 150.04/150.85
% 150.04/150.85 % --aig_mode false
% 150.04/150.85
% 150.04/150.85 % ------ Instantiation Options
% 150.04/150.85
% 150.04/150.85 % --instantiation_flag true
% 150.04/150.85 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 150.04/150.85 % --inst_solver_per_active 750
% 150.04/150.85 % --inst_solver_calls_frac 0.5
% 150.04/150.85 % --inst_passive_queue_type priority_queues
% 150.04/150.85 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 150.04/150.85 % --inst_passive_queues_freq [25;2]
% 150.04/150.85 % --inst_dismatching true
% 150.04/150.85 % --inst_eager_unprocessed_to_passive true
% 150.04/150.85 % --inst_prop_sim_given true
% 150.04/150.85 % --inst_prop_sim_new false
% 150.04/150.85 % --inst_orphan_elimination true
% 150.04/150.85 % --inst_learning_loop_flag true
% 150.04/150.85 % --inst_learning_start 3000
% 150.04/150.85 % --inst_learning_factor 2
% 150.04/150.85 % --inst_start_prop_sim_after_learn 3
% 150.04/150.85 % --inst_sel_renew solver
% 150.04/150.85 % --inst_lit_activity_flag true
% 150.04/150.85 % --inst_out_proof true
% 150.04/150.85
% 150.04/150.85 % ------ Resolution Options
% 150.04/150.85
% 150.04/150.85 % --resolution_flag true
% 150.04/150.85 % --res_lit_sel kbo_max
% 150.04/150.85 % --res_to_prop_solver none
% 150.04/150.85 % --res_prop_simpl_new false
% 150.04/150.85 % --res_prop_simpl_given false
% 150.04/150.85 % --res_passive_queue_type priority_queues
% 150.04/150.85 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 150.04/150.85 % --res_passive_queues_freq [15;5]
% 150.04/150.85 % --res_forward_subs full
% 150.04/150.85 % --res_backward_subs full
% 150.04/150.85 % --res_forward_subs_resolution true
% 150.04/150.85 % --res_backward_subs_resolution true
% 150.04/150.85 % --res_orphan_elimination false
% 150.04/150.85 % --res_time_limit 1000.
% 150.04/150.85 % --res_out_proof true
% 150.04/150.85 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_e4690c.s
% 150.04/150.85 % --modulo true
% 150.04/150.85
% 150.04/150.85 % ------ Combination Options
% 150.04/150.85
% 150.04/150.85 % --comb_res_mult 1000
% 150.04/150.85 % --comb_inst_mult 300
% 150.04/150.85 % ------
% 150.04/150.85
% 150.04/150.85 % ------ Parsing...% successful
% 150.04/150.85
% 150.04/150.85 %
% 150.04/150.85
% 150.04/150.85
% 150.04/150.85 % ------ Statistics
% 150.04/150.85
% 150.04/150.85 % ------ General
% 150.04/150.85
% 150.04/150.85 % num_of_input_clauses: 1423
% 150.04/150.85 % num_of_input_neg_conjectures: 3
% 150.04/150.85 % num_of_splits: 0
% 150.04/150.85 % num_of_split_atoms: 0
% 150.04/150.85 % num_of_sem_filtered_clauses: 0
% 150.04/150.85 % num_of_subtypes: 0
% 150.04/150.85 % monotx_restored_types: 0
% 150.04/150.85 % sat_num_of_epr_types: 0
% 150.04/150.85 % sat_num_of_non_cyclic_types: 0
% 150.04/150.85 % sat_guarded_non_collapsed_types: 0
% 150.04/150.85 % is_epr: 0
% 150.04/150.85 % is_horn: 0
% 150.04/150.85 % has_eq: 0
% 150.04/150.85 % num_pure_diseq_elim: 0
% 150.04/150.85 % simp_replaced_by: 0
% 150.04/150.85 % res_preprocessed: 0
% 150.04/150.85 % prep_upred: 0
% 150.04/150.85 % prep_unflattend: 0
% 150.04/150.85 % pred_elim_cands: 0
% 150.04/150.85 % pred_elim: 0
% 150.04/150.85 % pred_elim_cl: 0
% 150.04/150.85 % pred_elim_cycles: 0
% 150.04/150.85 % forced_gc_time: 0
% 150.04/150.85 % gc_basic_clause_elim: 0
% 150.04/150.85 % parsing_time: 0.056
% 150.04/150.85 % sem_filter_time: 0.
% 150.04/150.85 % pred_elim_time: 0.
% 150.04/150.85 % out_proof_time: 0.
% 150.04/150.85 % monotx_time: 0.
% 150.04/150.85 % subtype_inf_time: 0.
% 150.04/150.85 % unif_index_cands_time: 0.
% 150.04/150.85 % unif_index_add_time: 0.
% 150.04/150.85 % total_time: 0.083
% 150.04/150.85 % num_of_symbols: 149
% 150.04/150.85 % num_of_terms: 3893
% 150.04/150.85
% 150.04/150.85 % ------ Propositional Solver
% 150.04/150.85
% 150.04/150.85 % prop_solver_calls: 0
% 150.04/150.85 % prop_fast_solver_calls: 0
% 150.04/150.85 % prop_num_of_clauses: 1137
% 150.04/150.85 % prop_preprocess_simplified: 1409
% 150.04/150.85 % prop_fo_subsumed: 0
% 150.04/150.85 % prop_solver_time: 0.
% 150.04/150.85 % prop_fast_solver_time: 0.
% 150.04/150.85 % prop_unsat_core_time: 0.
% 150.04/150.85
% 150.04/150.85 % ------ QBF
% 150.04/150.85
% 150.04/150.85 % qbf_q_res: 0
% 150.04/150.85 % qbf_num_tautologies: 0
% 150.04/150.85 % qbf_prep_cycles: 0
% 150.04/150.85
% 150.04/150.85 % ------ BMC1
% 150.04/150.85
% 150.04/150.85 % bmc1_current_bound: -1
% 150.04/150.85 % bmc1_last_solved_bound: -1
% 150.04/150.85 % bmc1_unsat_core_size: -1
% 150.04/150.85 % bmc1_unsat_core_parents_size: -1
% 150.04/150.85 % bmc1_merge_next_fun: 0
% 150.04/150.85 % bmc1_unsat_core_clauses_time: 0.
% 150.04/150.85
% 150.04/150.85 % ------ Instantiation
% 150.04/150.85
% 150.04/150.85 % inst_num_of_clauses: undef
% 150.04/150.85 % inst_num_in_passive: undef
% 150.04/150.85 % inst_num_in_active: 0
% 150.04/150.85 % inst_num_in_unprocessed: 0
% 150.04/150.85 % inst_num_of_loops: 0
% 150.04/150.85 % inst_num_of_learning_restarts: 0
% 150.04/150.85 % inst_num_moves_active_passive: 0
% 150.04/150.85 % inst_lit_activity: 0
% 150.04/150.85 % inst_lit_activity_moves: 0
% 150.04/150.85 % inst_num_tautologies: 0
% 150.04/150.85 % inst_num_prop_implied: 0
% 150.04/150.85 % inst_num_existing_simplified: 0
% 150.04/150.85 % inst_num_eq_res_simplified: 0
% 150.04/150.85 % inst_num_child_elim: 0
% 150.04/150.85 % inst_num_of_dismatching_blockings: 0
% 150.04/150.85 % inst_num_of_non_proper_insts: 0
% 150.04/150.85 % inst_num_of_duplicates: 0
% 150.04/150.85 % inst_inst_num_from_inst_to_res: 0
% 150.04/150.85 % inst_dismatching_checking_time: 0.
% 150.04/150.85
% 150.04/150.85 % ------ Resolution
% 150.04/150.85
% 150.04/150.85 % res_num_of_clauses: undef
% 150.04/150.85 % res_num_in_passive: undef
% 150.04/150.85 % res_num_in_active: 0
% 150.04/150.85 % res_num_of_loops: 0
% 150.04/150.85 % res_forward_subset_subsumed: 0
% 150.04/150.85 % res_backward_subset_subsumed: 0
% 150.04/150.85 % res_forward_subsumed: 0
% 150.04/150.85 % res_backward_subsumed: 0
% 150.04/150.85 % res_forward_subsumption_resolution: 0
% 150.04/150.85 % res_backward_subsumption_resolution: 0
% 150.04/150.85 % res_clause_to_clause_subsumption: 0
% 150.04/150.85 % res_orphan_elimination: 0
% 150.04/150.85 % res_tautology_del: 0
% 150.04/150.85 % res_num_eq_res_simplified: 0
% 150.04/150.85 % res_num_sel_changes: 0
% 150.04/150.85 % res_moves_from_active_to_pass: 0
% 150.04/150.85
% 150.04/150.85 % Status Unsatisfiable
% 150.04/150.85 % SZS status Unsatisfiable
% 150.04/150.85 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------